2 Cowett and Bassett: Street Tree Diversity in Three Northeastern U.S. States and McPherson (2003) assessed street tree diversity for the city as a whole and for 11 sampling zones from a sample of 3,089 public and privately man- aged trees located within the city’s right-of-way. Street tree diversity also has been assessed at broader geographic levels, such as a region or state. Lesser (1996) assessed street tree diversity in south- ern California based on inventory data from 21 cities, Ball et al. (2007) assessed street tree diver- sity in South Dakota, U.S., based on inventory data from 34 communities statewide, and Raupp et al. (2006) assessed street tree diversity in the temperate zone of eastern North America based on inven- tory data from 12 cities and one college campus. Finally, street tree diversity has been assessed at still broader geographic levels involving multi- ple countries and continents. Sjöman et al. (2012) assessed Nordic street tree diversity based on inven- tory data from 10 cities in four countries, and Kendal et al. (2014) assessed global street tree diversity based on tree species lists from 108 cities in six continents. In all the studies cited here, deficiencies were found in street tree diversity using a variety of metrics. One common metric employed to assess street tree diversity is frequency distribution, where the relative abundances of street trees belonging to botanic species, genera, and families are calcu- lated as percentages of the population as a whole. Relative abundance metrics were popularized by Santamour (1990), who advocated for more even distributions of street tree species, genera, and families in municipal street tree populations. Santamour proposed as a general rule that no tree species should comprise more than 10%, no tree genus should comprise more than 20%, and no tree family should comprise more than 30% of a municipality’s street tree population. Thus, Sand- ers (1981) found Norway maple (Acer platanoides) to comprise 37.5% of all street trees in Syracuse, New York, U.S.; Lesser (1996) found American sweetgum (Liquidambar styraciflua) to comprise 14.27% of all street trees in 21 southern California cities; and Ball et al. (2007) found ashes (Fraxinus spp.) to comprise 36.3% of all street trees in 34 South Dakota communities. Santamour’s 10-20-30 benchmarks have become a widely accepted rule- of-thumb, even though there is a lack of scientific or empirical evidence to validate those numbers as effective thresholds. Additionally, it has been [1] [1] [1] [2] [2] ©2017 International Society of Arboriculture argued that applying the 10-20-30 rule in some urban landscapes may be counterproductive to street tree management by replacing well-adapted tree species with underperforming ones (Richards 1993; Kendal et al. 2014). Conversely, more strin- gent standards than Santamour’s have been offered before and since. Barker (1975) proposed that no tree species should comprise more than 5% of the street tree population, Bassuk et al. (2009) proposed limiting any one street tree species to between 5% and 10% of the street tree population, and Ball (2015) proposed that no tree genus should com- prise more than 5% of the street tree population. A diversity index is another metric employed in assessing street tree diversity. Many indices have been utilized in ecology and environmental science to make comparisons between biological populations. These indices usually consider more than simply relative abundance and include such factors as population size and species richness (the number of species in the population) in their calculation. Two indices oſten used in assessing street tree diversity are Simpson’s Diversity Index (Simpson 1949) and the Shannon-Wiener Diver- sity Index (Shannon 1948). Simpson’s Diversity Index calculates the proportion of species i rela- tive to the total number of species (pi ), sums the squared proportions for all the species, and then takes the reciprocal, according to the formula: 𝐷𝐷ሶ蟳 = 1/�𝑝𝑝ሶ蟳 i2 𝑠𝑠ሶ蟳 𝐷𝐷ሶ蟳 = 1/�𝑝𝑝ሶ蟳 i2 𝑠𝑠ሶ蟳 𝑖𝑖ሶ蟳 =1 𝑖𝑖ሶ蟳 =1 lates the proportion of species i relative to the total number of species (pi multiplied by -1, according to the formula: [2] tiplied by the natural logarithm of tion (lnpi 𝐻𝐻ሶ蟳 = −�𝑝𝑝ሶ蟳 i 𝑠𝑠ሶ蟳 𝑖𝑖ሶ蟳 =1 𝑖𝑖ሶ蟳 =1 𝐻𝐻ሶ蟳 = −�𝑝𝑝ሶ蟳 i 𝑠𝑠ሶ蟳 ln 𝑝𝑝ሶ蟳 i ln 𝑝𝑝ሶ蟳 i Simpson is sometimes preferred to Shannon- Wiener because it gives more weight to the more abundant species and is therefore more sensi- tive to the distribution evenness advocated by Santamour than to species richness; Shannon- The Shannon-Wiener Diversity Index calcu- ), which is then mul- this propor- ), summed across all species, and then
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