Forest Service Northern 

Research Station

General Technical Report

NRS-158

Publication Date 

March 2016

Urban Tree Mortality: a Primer on 

Demographic Approaches

United States Department of Agriculture

Lara A. Roman, John J. Battles, Joe R. McBride
Abstract

Realizing the benefits of tree planting programs depends on tree survival. Projections of urban forest 

ecosystem services and cost-benefit analyses are sensitive to assumptions about tree mortality rates. 

Long-term mortality data are needed to improve the accuracy of these models and optimize the public 

investment in tree planting. With more accurate population projections, urban forest managers can also plan 

for cycles of tree planting, death, removal, and replacement to achieve canopy cover goals. Analytical tools 

from demography, such as life tables and mortality curves, could be used to improve our understanding 

of urban tree mortality and longevity. Demographic approaches have been widely used in forest ecology 

to quantify population dynamics and project future changes in wildland systems. This report is a primer on 

demographic concepts applied to urban trees, with terms and analytical methods adapted to the cultivated 

urban landscape. We include an overview of the uses of urban tree mortality rate data for research and 

management, a summary of lessons learned from ecological monitoring in other systems, and a discussion of 

opportunities for long-term urban forest monitoring by researchers and practitioners.

The Authors

LARA A. ROMAN is a research ecologist with the USDA Forest Service’s Northern Research Station, 

Philadelphia Field Station in Philadelphia, PA. 

JOHN J. BATTLES is a professor in the Department of Environmental Science, Policy and Management at the 

University of California, Berkeley in Berkeley, CA. 

JOE R. McBRIDE is a professor emeritus in the Department of Environmental Science, Policy and 

Management and in the Department of Landscape Architecture and Environmental Planning at the University 

of California, Berkeley in Berkeley, CA.

Cover Photo: Trees in Center City Philadelphia, PA, as seen from the Philadelphia Museum of Art. Photo by Lara A. 

Roman, U.S. Forest Service. 

Disclaimer

The use of trade or firm names in this publication is for reader information and does not imply endorsement by the 

U.S. Department of Agriculture of any product or service.

Manuscript received for publication July 2015

Published by: For additional copies:

U.S. FOREST SERVICE U.S. Forest Service

11 CAMPUS BLVD SUITE 200 Publications Distribution

NEWTOWN SQUARE PA 19073-3294 359 Main Road

Delaware, OH 43015-8640

March 2016

Visit our homepage at: http://www.nrs.fs.fed.us

Printed on recycled paper
1

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Why Study Urban Mortality Rates? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Age-based Life Tables, Survivorship Curves, and Mortality Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Censored Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Calculating Annual Mortality from Survivorship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Lifespan Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Size-based Mortality Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Tracking Population Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

The Need for Urban Tree Monitoring and Longitudinal Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Lessons from Ecological Monitoring in Other Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Looking Ahead: Opportunities for Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2

Introduction

Urban forests are said to provide environmental, 

socioeconomic, and human health benefits, collectively 

referred to as ecosystem services (Dwyer et al. 1992, Nowak 

and Dwyer 2007, Tzoulas et al. 2007). Ambitious tree 

planting efforts in cities across the United States and around 

the world aim to expand the delivery of these benefits. 

Campaigns to plant a million trees have been a major force 

in urban sustainability initiatives (Young and McPherson 

2013). The value of tree planting is justified, in part, by 

models that quantify and monetize tree benefits (McPherson 

et al. 2005, Nowak et al. 2008, U.S. Forest Service 2015b). 

The ecosystem services concept has become mainstreamed 

in urban forest management among municipal arborists and 

urban greening nonprofit organizations (Silvera Seamans 

2013, Young 2013).

However, realizing the public value of urban forest programs 

depends on quantifiable locality-specific performance 

(Pataki et al. 2011), including tree survival (Roman et al. 

2014b). Altering the mortality rate assumptions in urban 

forest ecosystem services models drastically affects projected 

tree values (e.g., McPherson et al. 2008, Morani et al. 2011). 

But are these assumed rates accurate? What proportion 

of trees will survive decades after planting, when the 

anticipated benefits are greatest? What are the implications 

of future tree death for urban forest management that is 

designed to achieve canopy cover goals? Answers to these 

questions depend on the rates and processes of urban tree 

death. Thus, understanding urban tree mortality is critical to 

accurately modeling tree population changes over time and 

quantifying ecosystem services (Roman 2014).

This report is a primer on demographic concepts and 

analytical approaches relevant to the study of urban 

tree mortality. Demography—the statistical study of 

populations—is used to analyze mortality trends and project 

future changes in systems ranging from human societies to 

endangered wildlife communities and naturally occurring 

forests. The same concepts and calculations used by actuaries 

(to determine risk of death for issuing life insurance policies) 

and conservation biologists (to assess species extinction risk) 

can be used to study tree death in cities. Many terms have 

been used to describe tree mortality and longevity in the 

urban forestry literature (Roman and Scatena 2011, Roman 

et al. 2014b). To make meaningful comparisons across 

programs, it is important to use consistently defined terms. 

This primer is intended to aid municipal arborists and 

urban greening organizations that undertake their own 

tree monitoring studies to evaluate mortality as a metric 

of program success (Roman et al. 2013). This report also 

serves to introduce demographic terms and concepts to 

urban forest researchers. We begin by briefly reviewing 

the importance of tree mortality to urban forest planning 

and population models. Throughout the report, we situate 

urban tree mortality within the larger body of literature on 

tree mortality in wildland systems. We define demographic 

terms in the context of the cultivated urban forest landscape. 

Specifically, we focus on the rates of tree death and 

associated lifespan metrics. We then outline an approach 

to studying urban tree mortality that relies on long-term 

monitoring to produce the data necessary for demographic 

analyses, and call for partnerships among researchers and 

practitioners to produce such long-term studies. 

Why Study Urban Tree Mortality Rates?

Ecosystem services projections and cost-benefit analyses 

have used a variety of mortality assumptions (Table 1). 

Urban tree mortality rates vary by size class and time since 

planting, among other factors (Koeser et al. 2014, Nowak 

et al. 2004, Roman et al. 2014a). Some models accounted 

for such differences (Table 1), but rates were occasionally 

stated without differentiation by tree size or age (McPherson 

et al. 1999). McPherson et al. (2008) did not reference 

Chinese pistache (Pistacia chinensis) street trees in the West Oakland 

neighborhood of Oakland, CA. Photo by Lara A. Roman, U.S. Forest Service.
3

Table 1.—Mortality rate assumptions used in ecosystem services projections for urban tree planting. Most studies determined long-term cumulative 

mortality to time x based on differential mortality rates by age classes. Some also used size and condition classes. These studies included urban trees 

across a variety of land use types and planting locations. Most studies projected future benefits for newly planted tree cohorts, but one example (Nowak 

et al. 2002) assessed benefits based on an inventory of current tree stocks. Annual mortality rates used in each study are noted when available, and these 

assumed rates varied by years planted, age class, condition class, and tree locations.

Location

Time 

interval 

x (yrs)

Cumulative 

mortality to time x

(cumulative 

survivorship l

x), % Notes Citation

Los Angeles, CA

 High mortality

 

 Low mortality

35

35

56 (44)

17 (83)

Trees planted over 5 years 

High-mortality scenario: 5% annual mortality years 1 to 

5, and 2% annual mortality thereafter

Low-mortality scenario: 1% annual mortality years 1 to 5, 

and 0.5% annual mortality thereafter

McPherson et al. (2008)

Modesto, CA n/a n/a 1.4% annual mortality averaged across all age classes McPherson et al. (1999)a

Sacramento, CA

 High mortality

 Low mortality

30

30

42 (58)

30 (70)

Residential shade trees; long-term mortality assumptions 

based on field records of survival during young tree 

establishment

Hildebrandt and Sarkovich 

(1998)b

Sacramento, CA 30 67 (33) For 100 trees, 21 died by year 5, and 1 additional tree 

died annually thereafter

McPherson et al. (1998)

California urban forests 15 25 (75) 3% annual mortality years 1 to 5; 1% annual mortality 

thereafter

McPherson and Simpson 

(2001)

Chicago, IL 30 35 (65) Variable mortality for different tree site types (e.g., parks, 

residential yards, residential street trees)

McPherson (1994)a

Brooklyn, NY n/a n/a Annual mortality for different condition classes: dead 

100%; dying 50%; critical 13.08%; poor 8.86%; fair 

3.32%; good–excellent 1.92% for 0–7.6 cm d.b.h.,1.46% 

for >7.6 cm d.b.h.

Nowak et al. (2002) c, e

New York City, NY

 4% Avg. ann. mort.

 6% Avg. ann. mort.

 8% Avg. ann. mort.

100

100 

100 

95.4 (4.6)

99.1 (0.9)

99.8 (0.2)

Trees planted over 10 years and grown out with assumed 

diameter growth rates

Annual mortality for different d.b.h. size classes 

proportional to: 2.9% for 0–7 cm; 2.2% for 8–15 cm; 2.1% 

for 16–46 cm; 2.9% for 47–61 cm; 3.0% for 62–76 cm; 

5.4% for ≥77 cm

Morani et al. (2011) d, e

a

 McPherson et al. (1999) gave a single annual mortality rate across age classes, and explained that Modesto, CA, mortality rates were “supplied by 

the city.” This information was used to calculate carbon release from dead trees. Mortality rate assumptions in McPherson (1994) were also based on 

information provided by local managers.

b

 Hildebrandt and Sarkovich (1998) illustrated graphically that young trees have higher mortality rates than established trees, and provided information 

about observed young tree losses, but annual mortality rate values for different age classes were not provided. Note that “mortality” in this context also 

includes failure to plant because this is a shade tree giveaway program (Roman et al. 2014b).

c

 Nowak et al. (2002) used varying mortality rates based on size and condition class, and used these rates to calculate carbon release from dead trees over 

1 year. The Brooklyn study is an example of the i-Tree Eco (formerly UFORE) model for assessing current ecosystem services from a plot-based inventory; 

other i-Tree Eco reports use these same methods.

d

 Morani et al. (2011) used varying mortality rates for different size classes to project population size, in order to simulate air pollution removal throughout 

a 100-year time horizon. Mortality rates for individual trees changed as time passed and trees grew into a different size class. Mortality rates were set to 

average at 4 percent, 6 percent, or 8 percent, with size-specific mortality rates proportional to those reported in the table.

e

 Morani et al. (2011), Nowak et al. (2002), and others using the i-Tree Eco model and prototype i-Tree Forecast (Nowak et al. 2013) referenced Nowak 

(1986) empirical data from mortality of maple (Acer) species street trees in Syracuse, NY, with rates differentiated by size and health condition classes.
4

specific field data to support mortality scenarios, but 

other projections have used information supplied by local 

managers (Table 1). The mortality data cited in i-Tree Eco 

(formerly UFORE) and the prototype i-Tree Forecast models 

(Morani et al. 2011; Nowak et al. 2002, 2013) originated with 

a single study of maple (Acer spp.) street trees in Syracuse, 

NY (Nowak 1986). The Syracuse street tree mortality results, 

grouped by size class and condition rating, were then applied 

to different site types and land uses in other cities. 

