Abundance Estimates of Three Wild Populations

Executive Summary

Who should read this report?

• Desk researchers attempting to Fermi estimate which wild animal interventions are cost-effective.
• Field scientists who want to know how much value of information there would be in conducting research on the abundance of wild animal populations.
• Grant evaluators who need to assess whether a proposed empirical study to estimate population size is adopting rigorous methodology.
• Animal advocates who need practical guidance on whether to implement interventions when there is considerable uncertainty about the number of potential beneficiaries.

What we did

• There is an interest in identifying cost-effective interventions to help wild animals. A major factor affecting cost-effectiveness is the number of target beneficiaries.
• We searched the academic and gray literature for abundance estimates of populations for which there are already technically feasible interventions: Urban pigeons, urban rats, and birds who collide into windows.
• For each population, we compare five different ways to respond to uncertainty about population size:
  • Treating the best available estimates as though they were accurate.
  • Adjusting existing estimates for known biases.
  • Funding or conducting original empirical research.
  • Exploring if there are more abundant wild populations that can be helped.
  • Developing new interventions that can help a larger number of wild animals.

Findings for urban pigeons

• It seems unlikely that there is any single ratio of pigeon population density to human population density that would be appropriate to apply to any given city: We found pigeon-to-human ratios ranging from .001 to 5.08.
  • Methodological rigor may explain some of the variation– many studies did not empirically estimate detection probability.
• High-quality studies of pigeon abundance should be relatively cheap and easy to conduct. Hence, it may be worthwhile to measure the size of a city’s population before deciding whether to actually intervene.
• In the absence of reliable data, interventions should likely occur in older cities that attract tourists. This is because intentional pigeon feeding and old buildings are strong predictors of pigeon abundance.

Findings for urban rats

• High-quality data on urban rat abundance is exceedingly scarce. The best studies we are aware of are of Baltimore in the 1950s.
• A somewhat credible upper-bound estimate from New York City in 2011 suggests there are ~2 million rats (~.25 for every person).
• Mark-recapture, the gold standard for estimating the populations of small mammals, is labor-intensive and at odds with the population control goals of municipal governments. It could be worthwhile to invest in improving and validating “resight” methods that do not require capture or handling.
• The logistical barriers to accurately measuring urban rat populations will nevertheless remain formidable. An alternative to verifying that there are enough urban rats to help is to explore solutions that could also affect rodent population control in commercial settings (e.g., farms and food processing facilities).

Findings for bird-window collisions

• Most studies of bird-window collisions are of just a few buildings that are known to cause a large number of collisions.
• There are two large-scale Fermi estimates based on a 2010 survey of Edmonton residents. They suggest 16-42 million deaths in Canada, and 365 and 988 million deaths in the United States. Neither estimate the number of sub-lethal collisions.
• To account for imperfect detection, these studies applied a correction factor to all buildings. A major uncertainty is whether there are any bird-windows at the majority of buildings with no observed strikes, especially low-rise buildings.
• Given people’s interest in birds, it might be possible to cost-effectively coordinate an effort across universities located within cities to improve the evidence base.
• Scientists know enough about the spatial covariates of bird strikes to develop spatial risk maps, which would ensure that interventions occur in high-risk areas.
• Alternatively, reducing light pollution might help a large number of wild animals, though it would typically only modestly reduce bird-window collisions.

Limitations

• We limited our search of abundance estimates to ~35 hours per population.
• We did not attempt to measure the abundance of other populations that would be indirectly affected by interventions on behalf of the target populations.
• Given that it is still early days for the wild animal welfare movement, it is unclear whether cost-effectiveness should actually be a major factor in determining whether to implement an intervention. Accumulating a track record of accomplishments may be more important at this stage, even if it is on behalf of relatively few wild animals.

Introduction

Population Counts Inform Cost-effectiveness

Cost-effectiveness is a property of an intervention in a given context. It refers to the cost for providing an additional unit of value to a given beneficiary (Center for Disease Control and Prevention, 2021). Assuming a fixed budget, stakeholders maximize their impact by allocating resources to the most cost-effective interventions available. However, it is impractical to assess the cost-effectiveness of all available interventions before deciding which to implement. It is more efficient to closely scrutinize only those interventions for which there is some prima facie evidence of cost-effectiveness.

The number of individuals that could be affected by an intervention is one heuristic of which interventions might prove cost-effective if investigated more thoroughly. For one, some interventions affect an entire population at once. The larger the population is, the larger the aggregate benefit. Also, creating and fine-tuning interventions takes time and money. The larger the number of beneficiaries, the lower the cost of research and development per beneficiary.

Are Targetable Wild Animal Populations Large?

