Reliably Estimating Street Tree Counts, Species Diversity, and Pest Vulnerability with Random Sampling

Data Collection and Preparation

This study incorporates street tree data from 16 municipalities in the state of Indiana, USA (Figure 1). Tree data sets were acquired from the Indiana Green City Mapper (Environmental Resilience Institute 2023) or directly from municipal governments. The tree inventories were conducted by different entities between 2008 and 2021, and they represent municipalities ranging in population from 4,784 to 887,642 (Table 1). Tree data sets were acquired in geographic information systems (GIS) format, or they contained X-Y coordinates that were used to map the tree points. While the information reported for each tree varied by municipality, all municipalities included tree species information. Each tree species was assigned a unique numeric code to eliminate problems associated with inconsistent spellings or different names for the same species.

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Figure 1.

Map of the 16 study municipalities in Indiana, USA, by 2020 population (US Census Bureau 2025).

The unit of sampling effort in this study was defined as the street segment. Street segments include both sides of the street along one block between two intersections. For dead-end streets and cul-de-sacs, the street segment includes both sides of the street from the intersection to the end of the street. Streets data sets were acquired in TIGER/Line GIS format for each municipality from the US Census Bureau (2024). Many individual street records in these GIS data sets spanned multiple street segments, so we used GIS tools in ArcGIS Pro v2.9 (Esri, Redlands, CA, USA) to split the street lines at intersections. Then we used a GIS spatial join to associate each tree with the nearest street segment. Trees greater than 18 m (59 ft) from a street centerline were excluded from the analysis. Based on our observations, trees greater than 18 m from street centerlines were typically located in parks or on other public lands and should not be included as street trees. For each street tree, the final data set used for analysis included its species identifier, its municipality, and a street segment identifier.

To understand general data patterns among municipalities, we calculated pairwise Pearson correlation coefficients (r) using the R statistical software stats package (R Foundation, Vienna, Austria) among the following variables: human population, total street length (km), inventoried street trees (n), species richness, the inverse of the Simpson Diversity Index (Sun 1992), and ALB hosts (% of trees). Pearson correlations where r > |0.5| were considered strong correlations.

Estimating Total Trees

We started with inventory data from each municipality for which we knew the total number of inventoried trees, the number of species present, species diversity, and the percent of trees that were ALB hosts (Table 1). Then we drew a random sample from each inventory to estimate citywide street tree population statistics. Repeating the random sample many times allowed us to assess the reliability of the sample-based estimates compared to the known population statistics from the complete inventory data set. Adjusting the size of the sample allowed us to evaluate how the quality of the estimates changed according to the sample size. This information could be used to answer the question: what sample size is likely to generate a reliable estimate of the citywide street tree population characteristics?

We used an iterative approach to estimate the total number of street trees citywide based on a sample of street segments. We drew one street segment, used the number of trees on that street segment to estimate the number of trees citywide, and then repeated that 1,000 times to characterize the expected variability for a random sample containing one street segment. Then we repeated that for two street segments, three street segments, and so on, until the random sample contained all the street segments in the municipality. Random draws were conducted without replacement to emulate a real-world sampling strategy that would not repeat the same street segments multiple times.

These random draws were used to produce two analytical products. First, we assessed how the relative standard error changed with increasing sampling effort in each municipality. Relative standard error is calculated by dividing the standard error of the estimate by the estimate value; lower relative standard error indicates more precise estimates (but not necessarily more accurate estimates). We calculated relative standard error based on ratio estimates of the number of trees per unit street length. Street segment length was incorporated in the analysis because longer streets segments are likely to have more trees. We followed Nowak et al. (2015) to estimate the total number of trees (T) as

where $\overline{X}$ is the mean street segment length in the entire municipality, $\overline{x}$ is the mean street segment length in the sample, N is the number of street segments in the entire municipality, and ȳ is the mean number of trees per street segment in the sample. Standard error of the estimate T was calculated as

where

Nowak et al. (2015) describe a relative standard error of 10% as a target for cities to achieve a reasonable estimate of total street trees.

Second, we used the random draws from each municipality to generate so-called reliability thresholds, which indicate the sample size needed to reliably estimate the total number of trees within a given percent of the actual tree count. This analysis step was performed to give additional context to street tree managers, because relative standard error is a concept with which urban forestry professionals are likely unfamiliar.

