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Forest fragmentation and deforestation are subjects of great concern in tropical regions, namely in South America and Africa, contributing to a rapid loss of tropical forest area and with serious implications for ecosystem functioning and biodiversity conservation. Despite the decrease in deforestation rates in recent years, the Brazilian Amazon, with the largest continuous region of tropical forest in the world, has suffered the greatest recorded losses, which have been contributing to continuous habitat fragmentation and a reduction in the territory occupied by Amerindian populations. In an attempt to preserve the remaining habitats and forests, Brazil has been adopting land conservation policies, including the implementation of protected areas. Protected areas (PAs) possess the potential to significantly reduce habitat fragmentation by conserving large, contiguous areas of land. In order to examine how effective PAs are at conserving forest area in the Brazilian Legal Amazon, patterns of deforestation are analyzed and compared, inside and outside the PAs, through landscape metrics calculated using the Patch Analyst and V-LATE extensions of a Geographic Information System. Two different sources (the Hansen Global Forest Change Dataset and the Brazilian National Institute for Space Research's (INPE) PRODES project) of annual forest cover-loss data derived from satellite imagery at medium-to-high spatial and temporal resolutions are compared at two-yearly intervals across 2002-2016. Additionally, fragmentation levels associated with deforestation patterns are assessed through an index modeled using a set of uncorrelated landscape metrics, and the associated change factors and trend are discussed. Results show that there is greater fragmentation in some PAs located in Mato Grosso and Pará States, especially those near the "arc of deforestation", and that Yanomami Indigenous Lands (YIL) are tending towards more fragmentation. Although some PAs are in a critical condition, findings show they all actively contribute to improved conservation of the native ecosystem and, in conjunction with sustainable management policies, will continue to help reduce or avoid forest fragmentation and degradation processes.

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We extend our model of three-dimensional cosmic-ray propagation without energy change to that including energy change due to reacceleration and ionization energy loss. We assume that there is no boundary in both the radial spread of the disk and the latitudinal spread of the halo, and that the three critical parameters, the diffusion coefficient D, the gas density n, and the cosmic-ray source density Q, depend on both the space position r and the rigidity R of the cosmic-ray particle. It is possible to apply the weighted slab technique to the transport equation, even including the energy change process, if the diffusion coefficient is separable in r and R, i.e., D(r; R) ¼ (v/c)R D(r), and combining it with the first-pole approximation in the path length distribution, we can obtain the analytical solution rather easily. We show that the rigidity dependence of the secondary-to-primary ratio behaves as R À in the high-energy region and as vR in the low-energy region. We compare our numerical results with experimental data in both the low-and the high-energy regions and find that our model reproduces all components over the wide energy range 1 GeV nucleon À1 to 100 TeV nucleon À1 , with the adoption of appropriate scale heights in D, n, and Q. We also confirm that the reacceleration process actually occurs during the propagation in the Galaxy and that its magnitude is comparable with that expected from reasonable numerical choices for three parameters, D, n, and the velocity of the hydromagnetic turbulence v M .