Although there is substantial uncertainty about the number of wild animals, it is clear that collectively they are far more abundant than humans or captive animals (Bar-On et al., 2018, Table S1). All else equal, then, opportunities to help wild animals should be more cost-effective than interventions designed to help other groups. This is one of the premises of the wild animal welfare movement, which aims to advance the interests of wild animals (for an overview, see Elmore & McAuliffe, 2024).

On the other hand, actual interventions to help wild animals typically would not reach anywhere near all of the wild animals that could theoretically benefit. To give just one example, wildlife rehabilitation programs only help injured animals of certain species that people happen to find within a reasonably short distance of the rehabilitation clinic. Just because there are presumably a very large number of injured wild animals on Earth at any time does not mean that, say, funding a new wildlife rehabilitation center would help a large number of wild animals.

To determine whether implementing a wild animal intervention would be cost-effective, there is a need to define populations by our ability to effectively target them with an intervention. For example, the pigeons in the urban core of Los Angeles might be the relevant population when we ask whether enough pigeons would benefit to justify the cost of lobbying the city government there to adopt more humane pigeon control protocols.

Scrutinizing Population Estimates to Inform Decision-Makers

Our first goal is to search for population estimates of a few targetable wild animal populations¹: urban pigeons (Columba livia domestica), urban rats (Rattus norvegicus and Rattus rattus), and birds who endure window collisions (a wide variety of migratory and non-migratory species). Insofar as the estimates are based on valid methodology, summarizing them should help stakeholders decide whether these populations are abundant enough to be cost-effective to help.

Many estimates are not based on gold standard methodology. Because it can be difficult for non-experts to judge the credibility of particular estimates, our second goal is to give a non-technical primer on how to generate unbiased population estimates, and outline common deviations from best practices. This exercise should help stakeholders decide when existing evidence is rigorous enough for decision-making purposes. The basic methodological points generalize to measuring other wild populations as well.

When existing evidence is insufficient, stakeholders can instead devote resources to improving the evidence base. The most common situation that seems to require additional empirical research is when all existing evidence was collected in a different time and place than where a potential intervention would take place. Unfortunately, collecting new data in the geographical area of interest requires money, time, and sometimes political buy-in. As a shortcut, analysts often Fermi estimate (von Baeyer, 1988) the size of a local population based on data collected from elsewhere. For example, Liedholm (2021a) used data on pigeon density per square kilometer from 8 Italian cities to create a lognormal distribution of pigeon densities in urban areas of the US.

Not all Fermi estimates are reliable. To take an extreme example, one urban legend has it that, in cities, there is a rat for every person. A more data-driven Fermi analysis found an upper-bound ratio of one rat for every four humans (Auerbach, 2014). Moreover, expert testimony on rat abundance can disagree by an order of magnitude (Mokoena, 2014, February 13), suggesting that confidence in any particular ratio should be modest.

Fermi estimates work better when they depend on a number of assumptions, no one of which is necessarily particularly accurate, but that are plausibly biased in different directions. The overestimates and underestimates cancel each other out, reducing the net bias enough such that the discrepancy between the estimated value and the true value is not large enough to impact decision-making. Thus, our third goal is to identify the factors that analysts would need to consider in a Fermi estimate to make an extrapolation as unbiased as possible. Depending on the quantity and quality of data available to draw upon, the confidence intervals around such an estimate may be too wide to justify a robust conclusion about cost-effectiveness.

General Methodology

Given time constraints, we estimated the abundance of just three wild animal populations. We identified populations of urban pigeons, urban rats, and birds who collide into windows based on two criteria. First, we had to be aware of at least one intervention to help the population that is already technically feasible (i.e., the knowledge and ability to intervene is already available or likely will be in the next couple of years).² Second, we favored populations that basic principles of ecology would suggest have relatively large populations. For example, small-bodied animals generally are more abundant than large-bodied ones (White et al., 2007), which would lead us to expect that (for instance) feral boars are less abundant than the chosen populations.

We conducted a non-systematic search of electronic academic databases (viz., Google Scholar) and academic handbooks for population estimates and primers on methodological best practices. Due to time constraints, we spent an average of about 35 hours studying each population. We prioritized reading papers that were published more recently³ and appeared to use more rigorous methodology– that is, those that accounted for the probability of detection (see Box 1) and used random sampling (see Box 2). We only read reports written in English and Italian; we are likely overlooking some relevant literature written in other languages, which may correspond to geographical areas with systematically larger or smaller populations.

To limit the complexity of our task, we defined the populations in an intentionally narrow way. For one, we did not include all targetable subpopulations of the same taxa. For example, we only tried to count urban rats and pigeons, even though these animals are also subject to population control in agricultural and conservation settings. Similarly, birds collide with many human-made structures, such as wind turbines. But our population of interest is just birds who collide with windows. Other taxa that may directly benefit from the interventions motivating our choice of populations were also beyond scope, though we return to this topic in the Recommendations for Coping with Uncertainty section. Finally, wild populations are interdependent with an indefinite number of other species (e.g., predator-prey relationships, resource competition, ecosystem services, etc.). As a result, any intervention that affects the target populations likely also affects many other populations, which we made no attempt to capture here.