The mortality scenarios used in ecosystem services analyses 

and cost-benefit studies are essentially demographic 

population projections, although they are not generally 

labeled as such. In their simplest form, these predictions use 

a particular annual mortality rate, or alternative mortality 

rate scenarios, to estimate survivorship several decades after 

planting (e.g., McPherson et al. 2008). In a more complex 

example, Morani et al. (2011) used mortality and growth 

rates to estimate population counts and tree sizes over 100 

years for the MillionTreesNYC program in New York, NY. 

As Morani et al. (2011: 1045) noted, however, uncertainty 

in mortality rates is “the main limit for the population 

projector.”

Improving the accuracy of urban forest population 

projections is one reason to study tree mortality in cities. 

Urban tree mortality research can also help managers 

to identify leading risk factors for death, and then target 

program modifications that could enhance survival (Roman 

et al. 2014b, Vogt et al. 2015). Municipal foresters and local 

urban greening organizations have also expressed interest 

in tree mortality and monitoring as a way of quantifying 

success (Roman et al. 2013). Some practitioners have 

used monitoring as a proactive approach toward tree 

maintenance and management. For example, municipalities 

have undertaken systematic repeated inventories as part 

of pruning cycles and tree risk management, and planting 

initiatives have used monitoring data to give feedback 

to those responsible for tree care, such as residents and 

contractors (Roman et al. 2013). From a basic research 

perspective, urban tree mortality is central to urban forest 

population dynamics, and understanding mortality is essential 

to assessing temporal patterns in urban forest structure. 

Similarly, in natural forest ecosystems, tree monitoring and 

mortality research are crucial to understanding long-term 

dynamics, which are integral to sustainable management and 

model accuracy (Lines et al. 2010).

Before proceeding further, we must note that although 

urban forests can be broadly defined to include all trees 

in cities and urbanized areas (Konijnendijk et al. 2006, 

Piana and Troxel 2014), our report focuses on intentionally 

planted trees in street and residential lawn settings. Urban 

tree mortality rates differ by planting site type and land use 

(Koeser et al. 2014, Lawrence et al. 2012, Nowak et al. 2004). 

City trees in remnant patches or afforested parks of native 

and naturalized species, or forested areas on vacant lots and 

private lands (Zipperer et al. 1997), are probably closer to 

wildland forests in terms of demographic characteristics. 

In contrast, we focus on urban trees whose planting and 

removal are driven by human intervention. Our report is 

most relevant to heavily altered human-dominated portions 

of the urban forest: street and lawn trees.

As we draw on demographic concepts used in natural, 

wildland forests, we must bear in mind essential differences 

in the life cycle for wildland and urban trees. Wildland 

forests have natural processes of seed dispersal and 

germination; large amounts of seeds are produced, followed 

by competition among seedlings and saplings for light and 

other resources. Tree mortality in wildland forests is often 

a long process in which stressed individuals exhibit slow 

growth (Das et al. 2007, Pedersen 1998, Waring 1987), 

eventually succumbing to death through contributing factors 

such as wind, insects, or pathogens (Franklin et al. 1987, 

Harcombe and Marks 1983). Tree death as a cumulative 

process resulting from multiple factors was conceptualized 

Southern magnolia (Magnolia grandiflora) street trees in the West Oakland 

neighborhood of Oakland, CA. Photo by Lara A. Roman, U.S. Forest Service.
5

by Manion (1981) as the decline–disease spiral, later adapted 

by Franklin et al. (1987) as the mortality spiral. 

In contrast to wildland forests (and remnant forest patches 

in urban landscapes), urban street and yard trees are 

typically produced by nurseries and planted as saplings or 

whips in sidewalk cut-outs, planting strips, or manicured 

lawns. Urban environments pose many challenges for trees, 

such as compacted and contaminated soil (Craul 1999), 

construction (Hauer et al. 1994), and vandalism (Nowak 

et al. 1990), but urban trees may also have advantages not 

present for wildland trees, including fertilizer, irrigation, 

pest control (Harris et al. 2004), and reduced competition 

for light. Arborists aim to remove large unhealthy street 

and lawn trees before they die, in order to prevent 

property damage and reduce liability from falling limbs or 

infrastructure conflicts (Harris et al. 2004); this preemptive 

action kills the tree before the mortality spiral is completed. 

Additionally, some healthy city trees are removed due to 

human aesthetic preferences or land use changes. Tree 

mortality and removal are thus central elements of urban 

forest management. 

Cycles of tree planting, death, removal, and replacement 

shape the structure and function of our urban forests, and 

affect the amount of canopy available to provide ecosystem 

services. To apply demographic concepts used in wildland 

forest ecosystems, we must make adaptations to suit the 

circumstances of heavily managed urban trees. For example, 

although demographic methods are traditionally applied to 

a single species, we follow the convention of urban foresters, 

whereby “urban tree population” refers to all trees within a 

given area or from a particular planting program (Roman 

et al. 2014a). However, we acknowledge that urban tree 

populations are human-constructed systems with multiple 

species, and that species functional groups, such as drought 

tolerance, can be relevant to mortality analyses (Roman 

et al. 2014b). With sufficient sample size, separate mortality 

models can be developed for different species.

This primer is intentionally focused narrowly on mortality 

rates and associated lifespan metrics, so we do not address 

statistical techniques to assess factors related to mortality. 

For readers interested in such research, we point to several 

recent studies that have used multivariate analyses to 

investigate urban tree mortality (Ko et al. 2015; Koeser 

et al. 2014; Lawrence et al. 2012; Roman et al. 2014a, 2014b; 

Staudhammer et al. 2011; Vogt et al. 2015). Such techniques 

are widespread in the ecological and epidemiological 

literatures and can aid in interpreting the most relevant 

factors for mortality in a particular tree planting initiative or 

geographic area, as well as provide evidence for population 

projections (Table 1). Similarly, we do not cover spatial 

aspects of urban tree mortality, although spatial patterns 

can be an important component of population dynamics in 

wildland forests (e.g., Das et al. 2008) and probably urban 

forests as well. The techniques discussed in this report for 

quantifying mortality rates are a necessary first step for 

managers and researchers to determine what levels of loss 

are typical for urban trees as they age and grow.

London planetree (Platanus × acerifolia) street trees in Philadelphia, PA, 

including a tree that fell during an ice storm and was removed. Photo by 

Lara A. Roman, U.S. Forest Service.
6

Age-based Life Tables, Survivorship 

Curves, and Mortality Curves

In discussing tree mortality, urban foresters can use terms 

established in population biology and demography: annual 

mortality rates, annual survival rates, life tables, survivorship 

curves, mean life expectancy, and population half-life. We have 

defined these and other terms in the glossary. Mortality and 

survival information for urban trees can be broken down by 

age classes or size classes. Although forest ecologists typically 

use size classes (Harcombe 1987), we explore both approaches 

in this primer, as both are relevant to urban forest systems.

An age-based life table organizes survival information by age 

classes. In human demography, these life tables are broken 

down by sex, race, and other factors to assess mortality across 

different groups and calculate life expectancy. For urban trees, 

age-based life tables are appropriate for projects that monitor 

planting cohorts—trees planted around the same time (e.g., 

trees planted in the same year). Cohort survival data can also be 

depicted by using survivorship and mortality curves (Box 1).

As an example of an age-based life table for urban trees, we 

present survival data from Sacramento County, CA. These data 

are adapted from a study that monitored a cohort of shade 

trees that were distributed by the Sacramento Tree Foundation 

and the Sacramento Municipal Utility District in 2007 (Roman 

et al. 2014b). These trees were planted in residential lawns. 

Although the “clock” in an age-based life table typically begins 

at birth, in the context of urban trees, the “clock” begins at 

planting. Notation and formulas for the age-based life table, 

as applied to an urban tree planting cohort, are summarized 

in Table 2, and exemplified in the Sacramento cohort in Table 

3. The life table presented here considers only trees that were 

planted and omits trees that were distributed to residents but 

never planted (Roman et al. 2014b). The time interval between 

age classes in this example, and throughout the rest of our 

discussion of age-based life tables, is set to 1 year, meaning 

that px and qx are interpreted as annual survival and mortality 

at age x, respectively. However, age-based life tables may 

also be constructed with different age intervals, or varying 

time periods, which requires slight changes to the equations 

in Table 2 (Carey 1993). The “clock” could also begin at a 

different time to suit situations encountered by urban forest 

managers (e.g., begin counting time at the end of a 2-year 

contractor guarantee). 

Box 1: Classic Survivorship and Mortality Curve Shapes

A graph of ln (lx) vs. x is called a survivorship curve. For age-based 

cohort mortality, survivorship l

x is the proportion surviving to age x. In 

the survivorship curve, ln (lx) is the natural logarithm of survivorship; the 

natural log has base e, where e is a constant approximately equal to 

2.718. Survivorship curves are conventionally ln transformed to depict 

more clearly changes in the proportion of individuals surviving over 

time. The shape of the survivorship curve depends on how the mortality 

rate qx changes over time. The graph of qx vs. x is called the mortality 

rate curve. In the Type I survivorship curve, annual mortality is highest 

for old individuals, giving survivorship a convex shape. In Type II, annual 

mortality is constant, and ln (lx) vs. x is a straight line with negative 

slope. In Type III, annual mortality is highest for young individuals, 

leading to a concave survivorship curve. Another possible shape is 

the rotated sigmoid survivorship curve, and corresponding U-shaped 

(or bathtub-shaped) mortality curve. The sigmoid survivorship curve 

and U-shaped mortality curve represent high mortality for both old and 

young individuals, with low mortality rates in between.

Mortality curves for nonurban trees are typically drawn by using sizebased (not age-based) mortality rates, and the shape of the curve has 

implications for management and predictive modeling (more on sizebased mortality curves beginning on p. 12). For size-based mortality, 

Mx is the proportion of individuals dying in size class x (after Harcombe 

1987), and the survivorship curve is not relevant. 

Note that throughout this primer, x means time, with the exception of 

this graph, where x can also mean age class for mortality curves.

Survivorship and mortality curves depicted here are adapted from 

Harcombe (1987).

Type I

qx (or Mx)

ln (lx)

Type II

Type III

U-shaped mortality

x x
7

Table 2.—Notation and formulas for the age-based urban tree life table. Notation 

mostly follows Carey (1993), with censoring terms from Klein and Moeschberger 

(1997). 