For each municipality, the reliability thresholds were established by first calculating the absolute difference between the actual citywide tree count and each of the 1,000 estimates derived via random sampling and ranking each estimate by that absolute difference. Then we took the 5th percentile estimate (950th closest to the actual tree count out of 1,000 estimates) and calculated its percent difference from the actual tree total. In this study, we were able to use randomization to evaluate how citywide estimates vary according to different sample sizes by comparing to a known tree count from the complete inventory data sets. But an urban forest practitioner implementing a sample inventory only implements a single random sample in the field. These reliability thresholds can be interpreted as the percent difference you can reliably expect (≥ 95% of the time) any given field sample to fall within the actual number of total trees. For each municipality, we determined the respective sample sizes (in percent of citywide street segments) needed to reliably estimate the total tree count within 50%, 25%, 20%, 15%, 10%, 5%, 3%, 2%, and 1% of the actual value.

Estimating Species Diversity

Species diversity is often emphasized in urban forestry as a means to reduce vulnerability to pests and pathogens, but diversity also promotes climate resilience and supports a broad portfolio of ecosystem services (Kendal et al. 2014). Thus, it is important that sample inventories yield an accurate picture of a city’s street tree diversity. We computed how estimates of diversity changed with increasing sample depth according to two diversity measures, namely species richness and the inverse Simpson index.

Species richness is a simple measure of diversity that describes the number of different species represented in a street tree population. We used reliability thresholds to determine the respective sample size needed to reliably encounter 50%, 60%, 70%, 80%, 90%, and 95% of the species present in each municipality. Reliability was characterized as the sample size at which 95% of 1,000 random iterations yielded a species richness value exceeding a given threshold. We did not use samples to estimate citywide species richness because richness extrapolations are unreliable when based on relatively small sample sizes that are common in street tree sampling (Colwell et al. 2012).

The inverse Simpson index (1/D) characterizes diversity according to both species richness and evenness, with larger index values indicating less dominance and greater diversity. This index has been used widely to measure diversity in urban forestry research (Berland and Elliott 2014; Cowett and Bassuk 2020; Velasquez-Camacho et al. 2024). The inverse Simpson index can be interpreted as the effective number of species in a tree population; for example, an inverse Simpson index of 20 indicates a level of diversity equivalent to 20 equally represented species (Sun 1992). We used reliability thresholds to determine the respective sample sizes needed to estimate the citywide inverse Simpson index within 5, 4, 3, 2, 1, 0.5, and 0.25 units of the actual index value for each municipality’s full tree inventory. Reliability was characterized as the sample size at which 95% of 1,000 random iterations yielded a species diversity value within a given threshold of the true value.

Estimating Pest Vulnerability

Asian longhorned beetle (Anoplophora glabripennis) (ALB) is a beetle native to China and Korea that has become established as a pest in Europe and North America (Haack et al. 2010). Asian longhorned beetle has primarily infested urban forests in the Eastern United States, but it has also been found in nonurban settings (Dodds and Orwig 2011). We selected ALB as an example pest for this study because it has not been found in Indiana, but it is a potential threat, as it has been found in the neighboring states of Illinois and Ohio (USDA APHIS 2025). Asian longhorned beetle hosts were defined as either preferred or occasional to rare hosts, as described by Wang (2015). Hosts included trees from the following genera: Acer, Aesculus, Albizia, Betula, Cercidiphyllum, Fraxinus, Platanus, Populus, Salix, Sorbus, and Ulmus. Each tree was coded as host or nonhost.

We estimated the percent of trees that were ALB hosts in each municipality using the same approach that we used to estimate total street trees. We drew street segments in random order 1,000 times and calculated relative standard error to characterize how the precision of estimates improves with increasing sample size. We also calculated reliability thresholds to determine the percent of street segments that needed to be sampled in each municipality to estimate citywide ALB vulnerability within 25, 20, 10, 5, 3, 2, and 1 percentage points of the actual value, respectively. These calculations were based on 1,000 random draws where reliability was defined as 95% of randomized estimates falling within a given percentage of the actual estimate. For example, if the full data set for a municipality contained 35% of trees that were ALB hosts, the reliability threshold of 5 percentage points would indicate the street segment sample size needed to reliably (≥ 95% of the time) generate an estimate falling between 30% and 40% of trees. Statistical analyses were conducted using R software with the base, vegan (Oksanen et al. 2020), and ggplot2 (Wickham 2016) packages.