Box 1: Detection Probability

It is generally not possible to conduct a complete census of a population. Not every plot of land is accessible — some are on private property, others are physically difficult for humans to reach. Some individuals will only be detectable at certain times of the day or year, and researchers generally cannot monitor areas around the clock. Even under favorable conditions, the probability of detection is less than 1: an individual may be hidden behind a barrier, the observer may simply not notice them, etc. (Bart & Earnst 2002; Farnsworth et al. 2002; Nichols et al. 2018).

Researchers should adjust observed counts based on the true probability of detection. The estimated density of an animal population, N, is determined by the number of individuals observed, the total area sampled, and the detection probability as:

Abundance is computed by multiplying animal density per unit area by the total size of the study area. The detection probability varies according to spatial and temporal factors, so it is critical to validate that the detection probability is appropriate for the time and location.

Measures of abundance which do not explicitly account for probability of detection are not useless. For instance, municipalities often simply want to know whether their “pest” control efforts are working. So long as the conditions under which their measurements take place do not change over time, it is possible to get a rough sense of the direction and magnitude of the change in population size (Bart & Earnst, 2002). To avoid mixing up abundance measures that do incorporate detection probabilities from those that do not, it is useful to call the former “estimates” and the latter “indices.”

Urban Pigeons

Interventions

Urban pigeons are domesticated rock doves (Columba livia) that have become feral in cities around the world. The main complaints about pigeons are that they consume food from warehouses, carry diseases and parasites, damage buildings, and cause safety hazards (Stukenholtz et al., 2019). As a result, local governments sometimes resort to population control methods. One method is luring pigeons into traps, such as feeding them poisoned grain. Because the underlying conditions that allowed pigeons to flourish is left unchanged, the population will eventually bounce back, requiring future rounds of culling. A non-lethal option is to scare away pigeons from a certain area. Some municipalities use Avitrol, a pesticide that causes seizures in pigeons. Conspecifics who witness the seizures are allegedly scared away. However, apparently many pigeons die from ingesting Avitrol, and they possibly experience pain during the seizures (Liedholm, 2021b).

There are a variety of alternative population control methods that are arguably more humane (Stukenholtz et al., 2019). Dovecotes are habitats that humans attract pigeons to with food. After pigeons lay their eggs there, a municipal employee shakes the eggs or substitutes them with dummy eggs. This strategy prevents eggs from hatching without providing parents with a cue (i.e., missing eggs) that would cause them to reengage in reproductive effort. An alternative approach is reducing the viability of eggs. Nicarziban, which can be mixed into corn feed, reduces the hatchability of eggs (Gonzalez-Crespo, 2023). Finally, the reproductive rate can be reduced by restricting

the availability of food, as energetic resources are required for reproduction (Stock & Haag-Wackernagel, 2016). Although many interventions could accomplish this goal, public campaigns against feeding pigeons is perhaps the most common (Haag-Wackernagel, 1995).

Arguably, the population of interest includes only pigeons that are spared from an inhumane population control method. However, some population control interventions may benefit the entire local population (Liedholm et al., 2024). Perhaps, as the birth rate declines, the pigeons that remain enjoy better welfare due to reduced competition (Sol et al., 1998). Our estimates of pigeon abundance can be interpreted as an upper-bound estimate of the number of pigeons available to help.

Population Estimates

We found estimates of pigeon densities for a variety of different cities. Densities vary over two orders of magnitude between urban areas (Table 1). There are several (not mutually exclusive) explanations for the variation. Some of it may be due to measurement error. Most of the point estimates we found were not accompanied by standard errors or confidence intervals. The rare exceptions show that true levels of uncertainty can be non-trivial. For example, Tang et al.’s (2018) estimate of pigeon abundance in Singapore was 189,943, with a 95% confidence interval of 129,627 to 250,259.

Table 1: A selection of pigeon and human population densities from various locations.

Note. Distance sampling methods account for probability of detection, and stratified randomized sampling accounts for the impacts of different land use types.

Cities may also be delineated in different ways, with some studies only sampling the urban core, while others include suburban areas (Tang et al., 2018, p. 1605). Pigeon densities can vary widely across these landscape types. For example, Lancaster and Rees (1979) found the highest density in pigeons in the downtown core of Vancouver (6/ha), lower density in a residential environment (5/ha), and the lowest density in an industrial area (2/ha).

Densities may also vary across cities because those cities vary with respect to characteristics that affect how hospitable an area is for pigeons. For instance, old buildings may provide more roosting places because of their greater physical complexity (Haag-Wackernagel et al., 2008), or may be preferred because of similarities to the cave roosts for the wild species. Sometimes modern structures can be preferred: in Singapore, pigeons use the railway viaduct expansion gaps (Lim et al. 2023).

