In this short communication, following a brief introduction, we undertake a comprehensive analytical study of the weighted Simpson index. Our primary emphasis concerns the precise determination of the optimal point (minimizer) coordinates and of the minimum value of the index, a differentiable convex function, which is related to the harmonic mean concept. Furthermore, we address and solve the inversion problem and show the tight connection between both approaches. Last, we give some insights and final remarks on this subject.

Species diversity has been shown to be influenced by environmental factors, but the mechanism underlying their relationship remains unclear across spatial scales. Based on field investigation data collected from 3,077 sample plots in temperate forest ecosystems, we compared tree species richness, evenness and dominance at 10 km × 10 km, 30 km × 30 km and 90 km × 90 km spatial scales. Then, we detected the scale dependence of changes in tree species composition on climate, topography and forest structure using variation partitioning and quantified their contribution to tree diversity with gradient boosted models (GBMs) and fitted their relationships. The magnitude of tree richness, evenness and dominance significantly increased with spatial scale. Ecological factors jointly accounted for 24.3%, 26.5% and 38.5% of the variation in tree species composition at the three spatial scales, respectively. Annual mean temperature had a strong impact on tree richness, evenness and dominance and peaked at an intermediate scale. Tree evenness and dominance increased with the variation of temperature but had upper and lower limits. Tree richness obviously increased with annual precipitation on multiple scales and decreased with annual sunshine duration at large spatial scale. Tree richness, evenness and dominance obviously increased with the variation elevation and diameter at breast height at large scales and small scales, respectively. Tree dominance decreased with tree height in a hump at small scale. The dependence of tree diversity on ecological factors increased with spatial scales. Furthermore, different factors exert various controls on tree diversity at different spatial scales, representing a comprehensive mechanism regulating tree diversity.

Long-term, multi-decade research on planted tree survival in urban settings is sparse. One understudied urban environment is highway rights-of-way (ROW), lands adjacent to high-speed, unsignalized roadways. We conducted a re-inventory of tree planting cohort in northern Illinois, U.S. on a 48 km-long highway near Chicago which were 10-, 21-, and 30-years old to evaluate long-term patterns of survival and diversity. Using each randomly selected planting site along the highway as a unit of observation and analysis, we compared the number of trees documented in record drawing to the number of trees currently alive to determine percent survival. We evaluated 224 planting sites which originally contained 2,944 trees and collected data about the planting site location. For the oldest cohort, 26% of trees were still alive in 2018 (median survival by species = 16%, Q1 = 0%, Q3 = 48%), while 31% of the 21-year-old cohort (med. = 6%, Q1 = 0%, Q3 = 47%) and 86% of the 10-year-old cohort were still alive (med. = 85%, Q1 = 74%, Q3 = 96%). The survival of the 21- and 30-year-old cohort matches urban tree survival estimates by other researchers, while the 10-year-old survival is higher than expected. The only planting location characteristic that significantly affected survival was traffic islands (areas between the highway and entrance/exit ramps). Species with low drought tolerance were less likely to be alive for the 10-year-old cohort. Waterlogging tolerant species were more likely to be alive in the 10-year-old cohort. Since some species in the 21- and 30-year-old cohorts had very low survival, the tree species richness and diversity s in study areas declined between the initial record drawings and reinventory. This study demonstrates the challenges of maintaining long-term survival and diversity in the highway ROW and emphasizes the importance of species selection.