Overview of the Study Municipalities

The 16 municipalities included in the study varied widely in terms of human population (Figure 1), number and density of inventoried street trees, species diversity, and percent of trees that are potential ALB hosts (Table 1). City population was positively correlated with total street length (r = 0.998), the number of inventoried street trees (r = 0.992), and species richness (r = 0.763). Total street length was positively correlated with the number of trees (r = 0.988) and species richness (r = 0.759). The number of inventoried trees was positively correlated with species richness (r = 0.784). Species richness was positively correlated with the inverse Simpson index (r = 0.616). And finally, the inverse Simpson index was negatively correlated with ALB hosts (r = –0.838). Two intuitive patterns summarize these correlations. First, larger municipalities have longer total street length, more total street trees (but not necessarily higher street tree density), and higher species richness. Second, ALB vulnerability is generally lower for municipalities with greater species diversity according to the inverse Simpson index, but not necessarily for municipalities with greater species richness.

Estimating Total Trees

This study demonstrates that sample sizes need to include a larger percentage of street segments in smaller municipalities to generate reliable estimates of street tree populations (Table 2; Figure 2). This supports a similar finding by Nowak et al. (2015), and it is not surprising, given that a large percentage of street segments in a small town may include fewer total street segments than a small percentage of street segments in a large city. For example, a sample size of 22.5% of street segments is needed in Indianapolis to reliably estimate the number of trees within 10% of the actual value, while a sample size of 67.0% is needed to achieve the same reliability in the smaller city of Lafayette (Table 2). However, because Indianapolis has far more street segments than Lafayette, the number of street segments needed to reliably estimate the tree count within 10% of the actual value is far smaller in Lafayette (1,079 street segments) compared to Indianapolis (4,259 street segments).

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Figure 2.

Change in relative standard error of the total trees estimate with increasing sampling effort for 4 select municipalities from larger (Indianapolis) to smaller (Crawfordsville).

Compared to the findings of Nowak et al. (2015), we found that larger sample sizes were needed to achieve a relative standard error below 10%. Whereas Nowak et al. (2015) determined that sample sizes between 2.2% and 4.6% were needed to achieve a relative standard error of 10% for 5 of the 6 cities they studied, all 16 of the municipalities studied here required larger sample sizes to achieve this standard. Indianapolis required the lowest percent sample size at 6.4% (1,203 of 18,922 street segments) to reach 10% relative standard error (Figure 2). In Fort Wayne, the second largest city in our study, 9.6% of street segments yielded a relative standard error below 10%. A much larger sample including 82.4% of street segments was needed to achieve 10% relative standard error in Fortville, the smallest municipality in our study. It is not apparent why larger sample sizes were needed in our study municipalities to achieve the relative standard error target set by Nowak et al. (2015). One possible explanation is that the municipalities in this study had more variability in the number of trees per street segment as compared to the cities studied by Nowak et al. (2015). In light of this finding, we caution that the sample size of 3% of street segments recommended by Nowak et al. (2015) may be inadequate, particularly for smaller cities where a considerably larger percent of streets must be sampled to achieve precise estimates of street tree populations.

Smaller municipalities also required proportionally larger samples of street segments to reliably estimate tree counts within a given percent of the actual citywide value (Table 2). In Indianapolis, a random sample of 22.5% of the street segments was needed to reliably generate an estimate of total trees within 10% of the actual tree count. The sample size to reliably achieve the same standard was 27.5% in Fort Wayne and then 55.5% to 94.5% for the remaining 14 municipalities (Table 2). In the majority of municipalities, estimates of total trees within 50% of the actual street tree count can be achieved with sample sizes under 10% of the street segments, but an estimate within 50% is likely too imprecise to be useful for urban forestry planning and management. On the other hand, generating estimates that are reliably within 1% or 2% of the actual value requires very large sample sizes between 88% and 100% (Table 2). If such precise estimates are needed, municipalities should conduct a complete street tree inventory rather than a sample-based inventory. Municipalities designing a random sample of street trees should consider the balance between their budgetary limitations and the level of data quality needed to successfully use the estimated tree count for planning and management activities. Our results demonstrate general patterns across a gradient of large to small municipalities. However, we do not provide specific sample size guidance because Table 2 illustrates that sample size reliability thresholds can vary considerably across municipalities, even among municipalities with similar street tree populations.

Estimating Species Diversity

In terms of species richness, the percent sample size needed to encounter a given proportion of the species in a municipality is generally larger for municipalities with fewer inventoried trees (Table 3). For example, a 2.1% sample of street segments in Indianapolis will reliably encounter 50% of the species in the city, while a sample of 8.5% is needed to encounter 50% of the species in Lafayette. This pattern is not set in stone, however, as Muncie is similar in size to Lafayette but only requires a sample size of 4.8% to reliably encounter 50% of the species. This variability among municipalities is presumably driven by differences in species richness citywide and by the composition of species along street segments (i.e., whether individual street segments tend to be planted with one or two species or if they are planted more diversely).