The covariate that has received the most attention is human population density. A high population density means that there are more people to engage in intentional pigeon feeding, which causes local population growth (Tang et al., 2018, p. 1605). Haag-Wackernagel and Bircher (2010) predicted the global population of pigeons this way: “The average feral pigeon population is around 1 pigeon per 10–20 city inhabitants…The world population is therefore estimated to be between 165 and 330 million individuals (Johnston and Janiga 1995, Haag-Wackernagel 1993)” (p. 82). We were unable to find the cited calculations of this ratio in either Johnston and Janiga (1995) or Haag-Wackernagel (1993). Among the studies we uncovered, the ratio of pigeon density to human density varies widely from study to study (see Table 1).

With greater uniformity in methodology, it may be possible to justify a particular ratio that is roughly applicable to any given city. Jokimäki and Suhonen (1998) suggests there is a positive relationship between human density and pigeon density in 31 settlements in Finland, although the effect of land use explains more variation. In addition, Buijs and Wijnen (2001) find a positive correlation between human density and pigeon density of various districts of Amsterdam even without accounting for effects of land use. By fitting their data to a linear model, we observe a pigeon-human ratio of .024, or 1 pigeon per ~42 humans (p=1.063e-08, adj R2 = 0.93; see Figure 1). If it were sensible to use this relationship to estimate the global population of pigeons, we would then predict a population of 108 million based on an urban human population of 4.5 billion in 2022.

However, we caution that extrapolating from a relationship based on one region to obtain a global estimate may be unreliable given the strong reported impacts of land-use types. Indeed, if consistent ratios exist only within land-use types, then a generalizable city-level ratios may not be possible because entire cities contain multiple types of landscapes in different proportions.

Figure 1: Relationship between human and pigeon population density in Amsterdam neighborhoods

Note. Based on Tables 1 and 2 in Buijs and Wijnen (2001). We used an intercept of zero and assumed independence of the data points and normally distributed errors.

Methods of Estimating Pigeon Population Size

Distance sampling (Buckland et al., 2015, chapter 1-2) is the most practical option for estimating the population size of pigeons, since it also provides an integrated procedure to estimate detection probability. For example, in line transect sampling (Giunchi et al. 2007), the researcher defines a random or stratified sample of rectangular plots, each with area area 2lw. At the half-width of each plot, an observer walks the length l of the line looking for pigeons. Beyond distance w from the line, observed pigeons are not counted. Each time the observer sees a pigeon that is within the plot, they note the distance and the sighting angle. Researchers can later compute the perpendicular distance to model the probability of detection, which is assumed to decline with distance from the line. Note that not all line transect studies actually bother to compute or correct for imperfect detection (Ferman et al., 2010).

A perhaps more common method uses quadrat counts. The method is similar in that rectangular plots are sampled. However, there is no built-in way to establish detection probability. Researchers have three alternatives. First, they can try to establish that all birds actually are present. Amoruso et al. (2014) measured abundance in Padua, Italy by distributing pigeon food in sampled plots at times that would not introduce disturbances that could scare pigeons off, like common business opening hours. The authors assumed “virtually all birds of each sampling unit were attracted to the ground by the foraging procedure and thus detected” (p. 604). Unfortunately, Giunchi et al. (2014, pgs. 720-721) find several grounds on which to dispute Amoruso et al.’s (2014) optimism. To mention just one, pigeons rotate through different feeding sites rather than visiting the same ones every day.

Second, researchers can incorporate a more labor-intensive method that does involve detection probability. The classic example is mark-recapture where the ratio of the number of recaptures to the number of captures is used to quantify the probability of detection (see more details in the Methods of Estimating Rat Population Size section). Senar and Sol (1991) captured and marked 50 pigeons in Barcelona. Based on the number of marked pigeons observed in a second set of observations, they concluded that the detection probability was .28. Capture methods are not popular for pigeons because they are difficult to capture, and a precise estimate of the detection probability requires a fairly large sample.

Third, researchers can extrapolate detection probabilities estimated in one context to new, unstudied contexts. For example, if a previous mark-recapture study reported a detection probability of .25, the new study could multiply its observed count by 4 to account for unobserved pigeons. The question is whether a similar detection probability is likely to hold between the two studies. When the correction factor is applied based on a detection probability derived in the same city (e.g., Sacchi et al. (2002), the approach is defensible, so long as there are no confounding temporal factors. Beyond that, the authors would need to make a case that the two locations are comparable, because many cities are not. For example, Senar and Sol (1991) estimated a detection probability of only .28 in Barcelona, while Levesque and McNeil (1985) estimated .77 for Montreal.

All pigeon enumeration methods can face practical difficulties in randomly sampling plots. For instance, if transects can only be placed along roadways, for instance, then pigeons may be harder to observe because they are scared away by the traffic. This issue is to some degree unavoidable, and can only be addressed using ad-hoc statistical procedures (see page 401 of Giunchi et al., 2007).