Term Definition

x age, in this case measured in years, starting from time of planting 

( x = 0 )

Kx number of individuals alive at beginning of interval x to x + 1

Dx number of deaths in the interval x to x + 1

Wx number of individuals right censored (lost to follow-up) during the 

interval x to x + 1

Yx number of individuals at risk of death during the interval x to x + 

1 assuming that censoring times are uniformly distributed during 

the interval, and that causes of mortality and censoring are 

independent

 Yx = Kx – (Wx / 2 )

 (eqn. 1, after Klein and Moeschberger 1997: 138)

qx proportion dying from x to x + 1, annual mortality rate

 when there is no censoring:

 qx = Dx / Kx (eqn. 2)

 to compensate for censoring:

 qx = Dx / Yx (eqn. 3)

px proportion surviving from x to x + 1, annual survival rate

 px = 1 – qx (eqn. 4)

l

x proportion of the cohort surviving from planting to age x, commonly 

called survivorship to age x ; l

0 = 1 (i.e., 100 percent) by definition; 

eqns. 5 and 6 are equivalent when there is no censoring

 when there is no censoring:

 l

x = Kx / K0 (eqn. 5)

 to compensate for censoring:

 l

x = (lx–1) (px–1) 

 

(1–(Di–1/Yi–1 = )) i=1

x

 

 (eqn. 6, after Klein and Moeschberger 1997: eqn. 5.4.1)

Lx number of years lived by the average individual in the cohort from 

x to x + 1, called the cohort person-years in human demography

 Lx = (l

x + lx +1)/ 2

 (eqn. 7, after Carey 1993: eqn. 2-3a)

Tx total number of years remaining for the average individual from age 

x to the last possible year of life w:

 Tx = Lx + Lx+1+ Lx+2 + - - - + Lw

 

(Li)

w

i=x

=

 (eqn. 8, after Carey 1993: eqn. 2-4)

ex life expectancy at age x :

 ex = Tx / lx 

 (eqn. 9, after Carey 1993: eqn. 2-5)

Our example from Sacramento (Table 3) tracks a cohort for 

the first 5 years, and illustrates the key components of an 

age-based life table. Note that the first three columns 

(Kx , Dx ,Wx ) contain raw data; the other columns are 

demographic terms calculated from the data. Survivorship

l

x is cumulative from the time of planting to x while annual 

survival rate px and annual mortality rate qx are defined by 

a particular time interval x to x + 1 (i.e., 1 year). 

Note that survivability, a commonly used term in 

urban forestry, does not have a standard definition 

in demography and population biology. Indeed, 

survivability is also not generally defined in the urban 

forestry literature; survivability could mean annual 

survival, survivorship, or something else. Stating 

clear definitions—with equations and time periods 

specified—for terms such as annual survival, survivability, 

and survivorship (Roman et al. 2014b) is essential to 

comparing survival outcomes across cities and programs.

Censored Data

A complication in the Sacramento example (Table 

3), and in demographic studies in general, is that 

the survival outcome of all individuals could not be 

determined. We have only partial field data for a few 

of the Sacramento trees, in situations where we could 

not secure permission to enter the backyard every 

year. These incomplete observations are referred to as 

censored data. Specifically, some trees have been lost to 

follow-up: we do not know their survival status after the 

properties became inaccessible. This situation is called 

right censoring. (In fact, all trees that remain alive at 

the study’s conclusion are right censored, because we do 

not know when they will die.) For example, in medical 

research, when scientists permanently lose contact with 

patients during the course of the study, their information 

is considered right censored. There are many different 

approaches to censored data in survival analysis (Klein 

and Moeschberger 1997). We used a simple method 

to compensate for right censoring (Yx in Table 2) that 

depended on two assumptions: the causes of mortality 

and censoring were independent, and censoring times 

(i.e., times when individuals dropped from the study) 

were uniformly distributed. 
8

There are other forms of censoring, however. In urban 

forestry studies like the Sacramento example with private 

properties and incomplete observations, the analytical 

methods must ensure that censored data do not bias 

calculated vital rates. Interval censoring was present for 

every dead shade tree in the Sacramento study. The exact 

date of death was unknown; rather, the trees died between 

two known field dates, typically between two subsequent 

summers. Cohort life tables can accommodate interval 

censoring as long as the death event occurs within the predefined age classes. In other words, as long as death is known 

to occur between one summer field season and the next, 

the age-based life table works well. But interval censoring 

becomes problematic for the Sacramento life table when 

the interval length was longer than 1 year. For example, 

consider a tree seen alive in 2009, of unknown status in 

2010 and 2011, and observed missing in 2012. From the 

available information, we do not know which year the tree 

died. Our cohort life table (Table 3) had three such cases (<1 

percent of the 370 trees total). To retain these three cases in 

the life table, we assumed that those death events occurred 

at the midpoint of the longer interval. This is the simplest 

way to deal with interval-censored data; however, using the 

midpoint can lead to biased estimates (Giolo et al. 2009).

A different approach to mortality data, the Turnbull 

(1976) estimator to Kaplan-Meier survival curves, can 

accommodate both right and interval censoring. For more 

precise survivorship estimates than the life table can provide, 

we used the ‘interval’ package in the free statistical software 

R (Fay and Shaw 2010, R Development Core Team 2014), 

with specific planting dates and observation dates included 

(Roman et al. 2014b) (Fig. 1). In addition to dealing with 

interval censoring, this survivorship curve also accounts 

for the precise number of days between planting date and 

the first field observation for every tree, as well as the exact 

length of time between later field observations (e.g., when 

summer field work was not exactly 365 days apart). Trees 

were planted in the Sacramento program between January 

and December 2007, with annual mortality observations 

and field work each summer from 2008 through 2012. The 

first “year” in the cohort life table (Table 3) is therefore a 

range of about 6 to 21 months (Roman et al. 2014b). Thus 

there is a slightly different 5-year survivorship calculated 

from the cohort life table (Table 3, 71.3 percent, or stated 

equivalently, 0.713) and the survivorship curve (Figure 

1a, 70.9 percent, or equivalently, 0.709). The survivorship 

estimate from ‘interval’ is more precise because exact dates 

were included and censored information was appropriately 

incorporated. Nonetheless, the cohort life table is a simple 

approach that both researchers and practitioners in urban 

forestry may find useful to summarize cohort mortality 

data without specialized statistical analysis, or when exact 

planting dates are unavailable. Values in the age-based life 

table can be calculated in common spreadsheet programs 

(e.g., Microsoft® Excel). 

To further demonstrate the utility of assessing mortality 

data with more sophisticated survival analysis, we have also 

presented a graph comparing survival outcomes on stable 

versus unstable properties in Sacramento (Roman et al. 

2014b) (Fig. 1b). Stable properties are owner-occupied, 

Year Age, x

# alive at 

beginning of 

interval, Kx

# deaths in 

interval, Dx

# censored 

during 

interval, Wx

# at risk 

during 

interval, Yx

Annual 

mortality rate, 

qx

Annual 

survival rate, 

px

Survivorship 

to age x, lx

2007 0 370 45 0 370 0.122 0.878 1.000

2008 1 325 20 2 324 0.062 0.938 0.878

2009 2 303 18 5 300.5 0.060 0.940 0.824

2010 3 280 13 3 278.5 0.047 0.953 0.775

2011 4 264 9 6 261 0.034 0.966 0.739

2012 5 249 n/a n/a n/a n/a n/a 0.713

Table 3.—Life table example from field observations. Age-based life table from a cohort of residential lawn trees in Sacramento County, CA (Roman et al. 

2014b). The time of planting is x = 0. See Table 2 for notation and definitions. Note that 0.122 is equivalent to 12.2 percent.
9

and had the same resident throughout the study, whereas 

unstable properties had foreclosures, home sales, were renter 

occupied, or a combination thereof. Based on multivariate 

analysis with a data mining approach (specifically, 

conditional inference trees), stable home ownership was 

found to be the best predictor of shade tree establishment 

success. Trees on properties with stable home ownership 

were significantly more likely to survive, and more likely 

to have a higher maintenance rating. Residential yard 

tree planting programs therefore must be cognizant of 

resident turnover and associated changes in stewardship. 

The Sacramento Tree Foundation has used these and other 

findings from that 5-year survival study to guide program 

modifications (Roman et al. 2014b). 

Calculating Annual Mortality from Survivorship

When the annual mortality rate is constant (Type II), it 

can be calculated from survivorship by using the following 

equation: 

 qannual=1–(Kx /K0)1/x

 (eqn. 10, after Sheil et al. 1995: eqn. 6)

where K0 and Kx are the population sizes at the beginning and 

end of time interval x, respectively. As with the cohort life 

table, x is years. The fraction Kx /K0 is cumulative survivorship 

from the time of planting (Table 2, eqn. 5). Stated equivalently, 

when mortality is constant, annual survival and survivorship 

are related by pannual =(l

x )1/x

. Note that this relationship does 

not compensate for censoring. This equation is especially 

useful when a cohort is not visited annually. For example, 

Nowak et al. (1990) reported 66 percent survivorship 2 years 

after planting for street trees in Oakland, CA. Annual survival 

was therefore 81.2 percent, and annual mortality 19.8 percent, 

with the assumption of constant mortality: survivorship at 

2 years = 0.66 = 0.8122. Annual survival was estimated from 

survivorship data reported in other street tree studies in a 

similar fashion in Roman and Scatena (2011) (Table 4). Even 

when a cohort is observed annually, as with the Sacramento 

example, eqn. 10 can be used to report annual survival over 

the entire study period. Based on 70.9 percent survivorship at 

5 years (Fig. 1), annual survival of yard trees in Sacramento 

was 93.4 percent, with 6.6 percent annual mortality (Roman 

et al. 2014b).

Figure 1.—Survivorship curves for trees in single-family residential yards 

(n=370), Sacramento County, CA. Survivorship was assessed from 

Kaplan-Meier survival analysis with Turnbull (1976) estimator for censored 

observations (Fay and Shaw 2010). The gray rectangles indicate the range 

of possible values given censoring. Survivorship at 5 years equals 70.9 

percent for all trees (A). The most important variable for 5-year survival 

was stable home ownership (B); survivorship at 5 years was 61.3 percent 

for unstable properties and 76.6 percent for stable properties. A weighted 

logrank test (Fay and Shaw 2010) shows significant difference in the 

survival curves (p < 0.01). From Roman et al. (2014b).

A

B

 stable home ownership

 unstable home ownership

Survivorship (percent) Survivorship (percent)

Time Since Planting (yrs)

Time Since Planting (yrs)
10

Lifespan Metrics

Information about the typical lifespan for urban trees can help 

managers anticipate future tree losses. Although the “average 

lifespan” has been frequently discussed in urban forestry (Moll 

1989, Skiera and Moll 1992), the term is not clearly defined, 

and is rarely based on field data. The idea that street trees have 

an average lifespan of 7 years comes from a questionnaire sent 

to cities across the United States in which municipal foresters 

reported typical tree lifespans (Moll 1989). Another report 

claimed that downtown trees have an average lifespan of 13 

years (Skiera and Moll 1992). Nowak et al. (2004) estimated 

a 15-year average lifespan by using observed mortality rates 

for different tree size classes and land uses in Baltimore, MD, 

although the exact formula used to calculate lifespan was 

not specified. Demographers have different standard terms 

for lifespan that can be used in urban forestry: the mean life 

expectancy and population half-life.

