Linear and power models.

<p>Median DL, 10^th percentile and 90^th percentile DL values for the 101 counties groups for NMSA (A) and MSA (B). Population percentile distribution for each county group is also marked on X axis for Fig. 1A and 1B. NMSA counties generally have smaller populations with 9,054/16,900/31,667 for 25th percentile, median and 75th percentile, respectively. The corresponding percentiles for MSA counties are 64,350/122,934/241,423. There is an overlap of NMSA and NMSA for populations between 23,354 and 91,292 people. Direct comparison of median DL for NMSA and MSA counties in overlapping populations reveals a nearly constant additional DL consumption for NMSA counties (C).</p

Mean and standard deviation on training-testing accuracy deviations.

<p>Mean and standard deviation on training-testing accuracy deviations.</p

Activation function overlapping problem.

<p>Activation function overlapping problem.</p

Comparison of MAE and SDE metrics for MK and MS RBFs.

<p>Comparison of MAE and SDE metrics for MK and MS RBFs.</p

Mean comparison from ANOVA between MKRBF and MSRBF (All plots).

<p>Mean comparison from ANOVA between MKRBF and MSRBF (All plots).</p

Contrasting MK and MS RBF fitting capabilities for biophysical feature extraction.

<p>Contrasting MK and MS RBF fitting capabilities for biophysical feature extraction.</p

Contrasting MSRBF and MKRBF training progression.

<p>Contrasting MSRBF and MKRBF training progression.</p

FAD_Norm dynamics in landscape strata over six ecoregions. FADC_Norm values are depicted in bars.

<p>Percentage of land cover strata is shown in parentheses next to the name. Percentage of forest cover in ecoregions is shown in parentheses in the legend. Forest attrition is considerably higher in western ecoregions and federal and state lands while lower in urban and suburban regions.</p

Forest attrition visualized in four ecoregions.

<p>Forest losses during the 1990s are depicted as red pixels, forest present in 2000 is shown as green pixels and non-forest is shown as gray pixels. Forest attrition is considerably higher in western ecoregions than in eastern ecoregions as forest losses occurred more frequently in gap regions.</p

Forest dynamics in the U.S. indicate disproportionate attrition in western forests, rural areas and public lands

<div><p>Forests are experiencing significant changes; studying geographic patterns in forests is critical in understanding the impact of forest dynamics to biodiversity, soil erosion, water chemistry and climate. Few studies have examined forest geographic pattern changes other than fragmentation; however, other spatial processes of forest dynamics are of equal importance. Here, we study forest attrition, the complete removal of forest patches, that can result in complete habitat loss, severe decline of population sizes and species richness, and shifts of local and regional environmental conditions. We aim to develop a simple yet insightful proximity-based spatial indicator capturing forest attrition that is independent of spatial scale and boundaries with worldwide application potential. Using this proximity indicator, we evaluate forest attrition across ecoregions, land ownership and urbanization stratifications across continental United States of America. Nationally, the total forest cover loss was approximately 90,400 km², roughly the size of the state of Maine, constituting a decline of 2.96%. Examining the spatial arrangement of this change the average FAD was 3674m in 1992 and increased by 514m or 14.0% in 2001. Simulations of forest cover loss indicate only a 10m FAD increase suggesting that the observed FAD increase was more than an order of magnitude higher than expected. Furthermore, forest attrition is considerably higher in the western United States, in rural areas and in public lands. Our mathematical model (R² = 0.93) supports estimation of attrition for a given forest cover. The FAD metric quantifies forest attrition across spatial scales and geographic boundaries and assesses unambiguously changes over time. The metric is applicable to any landscape and offers a new complementary insight on forest landscape patterns from local to global scales, improving future exploration of drivers and repercussions of forest cover changes and supporting more informative management of forest carbon, changing climate and species biodiversity.</p></div