Urban Rats

Interventions

Rats in urban areas are primarily Norway rats (Rattus norvegicus) and black rats (Rattus rattus). The exact reason that humans regard rats as “pests” varies by landscape type, but in cities, the main concerns are disease transmission, contaminating food, and structural damage to buildings (Feng & Himsworth, 2014).

The most reliable standard pest control methods exclude rats from human spaces or reduce access to food, but they are labor-intensive and logistically difficult. Pest managers tend to use cheaper, simpler methods, such as rodenticides and traps. Rodenticides are poisons that are placed inside of baits. The poisons can cause hours to days of pain prior to death. Traps use baits to lure rats onto them. The traps prevent rats from leaving, typically using either an adhesive (“glue” traps) or maiming device (“snap” traps), both of which can cause pain and distress (Baker et al., 2022).

There are more humane alternatives to poisons and traps for reducing rodent populations. One option would be to place chemicals that reduce fertility into baits instead of poisons. Other options include lethal methods that are quicker or less painful, such as pumping carbon monoxide into burrows and bolt traps (Elmore, 2022).

As with urban pigeons, reforms to population control may extend beyond rats that actually would have otherwise died from an inhumane method (Liedholm et al., 2024). For example, most rats appear to die from competition for resources (Feng & Himsworth, 2014). Insofar as novel methods do a better job at keeping the rat population small, the remaining rats should face less resource competition. But since this type of indirect benefit is uncertain and varies across interventions, population estimates of urban rodents should be interpreted as upper-bound estimates of the number of beneficiaries.

Population Estimates

There are frequent news headlines regarding the cities with the most rats. For example, the pest company Orkin counts the number of new residential and commercial rodent treatments it performs in a 12-month period, and then releases a ranking of the “rattiest” cities (Orkin, 2023). However, there is no robust method for relating the number of contracted pest services in differing cities and the actual size of rat populations. Cities likely differ in the factors that lead to the probability of hiring a particular pest management company (e.g., number of competitors, availability of free municipal services, wealth of residents, condition of buildings, etc.).

We surveyed the literature for estimates of urban rat population size for an entire urban center. Studies differ in whether they report the number of rats outdoors or indoors, and/or in residential or commercial buildings. The best data available is for Baltimore during the 1950s, during which mark-recapture studies were conducted. Davis and Fales (1950). pegged the number of Norway rats in outdoor residential areas at 43,200, while Brown et al. (1955) estimated 44,700 (standard deviation not reported). More recently, Easterbrook et al. (2005) used trap-removal methods and reported 48,420±14,883 (mean ± 95% CI) rats in outdoor residential areas, which would imply ~0.08 rats for every person (Baltimore’s city population was ~635,000; US Census Bureau) and 2.02 rats per hectare (the independent city is 238 square kilometers). The similarity in findings over time using different methods could mean that the rat population was similar between these two periods, and that the trap removal method provides essentially the same information as mark-recapture studies in this setting. However, Gardner-Santana et al. (2009) also used a trapping-removal method in Baltimore and reported a rat population of 212,800 in outdoor residential areas (+-152000).

For New York City, Auerbach (2014) analyzed complaint call data from 2010 and 2011, which covers both indoor and outdoor areas, as well as most residential and commercial areas (NYC 311, n.d.). He treated the location of the complaint as a “capture” and by assuming an equal reportability of locations used a mark-recapture approach (2010 as the “mark” period, 2011 as the “recapture period”). Auerbach estimates ~2 million rats (± 150,000), which he describes as a likely overestimate since it assumes a large number of rats (50) per infestation, and that a colony was never shared between complaints with different addresses. This is a ratio of about .24 rats per human (~8.2 people in 2010, US Census Bureau), and just over 25 rats per hectare (790 square kilometers).

A similar analysis by a pest control company in 2023 suggested that the number of rats had increased to ~3 million (± 100,000), which is also described as an overestimate (MMPC, 2023, August 16). This comparison relies on the assumption that reporting behavior in 2010 and 2022 was similar. However, behavioral changes in rat populations associated with COVID-19 lockdowns increased rat visibility (Parsons et al., 2021), causing movements to novel locations. While the authors suggest that there was a real increase in the rat population in 2021 during the pandemic as a result of sanitation budget cuts and outdoor dining, other studies report changes in rat behavior associated with loss of prior food resources. We suggest that the 50% increase in estimated rat density from 2020 to 2021 reported by the pest control company is almost certainly partially or wholly related to these effects. Moreover, rat population growth seems to be tightly related to food resources, and is unlikely to have increased by 50% in one year.