With the constant mortality assumption (Type II), typical 

lifespan can be easily quantified. The mean life expectancy is 

the average age at death across the population. The mean life 

expectancy e0 from the time of planting, x = 0, is:

 e0 = –1/ln( pannual )

 (eqn. 11, after Seber 1982: eqn. 1.3)

As a clarification, the notation ex (with the subscript) is life 

expectancy from age x, whereas e (without a subscript) is a 

constant approximately equal to 2.718 and is the base for the 

natural logarithm. We use ex following conventional notation 

in demography (Carey 1993, Seber 1982).

The population half-life t0.5 , or the time at which half the 

planting cohort has died (i.e., survivorship is 50 percent), is:

 t0.5 = ln(0.5)/ln( pannual )

 (eqn. 12, after Sheil et al. 1995: eqn. 10)

For street trees, a meta-analysis (Roman and Scatena 2011) 

estimated annual survival rates and lifespan metrics (Table 

4). Survivorship data from 11 previous studies were pooled in 

a linear regression analysis, with the assumption of constant 

mortality, to estimate annual survival. Mean life expectancy 

was estimated at 19–28 years, and population half-life 13–20 

years. The 7- or 13-year average lifespans of street trees 

suggested by Moll (1989) and Skiera and Moll (1992) are 

therefore not supported by the available field data. A similar 

approach—pooling survivorship data from cohorts in different 

years—was also applied to street trees in Philadelphia, PA 

(Roman and Scatena 2011) (Table 4), and this technique can 

be used to estimate tree lifespan metrics for other planting 

programs.

However, mortality may not be constant over time, which 

complicates the calculation of mean life expectancy. Urban 

trees are said to have an establishment period, the first 

several years after planting when trees are more vulnerable 

to mortality (Miller and Miller 1991, Richards 1979). When 

mortality is not constant, mean life expectancy can still be 

determined, but the cohort life table must be completed to 

the oldest age classes. To determine life expectancy, several 

additional columns are added to the cohort life table: Lx, Tx, ex

(Table 2). For an individual that has reached age x, the average 

age of death is the current age plus the expectation of death 

for that age class, x + ex . For example, actuaries calculate life 

Table 4.—Estimated annual street tree survival rates, mean life expectancy, and population half-life. Adapted from Roman and Scatena (2011). Ranges in 

values are due to differences in estimation with and without weighting by sample size. Constant mortality was assumed. The terms annual mortality rate 

(with constant mortality assumption), mean life expectancy, and population half-life are defined in the text (eqns. 10, 11, 12). Note that 0.035 is equivalent 

to 3.5 percent.

Source

Annual mortality rate, 

qannual (pannual)

Mean life 

expectancy, e0

(years)

Population half-life, 

t0.5 (years)

Meta-analysis of 11 previous studies, survivorship data from 1–66 years 

after planting in different cities

0.035–0.051

(0.949–0.965)

19–28 13–20

Philadelphia, PA, field survey, survivorship 2–10 years after planting 0.034–0.045

(0.955–0.966)

22–29 15–20
11

expectancy for people of various ages and characteristics 

to determine life insurance premiums. Classic examples of 

calculating ex are given in Carey (1993) and Seber (1982), 

which focused on animal populations. The expectation of 

life when x = 0 is considered the life expectancy at birth (or 

in the case of urban trees, time of planting), similar to the 

mean life expectancy defined earlier by using the constant 

mortality assumption (eqn. 11). Mean life expectancy at birth 

can be thought of as the average age of death. Calculating e0 by 

using eqn. 9 (Table 2) when annual mortality is not constant 

requires having life table data for the cohort until the last 

individual has died.

Unfortunately for urban foresters and wildland forest 

ecologists, constructing complete cohort life tables for trees 

is generally not feasible. Trees are such long-lived organisms 

that following a cohort until the last possible year of life is 

beyond a researcher’s own lifespan. Forest ecologists typically 

use size classes, rather than chronological age, to build life 

tables and mortality curves. For urban trees, however, agebased life tables and survivorship curves are still relevant. 

Built into the mortality assumptions of many urban forestry 

ecosystem services projections (Table 1) are estimates of 

annual mortality rates for planting cohorts. As an example, 

we used the assumed low- and high-mortality scenarios in 

the Million Trees initiative for Los Angeles, CA (McPherson 

et al. 2008) to construct age-based life tables (Table 5) and 

survivorship curves (Fig. 2). The environmental benefits 

for the Los Angeles example were projected for 35 years 

after planting. Most tree losses were assumed to occur in 

the first 5 years after planting (McPherson et al. 2008). The 

High-mortality scenario Low-mortality scenario

Age, x

Survivorship to age 

x, lx

Annual survival 

rate, px

Annual mortality 

rate, qx

Survivorship to age 

x, lx

Annual survival 

rate, px

Annual mortality 

rate, qx

0 1.000 0.950 0.050 1.00 0.990 0.010

1 0.950 0.950 0.050 0.990 0.990 0.010

2 0.903 0.950 0.050 0.980 0.990 0.010

3 0.857 0.950 0.050 0.970 0.990 0.010

4 0.815 0.950 0.050 0.961 0.990 0.010

5 0.774 0.980 0.020 0.951 0.995 0.005

Table 5.—Life table example from a population projection. Age-based life table for annual mortality rate assumptions used in cost-benefit analysis for the 

Million Trees LA program in Los Angeles, CA. Adapted from McPherson et al. (2008). The terms survivorship, annual survival rate, and annual mortality rate 

are defined in Table 2 (eqns. 2, 4, 5). For years 5 and beyond, annual mortality remains constant at either 2 percent (high-mortality scenario) or 0.5 percent 

(low-mortality scenario). These assumptions are compared in the text to empirical observations for young tree mortality in Los Angeles (McPherson 2014).

Figure 2.—Assumed survivorship curves used in ecosystem services 

projections for the Million Trees LA program in Los Angeles, CA, with (A) 

and without (B) natural log (ln) transformation. Adapted from McPherson et 

al. (2008). See Table 5 for annual survival rates.

0 20 40 60 80 100 120 140

100

 

20

40

60

80

Time Since Planting (yrs)

Survivorship (percent)

low mortality

high mortality

half-life

0 20 40 60 80 100 120 140

5

 

1

2

3

4

Time Since Planting (yrs)

ln (Survivorship (percent)) A

B In (Survivorship (percent)) Survivorship (percent)

Time Since Planting (yrs)

Time Since Planting (yrs)
12

low-mortality scenario was projected to yield $1.95 billion 

in benefits, whereas the high-mortality scenario would 

reduce benefits by 32 percent, to $1.33 billion (McPherson 

et al. 2008). These mortality assumptions were checked by 

monitoring trees planted through the Los Angeles program; 

annual mortality rates during the establishment phase were 

4.4 percent for street trees, 3.1 percent for yard trees, and 4.6 

percent for park trees (McPherson 2014). These empirical 

mortality data, combined with growth observations, were 

used to revise simulations for ecosystem services (McPherson 

2014). The observed mortality during establishment is closer 

to the high-mortality scenario in the original projections 

(McPherson et al. 2008), although lower than mortality for 

Sacramento yard trees (Roman et al. 2014b).

Urban forest managers could plan ahead for replacement 

planting projects at the population half-life. Using the 

million tree campaigns as examples, we could ask: When 

will half the trees be dead? The population half-life for the 

Million Trees LA projected benefits (McPherson et al. 2008) 

can be calculated by using the assumed annual survival 

rates (Table 5). For example, in the high-mortality scenario, 

determine the half-life by solving for x :

 0.5=(0.95)5 (0.98)x-5

In this situation, we are calculating the time at which 

survivorship l

x equals 0.5 (or 50 percent) (eqn. 12). With the 

high-mortality scenario, half-life would be 27 years, based 

on 95 percent annual survival for the first 5 years followed 

by 98 percent survival thereafter. With the low-mortality 

scenario, half-life would be 133 years (using 0.99 and 0.995 

instead of 0.95 and 0.98, respectively). 

These half-life values are illustrated more intuitively in 

Figure 2. Both of these half-life estimates for Los Angeles 

are considerably higher than the half-life estimated in the 

street tree meta-analysis (Roman and Scatena 2011) (Table 

4). A half-life of 133 years seems unrealistic, and indeed, as 

previously mentioned, the mortality rates observed during 

establishment in Los Angeles are closer to the high-mortality 

scenario (McPherson et al. 2008). For comparison, for 

another large-scale planting initiative in New York City, 

73.8 percent of street trees remained alive 8 to 9 years 

after planting (Lu et al. 2010). Determining whether the 

population half-life for large-scale planting programs is 

10, 20, or 100 years has significant implications for urban 

forest management. For managers to anticipate the planting 

levels required for their canopy cover goals, it is essential 

to have accurate mortality rates (Roman 2014), as well as 

growth rates and allometric equations (McHale et al. 2009, 

McPherson and Peper 2012). The 7-year average lifespan 

figure appears overly pessimistic, and the low-mortality 

scenario in the Los Angeles population projections appears 

overly optimistic. For reasonable forecasts of planting 

program performance, we need realistic projections based 

on field observations, rather than overly optimistic or 

pessimistic speculations.

Note that the lifespan metrics described in this section are 

relevant only to age-based mortality data, not the size-based 

mortality data discussed in the next section.

Size-based Mortality Curves

In contrast to age-based mortality curves, an alternative is to 

display mortality curves by diameter at breast height (d.b.h.) 

size or size classes (Harcombe 1987). Forest ecologists have 

observed Type III or U-shaped size-based tree mortality rate 

curves (Box 1), with different mortality curve shapes from 

various forest systems and species (e.g., Coomes and Allen 

2007, Lorimer et al. 2001, Metcalf et al. 2009). In a recent 

large study of forests across the eastern United States with 

records of more than 430,000 stems (Lines et al. 2010), all 

21 species examined were found to have U-shaped mortality 

curves. Regardless of mortality curve shape, forest ecologists 

have generally reported very low rates of annual mortality 

for overstory or canopy trees, typically 1 to 3 percent or even 

less (e.g., Condit et al. 1995, Harcombe and Marks 1983, 

Lorimer et al. 2001), absent catastrophic disturbances (Lugo 

and Scatena 1996).

Urban tree mortality distributions using size classes can be 

created for repeated inventories, such as a repeated census 

of street trees in a particular neighborhood, or repeated 

monitoring of plots. We used the annual mortality rates 

reported for randomly located plots in Baltimore by Nowak 

et al. (2004) to construct a mortality curve (Fig. 3). Annual 

mortality was highest for small trees 0–7.6 cm (0–3 in) 

d.b.h. (9.0 percent) and lowest for midsized trees 30.6–45.7 

cm (12.1–18 in) d.b.h. (0.5 percent), then rose again for 

larger trees (>45.7 cm or 18 in), with some fluctuations 
13

(1.8–3.3 percent). This pattern corresponds to a U-shaped 

curve. Street trees in Oakland, CA, had a Type III mortality 

distribution (Roman et al. 2014b) (Fig. 4), in which 

mortality was again higher in the smallest size class (5.6 

percent) than in other size classes (0.0–1.6 percent). 