Naturally, it takes larger sample sizes to reliably encounter a larger percentage of the total species in a community (Table 3). The data in Table 3 demonstrate how additional sampling efforts increased the likelihood of encountering more species in our study municipalities. As with estimating the total number of street trees, municipalities should evaluate the tradeoffs in sampling effort costs versus the value of obtaining more complete data when determining the appropriate sample size for their urban forestry goals. For instance, practitioners in Fort Wayne may decide that it is insufficient to only encounter 50% of their species with a 3.9% sample, so they opt for a larger 7.4% sample that is likely to record at least 60% of the species citywide. However, the value they would gain from having a list of 90% of the species represented in the city may not be great enough to justify a much more ambitious sample of 55.4% of street segments to reliably achieve that 90% threshold (Table 3).

In general, a relatively larger percent of street segments must be sampled to achieve reliable estimates of the inverse Simpson diversity index when municipalities have more overall diversity and have fewer total trees (Table 4). Compared to estimates of the total number of inventoried trees, we achieved low relative standard errors for the inverse Simpson index; all municipalities achieved a relative standard error ≤ 3.6% with a 1% sample of street segments (data not shown). But only the municipalities with the lowest diversity (1/D < 6) could reliably produce an inverse Simpson index estimate that was accurate within 5 units of the actual value with a sample size of 1% of street segments (Table 4). This underscores the fact that relative standard error reflects the precision of estimates but not necessarily their accuracy (i.e., the repeated estimates are similar to one another but not correct). For higher diversity street tree assemblages, larger sample sizes are needed to accurately estimate the inverse Simpson index (Table 4). So while small sample sizes can generate precise estimates of diversity that are repeatable across model iterations, these estimates drastically underestimate the actual diversity of inventoried street trees. As such, these results suggest that reliability thresholds are useful to help place relative standard error values in context to provide a more complete picture of both precision and accuracy. In general, sample data sets are likely to underestimate diversity (and richness in particular), because additional species are encountered as sample size increases. Software tools are available to extrapolate diversity estimates beyond the sample data set (Hsieh et al. 2016), but note that these extrapolations may be unreliable for small sample sizes (Colwell et al. 2012).

Estimating Pest Vulnerability

Estimating the number of potential pest or pathogen hosts in a municipality can be useful for contingency planning in case that pest or pathogen arrives. Using the example of trees that are potentially vulnerable to ALB, we show that relative standard error behaves in much the same way as it did when estimating total street trees (Figure 3). However, the sample sizes needed to achieve 10% relative standard error are slightly higher for ALB vulnerability as compared to total tree counts (compare Figures 2 and 3). Reliably estimating the percent of vulnerable trees in a municipality within 25 percentage points of the actual value can be accomplished with very small sample sizes (Table 5); unfortunately, for a municipality with 35% of the trees vulnerable to ALB, it does not provide much useful information to generate an estimate within 25 percentage points that falls between 10% and 60% vulnerability. For all municipalities in our study except Indianapolis, sample sizes greater than 23% were required to reliably estimate the percent of trees vulnerable to ALB within 3 percentage points of the actual value (Table 5).

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Figure 3.

Change in relative standard error of the estimated vulnerability to ALB with increasing sampling effort for 4 select municipalities from larger (Indianapolis) to smaller (Crawfordsville).

Limitations

This study documents how the data quality of street tree inventories improves with sample size, but several limitations should be noted. Compared to similar studies, we included a relatively large number of study municipalities spanning a range of populations, but our results may not be representative of situations in other geographic regions or administrative contexts. For example, municipal governments are responsible for street tree management in the majority of Midwest United States municipalities, while street tree management is more frequently the responsibility of abutting property owners in the American West (Hauer and Peterson 2016); this could lead to differences in tree planting decisions such as species selections and heterogeneous planting densities that could impact how data quality varies with sample size. We relied on street tree data sets collected by other organizations that could have issues with data error or completeness. We did not stratify our sampling by urban zones (e.g., downtown, residential, commercial) because these zones were not defined consistently across our 16 study municipalities, but this could help improve data quality for practitioners implementing a sample-based inventory (Jaenson et al. 1992). Similarly, we did not filter out specific road types from the TIGER/Line streets data (US Census Bureau 2024), but this could be done in places where street trees are only planted along certain types of roads. Finally, we emphasize that our results demonstrate generally how data quality improves with increasing sample size across a range of municipality sizes, but a specific standard of data quality cannot be guaranteed in light of the observed variability among municipalities.