Battersby et al. (2002) used the mean number of rats per infestation of 2.2 and infestation rates calculated from UK household surveys in the late 1990s to suggest that the lowest estimate of rats living indoors or outdoors in residential areas is between 821,500 and over two million. We did not find direct data-based estimates for the urban rat population of London.

Methods of Estimating Rat Population Size

The mark-recapture method is commonly recommended for incorporating detection probability estimates into density estimates of small mammals, including urban rats (Davis et al. 1953; Desvars-Larrive et al. 2018). In the standard form of this technique, live traps are arranged, usually in a grid pattern, to adequately sample the target area and animals captured are marked in some way to allow identification (Battersby et al., 2002, Castillo et al., 2003; Cavia et al., 2009, Ceruti et al., 2002). Marking methods for rodents normally include ear tags, pit tags and toe clipping (Jung et al. 2020). Recapturing is attempted soon after the initial marking so that mortality, reproduction, or movement will not impact on the estimate, but after a lengthy enough period so that individuals may be assumed to have fully mixed with other individuals in the population.

The probability of detection is R/M where R is the number of animals in the second sample that are marked, and M is the initial number of animals captured and marked. We divide our sample estimate, C, by this probability to estimate the true population is the capture area.

where C is the total number of individuals in the 2nd sample, and N is the estimated population size (i.e., Petersen estimate; see Krebs, 1999).

For the simplest calculations like that above, we make three key assumptions:

• The target population is closed. That is, there are no rats emigrating beyond the study area or new rats immigrating into the study area from elsewhere.
• The mark from initial capture is reliable. It is not later lost, overlooked or misread.
• Individuals are equally likely to be sampled.

These conditions will not strictly be met in practice (see conceptual difficulties with even defining a study area as “closed” in Royle & Converse, 2020, pgs. 110-111). For example, random sampling in theory ensures that individuals are equally likely to be sampled, but it is difficult to apply in practice. One common concern is that capture events might not be independent. Because rats observe each other, capturing one rat may reduce the likelihood that another is caught.⁴ Similarly, capturing one rat may impact the likelihood that they can be recaptured. Differences in home range can also violate the equal likelihood assumption, because some individuals will encounter more traps than others.

The practical question is whether violations are severe enough to call for more flexible, complex models. Sometimes, researchers can design studies in ways that minimize the likelihood of violating these assumptions. For example, bolder rats are probably more likely to explore novel items like traps (Stryjek et al., 2019). Individual variability can be reduced (and overall trap success enhanced) by allowing rats to become habituated to traps using “prebaiting.” In this procedure, traps are baited, but not set for several days prior to use (Gurnell 1980; Krøjgaard et al. 2009; Taylor et al. 1974). Unfortunately, many recent studies do not use pre-baiting (Desvars-Larrive et al. 2017; Kajdacsi et al. 2013; Panti- May et al., 2016; Rouffaer et al. 2017).

Because rats are neophobic, trap success is expected to be quite low when abundant food is available (Clapperton 2006; Inglis et al. 1996). When the detection probability is low, the abundance estimate will be imprecise. Fortunately, it will still remain unbiased so long as there is no change in the probability through time or space for different groups of individuals. Still, a low detection probability can be a sign that some rats were easier to catch than others. For example, if food abundance varies across space, there could be differences in trap rates at different locations and times when there is no actual difference in the rat population.

The most formidable barrier to randomly sampling urban rats is spatial heterogeneity. Because food waste varies within environments and rats are social species, they tend to cluster (Battersby et al. 2002). These clusters can be quite small– rats are unlikely to move more than 40-150 m when sufficient resources are available (Davis et al., 1948; Gardner-Santana et. al. 2009; Kajdacsi et al. 2013; Richardson et al. 2017; although see Combs et al. 2018). Without extensive numbers of traps, it is possible to completely miss areas of high densities.⁵ Conversely, focusing exclusively on areas with known populations will produce an exaggerated estimate. For example, a study in Vancouver, BC found that trapping was only effective in city blocks with very high populations, and trap success probability varied from 0 to 0.94 (median 0.04) among city blocks (Himsworth et al 2014). Using a stratified sampling plan to determine how densely to lay traps based on predictors of rat nests may balance efficiency with the need for a sufficient number of traps.

Municipalities generally do not use mark-recapture methods, because their primary goal is to reduce the rat population, not to measure it. Removal trapping is an alternative by which trapped individuals are permanently removed from the population by lethal traps or euthanization following capture (e.g., Gardner-Santana et al. 2009). The trap is then reset. Still, the number of animals caught per unit of “effort” (e.g., the number of trapping nights) is thought to provide a meaningful index of actual abundance. For example, Easterbook et al (2005) used trapping data to determine the trappable rat population at each sample location in Baltimore, MD. Traps were set for 4 consecutive days and the number of rats counted. Using this data, a linear relationship was created where the number of new rats trapped is used to predict the cumulative number of rats trapped for each consecutive day. The y-intercept of this relationship is taken to represent the point at which the catch per unit effort (number of new rats trapped) was zero and represents the total trappable number of rats in the sample location.