Even though the general mortality curve shapes are similar 

to trees in wildland environments, with both having 

about 1 percent mortality for midsized trees, there are 

essential differences in the mortality process. As previously 

mentioned, large urban trees are sometimes cut down 

and removed before they fully succumb to pathogens, 

injuries, and stresses. These hazard removals may increase 

mortality rates for urban trees with large d.b.h., and cause 

a more distinct upswing at the tail of the U-shaped curve, 

in comparison to wildland trees. On the other end of 

the mortality curve, very small trees in urban street and 

lawn settings are generally newly planted, with fairly high 

mortality rates during the establishment phase (Miller and 

Miller 1991, Richards 1979). In contrast, some urban trees 

at risk for death recover from damage and disease through 

human intervention, which may lead to lower mortality rates 

compared to wildland trees. However, given the scarcity of 

data on urban tree mortality rates categorized by size class, 

these comments on the shape of the urban tree mortality 

curve remain speculative. 

When comparing the mortality rate curves of urban and 

wildland forests, we must also bear in mind that studies 

vary in their delineation of size classes. Some wildland 

tree demography studies have a minimum size that would 

exclude newly planted or small-stature urban trees (e.g., 

limiting forest inventories to trees ≥12.7 cm or 5 in). Other 

studies include young seedlings (e.g., 3-year-old seedlings in 

Cleavitt et al. 2011) that would commonly be in the nursery 

production stage for urban forests. Classes of d.b.h. in 

wildland tree demography are often set to represent canopy 

position, but these positions (e.g., sapling, understory, codominant, dominant) do not carry the same meaning in 

urban street and lawn environments. For some plot-based 

urban tree inventories (e.g., i-Tree Eco methods; U.S. Forest 

Service 2015b), woody stems are included if their d.b.h. is 

at least 2.54 cm (1 in). Therefore some plants considered 

shrubs or saplings in classic forest ecology studies are 

included as trees in urban forest research. Indeed, even the 

2.54 cm (1 in) threshold excludes some small newly planted 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

<7.6 7.7-15.2 15.3-30.5 30.6-45.7 45.8-61.0 61.1-76.2 >76.2 

Annual Mortality (percent) 

d.b.h. Size Class (cm) 

Figure 3.—Urban tree mortality rates for Baltimore, MD, based on size 

class. Trees (n=1,396) were observed over a 2-year study period in plots 

located randomly throughout Baltimore, and included many species, land 

uses, and site types. Adapted from Nowak et al. (2004).

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

<7.6 7.7-15.2 15.3-30.5 30.6-45.7 45.8-61.0 >61.1 

Annual Mortality (percent) 

d.b.h. Size Class (cm) 

Figure 4.—Street tree mortality rates for Oakland, CA. Trees (n=940) were 

observed over a 5-year study period, and included many species and 

land uses. Planting site types were sidewalk cut-outs, planting strips, and 

medians. From Roman et al. (2014a).

Dead street tree in the West Oakland neighborhood of Oakland, CA. Photo 

by Lara A. Roman, U.S. Forest Service.
14

trees, such as those included in the Sacramento (Roman 

et al. 2014b) and Oakland (Roman et al. 2014a) studies. 

Thus these saplings are particularly important to understand 

population dynamics in the urban setting. Size-based 

mortality curves and life tables will aid our understanding 

of urban tree mortality trends, but as with other aspects 

of wildland forest demography, we must adapt these tools 

to urban systems, including explicitly defining “tree” for 

monitoring purposes. 

Tracking Population Dynamics

Urban forests change over time through inputs to and 

outputs from the system. In human and animal populations, 

those fluxes are birth, death, immigration, and emigration. 

In the urban forest, we have losses from mortality and 

removal, and inputs from planting and natural regeneration 

of seedlings. Across all site types in the urban forest, Nowak 

(2012) concluded that only one out of three trees in cities is 

planted. Regeneration is thus critical to maintaining canopy 

in remnant forest patches on public and private property, as 

well as afforested vacant lots (Zipperer et al. 1997). In the 

heavily managed street tree environment, however, natural 

regeneration is negligible, so the main source of new trees is 

planting.

Tracking the inputs (from planting) and the losses (from death 

and removal) in street tree populations aids our understanding 

of the impact of planting initiatives. An example of such 

fluxes comes from 5 years of annual monitoring in Oakland 

(Roman et al. 2014a). This study assessed net changes in street 

tree population counts, in relation to annual planting and 

mortality. The classic demographic balancing equation, which 

quantifies inputs and losses of individuals from a population, 

was adapted to the street tree context (Roman et al. 2014a) 

(Fig. 5). The West Oakland neighborhood has been the focus 

of recent planting efforts by both the City of Oakland and a 

local nonprofit organization, Urban Releaf. These planting 

programs seek to provide socioeconomic benefits and address 

environmental injustices in an underserved community. 

After an initial neighborhood street tree inventory in 

2006, an annual census was conducted to observe tree 

mortality, removals, and new plantings. There was an overall 

population increase during the 5-year study period: 995 live 

street trees in 2006, and 1,166 in 2011, for an increase of 

17 percent. The annual mortality rate across all size classes 

was 3.7 percent, which is within the range of typical street 

tree mortality rates from the literature review discussed 

earlier (Roman and Scatena 2011). Thus the mortality rates 

are within the “normal” range and the population is on the 

rise. However, mortality of small, young trees suppressed 

population growth. Roughly half of the 2006 trees were 

small, with trunks 7.6 cm (3 in) in diameter or less (Roman 

et al. 2014b). As previously mentioned, annual mortality 

in that smallest size class was 5.6 percent, about four times 

the rate for all the other size classes (Fig. 5). Additionally, 

in a complementary analysis of planting cohorts, survival 

of new young trees added to the system was fairly low, with 

only 83 percent of new trees surviving for 2 years. Although 

the age-based and size-based mortality rates organize the 

data differently, they both lead to the same conclusion: most 

of the tree losses came from recently planted, small trees. 

The planting campaigns in this neighborhood were barely 

outpacing young tree deaths, and could have had a larger 

impact if young tree survival had been enhanced. These 

Red maple (Acer rubrum) yard tree from the Sacramento Shade program in 

Sacramento County, CA. Photo by Lara A. Roman, U.S. Forest Service.
15

findings support the assertions in Richards (1979) that the 

death of young street trees drives population cycles. 

Monitoring studies to track fluxes in urban tree populations, 

such as the Oakland example, can provide critically needed 

empirical evidence for models and managers. Miller and 

Marano (1984) and Bartch et al. (1985) presented street tree 

simulations, using tree inventory data combined with userdefined planting, growth, mortality, and removal rates. These 

models were designed to help meet management objectives 

related to costs and desired benefits, enabling urban forest 

managers to project the impacts of various planting and 

removal actions. Local managers continue to conduct 

monitoring to assess population dynamics. In a survey about 

practitioner-driven monitoring (Roman et al. 2013), one 

respondent summarized the motivation for data collection 

as follows: “The sense that we were losing trees as fast as they 

were being planted made [us] want to see whether that was 

true, so getting some data together was essential to know 

if we were in fact gaining or losing ground.” This statement 

essentially calls for analyzing demographic change in the 

urban tree population. The adapted balancing equation 

(Roman et al. 2014b) (Fig. 5) provides a conceptual and 

computational approach for applying demographic methods 

to street tree population simulations.

The Need for Urban Tree Monitoring 

and Longitudinal Data

The specific type of monitoring we discuss in this paper 

concerns longitudinal data: repeated observations on the 

same individual trees over time. Longitudinal urban tree 

studies can provide mortality and growth rates to build life 

tables, survivorship and mortality curves, and balancing 

equations, as well as more advanced analyses such as 

matrix models (Caswell 2001). Other types of long-term 

monitoring data are also useful to understand changes in the 

urban landscape over time, such as canopy cover, land use, 

institutional structures, and program operations. However, 

only data tracking the fate of individual trees are suitable for 

the analyses discussed here. 

Although urban forest inventory systems have been 

developed to provide managers with quantitative data on 

forest composition and structure (McPherson et al. 2005, 

Nowak et al. 2008), monitoring involves more than a onetime inventory (Baker 1993). When repeated observations 

are intended, researchers encounter issues that extend 

beyond the needs of a single inventory, such as reliably 

finding plots and individual trees during subsequent visits 

(Roman et al. 2013), and determining the appropriate 

Trees observed at time x

Trees observed at time x + 1

Removed

Newly planted Newly planted

Removed

Survived Died Still dead

# alive

# alive

# standing dead

# standing dead

Figure 5.—Diagram illustrating street tree balancing equations for live and standing dead street trees (after Roman et al. 2014a). Arrows indicate 

transitions between pools of live and standing dead trees from time x to time x+1. The bottom right arrow indicates newly planted trees that were 

observed dead during the summer field work (but were presumably alive when planted).
16

observation intervals. As previously mentioned, some 

local urban forestry organizations in the United States 

already gather mortality data (Roman et al. 2013). These 

practitioner-driven studies rarely result in peer-reviewed 

journal articles (although two notable exceptions are Boyce 

2010 and Lu et al. 2010), but sometimes lead to internal 

program reports. 

To promote data-sharing among professionals and 

researchers, and to advance monitoring efforts already 

underway, standardized protocols for urban tree monitoring 

have been developed (Urban Tree Growth and Longevity 

Working Group 2015). Standardization can enable 

comparisons across and within cities, and avoid duplicated 

efforts to develop monitoring methods. For example, a 

protocol for tracking recently planted street trees (Vogt 

and Fischer 2014) was recently applied across several 

United States cities, in collaboration with local nonprofit 

organizations. Such partnerships can provide urban forestry 

professionals with improved mortality information to 

evaluate the success of planting and management programs, 

while expanding the long-term datasets available to 

researchers. Participatory research approaches (McKinley 

et al. 2013, Minkler and Wallerstein 2008) will be critical 

to these research-practice partnerships for urban forests 

(Campbell et al. 2014). 

Lessons from Ecological 

Monitoring in Other Systems

Ecologists have developed strategies and tools for effective 

monitoring, and the lessons learned from these projects 

provide guidance for monitoring efforts in urban forestry. 

Lindenmayer and Likens (2010) argued that monitoring 

programs should be driven by conceptual models of the 

study system with clear research questions and rigorous 

study design. Other attributes of effective monitoring are 

dedicated leadership; strong partnerships among scientists, 

resource managers, and policy-makers; frequent use of 

the collected data; and an adaptive monitoring framework 

that responds to new technologies and research questions 

(Lindenmayer and Likens 2009, 2010). Urban forest 

practitioners who collect monitoring data also stressed the 

importance of clear objectives and uses of the data (Roman 

et al. 2013).

There have been several long-term monitoring programs 

in forest ecosystems in the United States, including the 

Forest Inventory and Analysis (FIA) program of the U.S. 