Himsworth et al. (2014) suggest that systematic trapping-removal is among the most accurate methods for enumerating urban rats. Yet, comparisons between mark-recapture methods and trap-removal methods in natural areas indicate that removal of individuals from the population biases estimated abundance upwards because the removal of animals attracts new individuals to the area (Sullivan et al. 2003). In a study of small mammals, Wiewel et al (2010) found that for all species considered, mark-recapture estimates were consistently more precise than removal estimates.

The primary means of routine rat population monitoring urban rat populations is human complaint call data. Municipal authorities use the frequency of complaint calls to determine whether rat populations are increasing or decreasing, or whether some areas have greater rat infestations than others. For example, Murray et al. (2018) found that trap success was linearly correlated with the number of complaint calls in Chicago. Complaints cannot be used to estimate actual rat abundance– the number of rats is generally not known by the complainant and probability of both noticing and calling in a given infestation are unknown – but they potentially serve as comparative indices between locations and related trends through time. Complaint call reliability depends on whether the relationship between rat abundance and human reporting behavior remains stable across locations and time.

Unfortunately, the likelihood of filing rat complaints varies by factors such as knowledge on how to file a complaint and individual rat tolerance level or attitude. Most notably, there is an association of complaint calls with human population density (e.g., Murray et al. 2018), which can then lead to underestimates of rat population density for areas without active habitation. For example, de Cock et al. (2024) found there were more municipal rat complaints in residential areas compared to parks, while there was a higher relative abundance of rats in parks as indicated by trap success data. Reporting activity also fluctuates over time. For example, rats may be more frequently observed when they are displaced by construction activity (Byers et al 2019), which could also lead to an increase in complaints when there is probably no change in population.

Survey data could be a more accurate index of rat abundance than complaint call data, since it does not depend on proactive behavior on the part of residents. In the UK, the 1993 commensal rodent survey was implemented to determine whether rodent infestation levels had changed as compared to survey data from the late 1970s. The 1993 survey found 4.6% of all domestic premises (excluding those associated with commercial activities) to be infested by rats, compared with 3.3% in 1976-79 (Battersby et al. 2002). However, baiting data from London sewers suggested that rats had experienced an exponential decline in abundance (Channon et al. 2020). As a result, it is unclear whether there was an increase in rats, changes in survey responses, or relocations in centers of abundance. It also seems likely that survey responses are biased upwards. Results from a survey with different methods, which included a search for signs of infestation in addition to survey response (Langton et al., 2001), indicate that 0.23% of occupied properties had rat infestations inside and 1.6% had infestations outside.

Birds in Window Collisions

Interventions

For birds, the reflection in clear windows looks like an area they can fly through. This mirror effect causes collisions. Estimates of bird strikes often focus on the most extreme outcome– death. However, the majority of bird strikes probably do not lead to death, at least not right away.

There are a wide variety of interventions to reduce bird strikes, but they generally fall into two categories. The first involves either designing or retrofitting the appearance of windows themselves so they no longer create an illusion of habitat. UV signals, circular markers, and parachute chords have all been found to help alert avoid windows without greatly disturbing humans’ abilities to see outside of them (Klem & Saenger, 2013; Riggs et al., 2022).

The second type of intervention is to reduce light pollution. Artificial light at night plays a significant role in why nocturnally migrating birds are in the vicinity of windows in the first place (Lao et al., 2020; Van Doren et al., 2021). Species that migrate at night have evolved to use light (e.g., moonlight) as navigation cues. Streetlights, facade lighting and indoor lighting shining from unshaded windows can disorient them from their migration paths into urban areas. Downshielding lights and automatic use of window blinds are common proposals to reduce artificial light at night (Van Doren et al., 2021).

Some interventions to reduce window collisions would also help other birds. For example, not all migrating birds attracted to artificial light end up colliding into windows. Nevertheless, reducing light pollution would reduce harms caused by deviating from their path, such as exhaustion arriving to their destinations late (Neme et al., 2023). In this sense, our estimates of bird collisions are a lower-bound for how many birds could benefit from intervention. In another sense, the target population is overly broad, as no one population could realistically benefit from any one intervention. For instance, artificial light at night is mainly an issue for tall buildings in urban areas, but far more bird strikes occur in residential areas.

Population Estimates

There are two studies that attempt to Fermi estimate bird deaths from building collisions. Machtans et al. (2013) reports 16-42 million deaths in Canada, while Loss et al. (2014) reports between 365 and 988 million deaths in the United States. Neither estimate the number of sub-lethal collisions.