Forest Service and Long-Term Ecological Research (LTER) 

sites sponsored by the National Science Foundation. The 

FIA program serves as a census for forest ecosystems in the 

United States (Smith 2002, U.S. Forest Service 2015a), with 

recent integration of the Forest Health Monitoring program 

(U.S. Forest Service, Forest Health Monitoring 2015) and 

annual field measurements (McRoberts et al. 2005) to 

generate longitudinal data. Many studies of tree mortality 

have used FIA data (e.g., Lines et al. 2010, Woodall et al. 

2005). Globally, the Center for Tropical Forest Science 

is a network of dozens of tropical and temperate plots, 

all following the same methods to re-census trees every 

5 years (Condit 1995, Smithsonian Tropical Research 

Institute 2015). Although these programs focus primarily 

on nonurban forests, the methods and analytical tools have 

been adapted to urban systems, such as the emerging Urban 

FIA program (Cumming et al. 2007). 

The LTER sites (which are not exclusive to forest systems) 

were developed with a recognition that many ecological 

phenomena operate over decades and longer, requiring 

long-term investment in data collection (LTER Network 

2011). There are two LTER sites in urban environments: 

Baltimore (Cary Institute of Ecosystem Studies 2014) and 

London planetree (Platanus × acerifolia) trees at the Rodin Museum in 

Philadelphia, PA. Photo by Lara A. Roman, U.S. Forest Service.
17

Phoenix, AZ (Arizona State University 2015). In Baltimore, 

repeated i-Tree plot data have been collected (Nowak et al. 

2004), and in Phoenix, annual tree surveys were conducted 

across an urban to rural gradient (Martin and Stutz 2013). 

To gather comprehensive longitudinal data on urban trees, 

it is essential that urban foresters and urban ecologists 

coordinate efforts, with clear research questions and strong 

partnerships, learning from the experiences of forest 

ecologists working in long-term monitoring programs. 

The practitioner-driven monitoring initiatives discussed 

earlier can complement these national programs for plotbased monitoring. Long-term data collected by practitioners 

have the potential to produce higher volumes of 

information, but because local organizations sometimes rely 

on volunteers and citizen scientists, there are concerns about 

data quality (Roman et al. 2013). Although ecological data 

collected by volunteers have the potential for errors, those 

errors can be minimized with effective training and data 

validation procedures (Bonter and Cooper 2012, Gardiner 

et al. 2012). Indeed, ecological monitoring programs with 

citizen science have become increasingly popular (Dickinson 

et al. 2012, Silvertown 2009). Monitoring programs 

incorporating local practitioners and volunteers can provide 

higher volumes of data across broad geographic regions, 

while expanding opportunities for public engagement in 

research and fostering environmental stewardship (Silva and 

Krasny 2014).

Looking Ahead: Opportunities for 

Future Research

To promote research-practice dialogue and data sharing 

regarding urban tree mortality, researchers are collaborating 

with municipal foresters and nonprofit organizations through 

the Urban Tree Growth and Longevity Working Group 

(Leibowitz 2012, Scharenbroch et al. 2014). Many municipal 

foresters, urban greening nonprofit organizations, and states 

are interested in collecting long-term monitoring data. 

Additionally, research articles on urban tree mortality have 

become more frequent in the past few years. This confluence 

of interests from researchers and professionals can generate 

the observational data called for in earlier population 

projections (McPherson et al. 1999, Morani et al. 2011). 

As researchers and communities gather more long-term 

urban tree monitoring data, we will be better equipped to 

understand the patterns and processes of urban tree death.

However, there are challenges to long-term urban tree 

monitoring and demographic approaches. Gathering 

longitudinal data over many years requires adequate 

funding, continuity in leadership, and robust study design 

for statistical analysis (Lindenmayer and Likens 2010). 

To facilitate permanent plots, the initial inventory or 

tree planting information should include detailed site 

maps, geospatial coordinates, site photos, or tagged tree 

identification numbers. Such practical considerations are 

often overlooked with static snapshot urban tree inventories 

(Roman et al. 2013). Additionally, demographic analyses 

and mortality studies of wildland and plantation forests 

are traditionally applied to a single species, in systems 

with natural reproduction. Our examples of urban street 

and lawn trees lump many species together, and are open 

systems with human-driven planting and removal. Although 

we can adapt demographic tools, we must be aware of the 

different assumptions and interpretations for urban trees in 

the cultivated urban landscape. Nevertheless, by borrowing 

concepts from other disciplines, urban forestry gains clearly 

defined terms and well-established methods for quantifying 

mortality. 

As we gather more long-term urban tree monitoring data, 

we will be better equipped to understand urban forest 

population dynamics through the lens of empirical evidence. 

Tree monitoring and mortality have long been recognized 

as important components of sustainable urban forest 

management (Baker 1993, Clark et al. 1997). Urban tree 

demography is essential to understanding temporal changes 

in urban forest systems, just as tree demography is used to 

analyze change in natural forest systems (e.g., van Doorn 

et al. 2011). This primer lays the foundation for future 

studies that will use demographic approaches in urban 

forestry for basic and applied research.

In this primer, we only scratched the surface of population 

biology methods. For further reading, we recommend the 

following: Harcombe (1987) and Sheil et al. (1995) for classic 

overview articles, and textbooks by Seber (1982), Carey 

(1993), Caswell (2001), and Morris and Doak (2002). 
18

Acknowledgments

We thank the staff of many nonprofit organizations whose 

dedication to urban forestry and desire to understand 

tree mortality have motivated this research—University 

City Green and the Pennsylvania Horticultural Society 

(Philadelphia, PA), the Sacramento Tree Foundation 

(Sacramento, CA), Friends of the Urban Forest (San 

Francisco, CA), Urban Releaf (Oakland, CA), and Canopy 

(Palo Alto, CA)—and many other practitioners who shared 

their perspectives in Roman et al. (2013). We are grateful 

to M. Sarkovich (SMUD) and R. Tretheway, C. Blain, L. 

Leineke, C. Cadwallader, and J. Caditz (Sacramento Tree 

Foundation) for logistical and financial support of the 

Sacramento shade tree study, and to E.G. McPherson and Q. 

Xiao (U.S. Forest Service) and K. Shakur and G.W.T. Tarver, 

Jr. (Urban Releaf) for collaboration on the Oakland street 

tree study. Numerous University of California, Berkeley 

student interns and volunteers assisted in data collection for 

those projects, making the demographic analyses described 

here possible. We also thank I. Laçan, J. Grabosky, J. 

Fristensky, J. Henning, M. Mitchell, D. Nowak, J. Stanovick, 

and two anonymous reviewers for helpful comments on 

earlier versions of this manuscript. This report is dedicated 

to the memory of F.N. Scatena.
19

Literature Cited

Arizona State University. 2015. Central Arizona–Phoenix 

Long-Term Ecological Research. Tempe, AZ. Available at 

https://caplter.asu.edu. (Accessed October 22, 2015).

Baker, F.A. 1993. Monitoring the urban forest: case 

studies and evaluations. Environmental Monitoring and 

Assessment. 26: 153-163. 

Bartsch, F.A.; Hook, J.; Prince, E.; Schrom, D. 1985. Using 

computer simulation to plan a sustained-yield urban 

forest. Journal of Forestry. 83: 372-375.

Bonter, D.N.; Cooper, C.B. 2012. Data validation in citizen 

science: a case study from Project FeederWatch. Frontiers 

in Ecology and the Environment. 10: 305-307.

Boyce, S. 2010. It takes a stewardship village: effect of 

volunteer tree stewardship on urban street tree mortality 

rates. Cities and the Environment. 3: Article 3.

Campbell, L.K.; Monaco, M.; Falxa-Raymond, N.; 

Lu, J.; Newman, A.; Rae, R.A.; Svendsen, E.S. 2014. 

MillionTreesNYC: the integration of research and 

practice. New York, NY: New York City Parks & 

Recreation. 43 p.

Carey, J.R. 1993. Applied demography for biologists: with 

special emphasis on insects. New York, NY: Oxford 

University Press. 224 p.

Cary Institute of Ecosystem Studies. 2014. Baltimore 

Ecosystem Study. Millbrook, NY. Available at 

www.beslter.org. (Accessed October 22, 2015).

Caswell, H. 2001. Matrix population models: construction, 

analysis, and interpretation. Sunderland, MA: Sinauer 

Associates, Inc. 722 p.

Clark, J.R.; Matheny, N.P.; Cross, G.; Wake, V. 1997. A model 

of urban forest sustainability. Journal of Arboriculture. 

23: 17-30.

Cleavitt, N.L.; Fahey, T.J.; Battles, J.J. 2011. Regeneration 

ecology of sugar maple (Acer saccharum): seedling 

survival in relation to nutrition, site factors, and damage 

by insects and pathogens. Canadian Journal of Forest 

Research. 41: 235-244.

Condit, R. 1995. Research in large, long-term tropical forest 

plots. Trends in Ecology & Evolution. 10: 18-22.

Condit, R.; Hubbell, S.P.; Foster, R.B. 1995. Mortality rates 

of 205 neotropical tree and shrub species and the impact 

of severe drought. Ecological Monographs. 65: 419-439.

Coomes, D.A.; Allen, R.B. 2007. Mortality and tree-size 

distributions in natural mixed-age forests. Journal of 

Ecology. 95: 27-40.

Craul, P.J. 1999. Urban soils: applications and practices. 

New York, NY: John Wiley & Sons. 366 p.

Cumming, A.B.; Nowak, D.J.; Twardus, D.B.; Hoehn, R.; 

Mielke, M.; Rideout, R. 2007. Urban forests of Wisconsin: 

pilot monitoring project 2002. NA-FR-05-07. Newtown 

Square, PA: U.S. Department of Agriculture, Forest 

Service, Northeastern Area, National Forest Health 

Monitoring Program. 33 p.

Das, A.J.; Battles, J.J.; van Mantgem, P.J.; Stephenson, N.L. 

2008. Spatial elements of mortality risk in old-growth 

forests. Ecology. 89: 1744-1756.

Das, A.J.; Battles, J.J.; Stephenson, N.L.; van Mantgem, P.J. 

2007. The relationship between tree growth patterns and 

likelihood of mortality: a study of two tree species in the 

Sierra Nevada. Canadian Journal of Forest Research. 37: 

580-597.

Dickinson, J.L.; Shirk, J.; Bonter, D.; Bonney, R.; Crain, 

R.L.; Martin, J.; Phillips, T.; Purcell, K. 2012. The current 

state of citizen science as a tool for ecological research 

and public engagement. Frontiers in Ecology and the 

Environment. 10: 291-297.

Dwyer, J.F.; McPherson, E.G.; Schroeder, H.W.; Rowntree, 

R.A. 1992. Assessing the benefits and costs of the urban 

forest. Journal of Arboriculture. 18: 227-234.

Fay, M.P.; Shaw, P.A. 2010. Exact and asymptotic weighted 

logrank tests for interval censored data: the interval R 

package. Journal of Statistical Software. 36: 1-34.

Franklin, J.F.; Shugart, H.H.; Harmon, M.E. 1987. Tree death 

as an ecological process. BioScience. 37: 550-556.
20

Gardiner, M.M.; Allee, L.L.; Brown, P.M.J.; Losey, J.E.; 

Roy, H.E.; Smyth, R.R. 2012. Lessons from lady 

beetles: accuracy of monitoring data from US and UK 

citizen-science programs. Frontiers in Ecology and the 

Environment. 10: 471-476.

Giolo, S.R.; Colosimo, E.A.; Demétrio, C.G.B. 2009. 

Different approaches for modeling grouped survival 

data: a mango tree study. Journal of Agricultural, 

Biological, and Environmental Statistics. 14: 154-169.

Harcombe, P.A. 1987. Tree life tables. BioScience. 37: 550-

597.

Harcombe, P.A.; Marks, P.L. 1983. Five years of tree death 

in a Fagus-Magnolia forest, southeast Texas (USA). 

Oecologia. 57: 49-54.

Harris, R.W.; Clark, J.R.; Matheny, N.P. 2004. Arboriculture: 

integrated management of landscape trees, shrubs, and 

vines. 4th ed. Upper Saddle River, NJ: Prentice Hall. 592 p.

Hauer, R.J.; Miller, R.W.; Ouimet, D.M. 1994. Street 

tree decline and construction damage. Journal of 

Arboriculture. 20: 94-97.

Hildebrandt, E.W.; Sarkovich, M. 1998. Assessing the 

cost-effectiveness of SMUD’s shade tree program. 

Atmospheric Environment. 32: 85-94.

Klein, J.P.; Moeschberger, M.L. 1997. Survival analysis: 

techniques for censored and truncated data. New York, 

NY: Springer-Verlag. 516 p.

Ko, Y.; Lee, J.; McPherson, E.G.; Roman, L.A. 2015. Factors 

affecting long-term mortality of residential shade trees: 

evidence from Sacramento, California. Urban Forestry & 

Urban Greening. 14: 500-507.

Koeser, A.K; Gilman, E.F.; Paz, M.; Harchick, C. 2014. 

Factors influencing urban tree planting programs growth 

and survival in Florida, United States. Urban Forestry & 

Urban Greening. 13: 655-661.

Konijnendijk, C.C.; Ricard, R.M.; Kenney, A.; Randrup, 

T.B. 2006. Defining urban forestry—a comparative 

perspective of North America and Europe. Urban 

Forestry & Urban Greening. 4: 93-103.

Lawrence, A.B.; Escobedo, F.J.; Staudhammer, C.L.; Zipperer, 

W. 2012. Analyzing growth and mortality in a subtropical 

urban forest ecosystem. Landscape and Urban Planning. 

104: 85-94.

Leibowitz, R. 2012. Urban tree growth and longevity: an 

international meeting and research symposium white 

paper. Arboriculture & Urban Forestry. 38: 237-241.

Lindenmayer, D.B.; Likens, G.E. 2009. Adaptive monitoring: 

a new paradigm for long-term research and monitoring. 

Trends in Ecology & Evolution. 24: 482-486.

Lindenmayer, D.B.; Likens, G.E. 2010. The science and 

application of ecological monitoring. Biological 

Conservation. 143: 1317-1328.

Lines, E.R.; Coomes, D.A.; Purves, D.W. 2010. Influences of 

forest structure, climate and species composition on tree 

mortality across the eastern US. PLOS ONE. 5:e13212.

Long-Term Ecological Research [LTER] Network. 2011. 

Long-Term Ecological Research Network Strategic and 

Implementation Plan 2011. Available at http://www.

lternet.edu. (Accessed October 1, 2011). 

Lorimer, C.G.; Dahir, S.E.; Nordheim, E.V. 2001. Tree 

mortality rates and longevity in mature and old-growth 

hemlock-hardwood forests. Journal of Ecology. 89: 960-

971.

Lu, J.W.T.; Svendsen, E.S.; Campbell, L.K.; Greenfeld, 

J.; Branden, J.; King, K.L.; Falxa-Raymond, N. 2010. 

Biological, social, and urban design factors affecting 

young street tree mortality in New York City. Cities and 

the Environment. 3: Article 5. 

Lugo, A.E.; Scatena, F.N. 1996. Background and 

catastrophic tree mortality in tropical moist, wet, and 

rain forests. Biotropica. 28: 585-599.

Manion, P.D. 1981. Tree disease concepts. Englewood Cliffs, 

NJ: Prentice-Hall. 399 p.

Martin, C.A.; Stutz, J. 2013. Tree health in Phoenix, 

Arizona, U.S. Arboriculture & Urban Forestry. 39: 286-

291.
21

McHale, M.R.; Burke, I.C.; Lefsky, M.A.; Peper, P.J.; 

McPherson, E.G. 2009. Urban forest biomass estimates: 

Is it important to use allometric relationships developed 

specifically for urban trees? Urban Ecosystems. 12: 95-113.

McKinley, D.C.; Briggs, R.D.; Bartuska, A.M. 2013. When 

peer-reviewed publications are not enough! Delivering 

science for natural resource management. Forest Policy 

and Economics. 37: 9-19.

McPherson, E.G. 1994. Benefits and costs of tree planting 

and care in Chicago. In: McPherson, E.G.; Nowak, D.J.; 

Rowntree, R.A., eds. Chicago’s urban forest ecosystem: 

results of the Chicago Urban Forest Climate Project. 

Gen. Tech. Rep. NE-186. Radnor, PA: U.S. Department 

of Agriculture, Forest Service, Northeastern Research 

Station: 115-133.

McPherson, E.G. 2014. Monitoring Million Trees LA: tree 

performance during the early years and future benefits. 

Arboriculture & Urban Forestry. 40: 285-300.

McPherson, E.G.; Peper, P.J. 2012. Urban tree growth 

modeling. Arboriculture & Urban Forestry. 38: 172-180.

McPherson, E.G.; Scott, K.I.; Simpson, J.R. 1998. Estimating 

cost effectiveness of residential yard trees for improving 

air quality in Sacramento, California using existing 

models. Atmospheric Chemistry. 32: 75-84.

McPherson, E.G.; Simpson, J.R. 2001. Effects of California’s 

urban forests on energy use and potential savings from 

large-scale tree planting. Davis, CA: U.S. Department 

of Agriculture, Forest Service, Center for Urban Forest 

Research. 34 p.

McPherson, G.; Simpson, J.R.; Peper, P.J.; Maco, S.E.; Xiao, 

Q. 2005. Municipal forest benefits and costs in five US 

cities. Journal of Forestry. Dec.: 411-416.

McPherson, E.G.; Simpson, J.R.; Peper, P.J.; Xiao, Q. 1999. 

Benefit-cost analysis of Modesto’s municipal urban 

forest. Journal of Arboriculture. 25: 235-248.

McPherson, E.G.; Simpson, J.R.; Xiao, Q.; Wu, C. 2008. Los 

Angeles 1-million tree canopy cover assessment. Gen. 

Tech. Rep: PSW-GTR-207. Albany, CA: U.S. Department 

of Agriculture, Forest Service, Pacific Southwest Research 

Station. 52 p.

McRoberts, R.E.; Bechtold, W.A.; Patterson, P.L.; Scott, 

C.T.; Reams, G.A. 2005. The enhanced Forest Inventory 

and Analysis Program of the USDA Forest Service: 

historical perspective and announcement of statistical 

documentation. Journal of Forestry. 103: 304-308.

Metcalf, C.J.E.; McMahon, S.M.; Clark, J.S. 2009. 

Overcoming data sparseness and parametric constraints 

in modeling of tree mortality: a new nonparametric 

Bayesian model. Canadian Journal of Forest Research. 39: 

1677-1687.

Miller, R.H.; Miller, R.W. 1991. Planting survival of selected 

street tree taxa. Journal of Arboriculture. 17: 185-191.

Miller, R.W.; Marano, M.S. 1984. URFOR/SIMULATION: 

an urban forest management computer simulation/game.

Journal of Arboriculture. 10: 55-63.

Minkler, M.; Wallerstein, N., eds. 2008. Community-based 

participatory research for health: from processes to 

outcomes. 2nd ed. San Francisco, CA: Jossey-Bass. 544 p.

Moll, C.W. 1989. The state of our urban forest. American 

Forests. 95: 61-64.

Morani, A.; Nowak, D.J.; Hirabayashi, S.; Calfapietra, C. 

2011. How to select the best tree planting locations to 

enhance air pollution removal in the MillionTreesNYC 

initiative. Environmental Pollution. 159: 1040-1047.

Morris, W.F.; Doak, D.F. 2002. Quantitative conservation 

biology: theory and practice of population viability 

analysis. Sunderland, MA: Sinauer Associates, Inc. 480 p.

Nowak, D.J. 1986. Silvics of an urban tree species: Norway 

maple (Acer platanoides L.). Syracuse, NY: State 

University of New York, College of Environmental Science 

and Forestry. 148 p. M.S. thesis.

Nowak, D.J. 2012. Contrasting natural regeneration and 

tree planting in fourteen North American cities. Urban 

Forestry & Urban Greening. 11: 374-382.

Nowak, D.J.; Bodine, A.R.; Hoehne, R.E.; Crane, D.E.; Ellis, 

A.; Endreny, T.A.; Yang, Y.; Jacobs, T.; Shelton, K. 2013. 

Assessing urban forest effects and values: the greater 

Kansas City region. Resour. Bull. NRS-75. Newtown 

Square, PA: U.S. Department of Agriculture, Forest 

Service, Northern Research Station. 72 p.
22

Nowak, D.J.; Crane, D.E.; Stevens, J.C.; Hoehn, R.E.; 

Walton, J.T.; Bond, J. 2008. A ground-based method of 

assessing urban forest structure and ecosystem services. 

Arboriculture & Urban Forestry. 34: 347-358.

Nowak, D.J.; Crane, D.E.; Stevens, J.C.; Ibarra, M. 2002. 

Brooklyn’s urban forest. Gen. Tech. Rep. NE-290. 

Newtown Square, PA: U.S. Department of Agriculture, 

Forest Service, Northeastern Research Station. 107 p.

Nowak, D.J.; Dwyer, J.F. 2007. Understanding the benefits 

and costs of urban forest ecosystems. In: Kuser, J.E., ed. 

Urban and community forestry in the Northeast. 2nd ed. 

New York, NY: Springer: 25-46. 

Nowak, D.J.; Kuroda, M.K.; Crane, D.E. 2004. Tree mortality 

rates and tree population projections in Baltimore, 

Maryland, USA. Urban Forestry & Urban Greening. 2: 

139-147.

Nowak, D.J.; McBride, J.R.; Beatty, R.A. 1990. Newly planted 

street tree growth and mortality. Journal of Arboriculture. 

16: 24-129.

Pataki, D.E.; Carreiro, M.M.; Cherrier, J.; Grulke, N.E.; 

Jennings, V.; Pincetl, S.; Pouyat, R.V.; Whitlow, T.H.; 

Zipperer, W.C. 2011. Coupling biogeochemical cycles 

in urban environments: ecosystem services, green 

solutions, and misconceptions. Frontiers in Ecology and 

the Environment. 9: 27-36.

Pedersen, B.S. 1998. The role of stress in the mortality of 

midwestern oaks as indicated by growth prior to death. 

Ecology. 79: 79-93.

Piana, M.; Troxel, B. 2014. Beyond planting: an urban 

forestry primer. Philadelphia, PA: Scenario Journal 4. 

http://scenariojournal.com/article/beyond-planting.

R Development Core Team. 2014. R: a language and 

environment for statistical computing. Vienna, Austria: 

R Foundation for Statistical Computing. Available at 

www.r-project.org. (Accessed November 15, 2015).

Richards, N.A. 1979. Modeling survival and consequent 

replacement needs of a street tree population. Journal of 

Arboriculture. 5: 251-255. 

Roman, L.A. 2014. How many trees are enough? Tree death 

and the urban canopy. Scenario Journal 4. Available at 

http://scenariojournal.com/article/how-many-trees-areenough.

Roman, L.A.; Battles, J.J.; McBride, J.R. 2014a. The balance 

of planting and mortality in a street tree population.

Urban Ecosystems. 17: 387-404.

Roman, L.A.; Battles, J.J.; McBride, J.R. 2014b. Determinants 

of establishment survival for residential trees in 

Sacramento County, CA. Landscape and Urban Planning. 

129: 22-31. 

Roman, L.A.; McPherson, E.G.; Scharenbroch, B.C.; Bartens, 

J. 2013. Identifying common practices and challenges for 

local urban tree monitoring programs across the United 

States. Arboriculture & Urban Forestry. 39: 292-299.

Roman, L.A.; Scatena, F.N. 2011. Street tree survival rates: 

meta-analysis of previous studies and application to a 

field survey in Philadelphia, PA, USA. Urban Forestry & 

Urban Greening. 10: 269-274.

Scharenbroch, B.C.; Roman, L.A.; McPherson, E.G.; 

Bartens, J.; Boyer, D. 2014. Taking the urban forest’s 

pulse: working group focused on urban tree growth and 

longevity. Arborist News. 23: 54-55.

Seber, G.A.F. 1982. The estimation of animal abundance 

and related parameters. 2nd ed. New York, NY: 

MacMillan. 672 p.

Sheil, D.F.; Burslem, R.P.; Alder, D. 1995. The interpretation 

and misinterpretation of mortality rate measures. 

Journal of Ecology. 83: 331-333.

Silva, P.; Krasny, M.E. 2014. Parsing participation: models 

of engagement for outcomes monitoring in urban 

stewardship. Local Environment: The International 

Journal of Justice and Sustainability. July. DOI: 

10.1080/13549839.2014.929094.

Silvera Seamans, G. 2013. Mainstreaming the 

environmental benefits of street trees. Urban Forestry & 

Urban Greening. 12: 2-11.

Silvertown, J. 2009. A new dawn for citizen science. Trends 

in Ecology & Evolution. 24: 467-471.
23

Skiera, B.; Moll, G. 1992. The sad state of city trees. 

American Forests. Mar./Apr.: 61-64.

Smith, W.B. 2002. Forest inventory and analysis: a national 

inventory and monitoring program. Environmental 

Pollution. 116: S233-S242.

Smithsonian Tropical Research Institute. 2015. CTFSForestGEO data management. Center for Tropical Forest 

Science. Available at www.stfs.si.edu. (Accessed October 

21, 2015).

Staudhammer, C.; Escobedo, F.; Lawrence, A.; Duryea, 

M.; Smith, P.; Merritt, M. 2011. Rapid assessment of 

change and hurricane impacts to Houston’s urban forest 

structure. Arboriculture & Urban Forestry. 37: 60-66.

Turnbull, B.W. 1976. The empirical distribution function 

with arbitrarily grouped, censored and truncated data. 

Journal of the Royal Statistical Society, Series B. 38: 290-

295.

Tzoulas, K.; Korpela, K.; Venn, S.; Yli-Pelkonen, V.; 

Kazmierszak, A.; Niemela, J.; James, P. 2007. Promoting 

ecosystem and human health in urban areas using green 

infrastructure: a literature review. Landscape and Urban 

Planning. 81: 167-178.

Urban Tree Growth and Longevity Working Group. 2015. 

Home page. Lisle, IL. Available at www.urbantreegrowth.

org. (Accessed October 29, 2015).

U.S. Forest Service. 2015a. Forest Inventory and Analysis 

national program home page. Washington, DC: U.S. 

Department of Agriculture, Forest Service. Available at 

www.fia.fs.fed.us. (Accessed October 15, 2015).

U.S. Forest Service. 2015b. i-Tree: tools for assessing and 

managing community forests. Home page. Kent, OH: U.S. 

Department of Agriculture, Forest Service. Available at 

www.itreetools.org. (Accessed October 22, 2015).

U.S. Forest Service, Forest Health Monitoring. 2015. USDA 

Forest Service National Forest Health Monitoring home 

page. Arlington, VA: U.S. Department of Agriculture, 

Forest Service. Available at www.fhm.fs.fed.us. (Accessed 

October 15, 2015).

van Doorn, N.S.; Battles, J.J.; Fahey, T.J.; Siccama, T.G.; 

Schwarz, P.A. 2011. Links between biomass and tree 

demography in a northern hardwood forest: a decade 

of stability and change in Hubbard Brook Valley, New 

Hampshire. Canadian Journal of Forest Research. 41: 

1369-1379.

Vogt, J.M.; Fischer, B.C. 2014. A protocol for citizen science 

monitoring of recently-planted urban trees. Cities and 

the Environment. 7: Article 4.

Vogt, J.M.; Watkins, S.L.; Mincey, S.K.; Patterson, M.S.; 

Fischer, B.C. 2015. Explaining planted-tree survival and 

growth in urban neighborhoods: a social-ecological 

approach to studying recently planted trees in 

Indianapolis. Landscape and Urban Planning. 136: 130-

143.

Waring, R.H. 1987. Characteristics of trees predisposed to 

die. BioScience. 37: 569-574.

Woodall, C.W.; Grambusch, P.L.; Thomas, W. 2005. Applying 

survival analysis to a large-scale forest inventory for 

assessment of tree mortality in Minnesota. Ecological 

Modelling. 189: 199-208.

Young, R.F. 2013. Mainstreaming urban ecosystem 

services: a national survey of municipal foresters. Urban 

Ecosystems. 16: 703-722.

Young, R.F.; McPherson, E.G. 2013. Governing 

metropolitan green infrastructure in the United States. 

Landscape and Urban Planning. 109: 67-75.

Zipperer, W.C.; Sissini, S.M.; Pouyat, R.V.; Foresman, T.W. 

1997. Urban tree cover: an ecological perspective. Urban 

Ecosystems. 1: 229-246.
24

Glossary

annual mortality rate: proportion of individuals dying over 

a year, from time x to x + 1 

annual survival rate: proportion of individuals surviving 

over a year, from time x to x + 1 

censored data: incomplete observations in longitudinal data

cohort: trees planted around the same time (for example, 

trees planted in the same year)

demography: the statistical study of populations and vital 

rates, such as birth and mortality, or in the case of urban 

trees, planting, death, and removal rates

life table: a table with survival and mortality information 

organized by age or size classes

longitudinal: involving repeated observations on the same 

individuals over time

mean life expectancy: the average age at death across the 

population

mortality curve: a graphic representation of mortality rate 

over time or across size classes

population half-life: the time at which half of a planting 

cohort has died

survivorship: proportion of a cohort surviving from 

planting to year x (in other words, cumulative survival)

survivorship curve: a graphic representation of survivorship 

over time, typically displaying natural logarithmtransformed data; survivorship curves are relevant to display 

survival for planting cohorts
In accordance with Federal civil rights law and U.S. Department of Agriculture (USDA) civil rights regulations and policies, the USDA, its Agencies, offices, and employees, and institutions 

participating in or administering USDA programs are prohibited from discriminating based on race, color, national origin, religion, sex, gender identity (including gender expression), sexual 

orientation, disability, age, marital status, family/parental status, income derived from a public assistance program, political beliefs, or reprisal or retaliation for prior civil rights activity, in any 

program or activity conducted or funded by USDA (not all bases apply to all programs). Remedies and complaint filing deadlines vary by program or incident.

Persons with disabilities who require alternative means of communication for program information (e.g., Braille, large print, audiotape, American Sign Language, etc.) should contact the 

responsible Agency or USDA’s TARGET Center at (202) 720-2600 (voice and TTY) or contact USDA through the Federal Relay Service at (800) 877-8339. Additionally, program information may 

be made available in languages other than English.

To file a program discrimination complaint, complete the USDA Program Discrimination Complaint Form, AD-3027, found online at http://www.ascr.usda.gov/complaint_filing_cust.html and at 

any USDA office or write a letter addressed to USDA and provide in the letter all of the information requested in the form. To request a copy of the complaint form, call (866) 632-9992. Submit 

your completed form or letter to USDA by: (1) mail: U.S. Department of Agriculture, Office of the Assistant Secretary for Civil Rights, 1400 Independence Avenue, SW, Washington, D.C. 20250-

9410; (2) fax: (202) 690-7442; or (3) email: program.intake@usda.gov.

Manuscript received for publication July 2015

Published by: For additional copies:

U.S. FOREST SERVICE U.S. Forest Service

11 CAMPUS BLVD SUITE 200 Publications Distribution

NEWTOWN SQUARE PA 19073-3294 359 Main Road

Delaware, OH 43015-8640

March 2016

Visit our homepage at: http://www.nrs.fs.fed.us

Roman, Lara A.; Battles, John J.; McBride, Joe R. 2016. Urban tree mortality: a primer on demographic approaches. Gen. Tech. 

Rep. NRS-158. Newtown Square, PA: U.S. Department of Agriculture, Forest Service, Northern Research Station. 24 p.

Realizing the benefits of tree planting programs depends on tree survival. Projections of urban forest ecosystem services and costbenefit analyses are sensitive to assumptions about tree mortality rates. Long-term mortality data are needed to improve the accuracy 

of these models and optimize the public investment in tree planting. With more accurate population projections, urban forest managers 

can also plan for cycles of tree planting, death, removal, and replacement to achieve canopy cover goals. Analytical tools from 

demography, such as life tables and mortality curves, could be used to improve our understanding of urban tree mortality and longevity. 

Demographic approaches have been widely used in forest ecology to quantify population dynamics and project future changes in 

wildland systems. This report is a primer on demographic concepts applied to urban trees, with terms and analytical methods adapted 

to the cultivated urban landscape. We include an overview of the uses of urban tree mortality rate data for research and management, 

a summary of lessons learned from ecological monitoring in other systems, and a discussion of opportunities for long-term urban 

forest monitoring by researchers and practitioners.

KEYWORDS: survivorship, survival rate, urban forest, tree monitoring, street tree, longitudinal, life table