Both sets of authors classify buildings into three different groups: houses, low-rise buildings, and tall buildings. Machtans et al. (2013) attribute 90% of deaths to houses, 10% to low-rise buildings and 1% to tall buildings. Loss et al (2014) attributes 56% to low-rise buildings, followed by 44% at houses and 1% at tall buildings. Although the buildings that cause the most mortality are probably mostly tall buildings, in aggregate houses and low-rises are responsible for much more mortality because there are so many more of them.

Both studies based estimates of bird deaths from collisions with houses on Bayne et al.’s (2012) survey of Edmonton residents. As shown in Figure 2, less than 20% of them reported a bird death.

Figure 2: Partial reconstruction of # bird kills per residential home reported in Bayne et al. (2012).

Machtans et al. (2013) estimated that there were 2.2 bird deaths per residential home per year in Canada. Thus, across 10.1 million residential dwellings in Canada, the total annual residential mortality is 22.4 ±2.4 million (SD) birds. Behind these estimates are a number of substantive assumptions. First, the authors had to decide what correction factor to use for imperfect detection. They conducted sensitivity analyses, varying the correction factor between 2.3 and 5 overlooked birds for each death recorded.

Next, they had to decide how to apply this correction, given the zero-inflated distribution in Bayne et al. (2012): Should the majority of homes still be treated as having zero kills, or should they assume that the reports of zero kills are due to residents not paying attention to the issue? The authors used a uniform random distribution for the correction factor, which had an effect on all homes, because they imposed a minimum value of .1 kills for each house.

Last, they had to decide how to account for covariates that affect collision rates. Machtans et al. (2013) used house age (a proxy for the amount of vegetation in the area), number of houses, percent of urban houses, and percent houses with feeders. The actual data on increased mortality where there are bird feeders seems somewhat mixed (Dunn, 1993; Hager et al., 2013; Kummer & Bayne 2015), but proximity to natural areas, vegetated landscaping in the immediate vicinity, and proximity to major migration flyways and stopover points are major spatial factors affecting collision risk in residential areas⁶ (Hager et al., 2008; Kahle et al. 2016).

Loss et al. (2014) estimated 2.1 bird deaths per residential home per year. For 122.9 million 1-3 story residential buildings in the US, they predict total annual residential mortality 253.2 million (95% confidence interval of 159.1–378.1 million). The correction factor explained 70.4% of the uncertainty about mortality at residences.

Although some of the methodological details differ between the two studies, their substantive assumptions are quite similar. In our view, the most questionable choice was treating all houses as if they all experience at least some mortality, as we think it is likely that a substantial portion of homes reporting no strikes in fact caused no deaths in the prior year. For example, in Kummer et al.’s (2016) prospective study, only ~43% of respondents reported any strikes, fatal or otherwise.

For low-rise buildings (roughly 4-12 stories), Machtans et al. (2013) created separate distributions for three separate categories: least likely (e.g., warehouses), somewhat likely (e.g., sports stadiums), and most likely (e.g., banks). They had just two studies they considered high-quality to draw upon for the “most likely” distribution, and relied on intuition for the other two categories. Overall, the authors simulated a range of 0.4 to 55 deaths per building per year for low-rise buildings in Canada. With an estimated 441,000 such buildings, the combined predicted average annual mortality was 2.4 million ± 1.1 million (sd) with lower and upper bounds of 300,000 to 11.4 million. This is roughly 5.4 birds per building per year.

For low-rises in the US, Loss et al. (2014) produced two separate estimates of collision mortality, one based on 8 studies that met inclusion criteria, and one with just the 4 studies that contained year-round data. They estimated the number of low-rise buildings as described by a uniform distribution with minimum and maximum of 14.0 million and 16.2 million, respectively. The two estimates of annual low-rise mortality were between 62 and 664 million birds (95% CI with median 246 million or 16.3 birds/building) for 8 studies and between 115 million and 1.0 billion birds (median 409 million or 27.1 birds/building) for the values based on the 4 year-round studies. The average of the two median figures is 339 million (95% CI 136–715 million), which gives 21.7 birds per building per year (95% CI 5.9–55), or roughly 4x the value predicted by Machtans et al. (2013).

The substantial difference in per-building mortality rate between the two studies is partly due to Loss et al. (2014) not stratifying low-rise buildings into categories with different mortality rates. As a result, there were very few buildings that were presumed to have zero collision-related mortality. The correction factor (minimum 1.28 and maximum 2.56) therefore resulted in a non-zero estimate for nearly all buildings.

For tall buildings (roughly greater than 12 stories), both research groups compiled citizen science data. Machtans et al. (2013) had information for Calgary and Toronto. To account for the bias towards buildings with high mortality, they fit a rank order curve to extrapolate from studied buildings (which were assumed to be disproportionately high-risk buildings) to unstudied buildings (which presumably cause far fewer kills). They increased the estimate from this curve to account for failed detection. Correction factors ranged from 1.72 to 5.19. The estimated total from their Canada-wide calculation was 64,000 birds per year (~10 birds per building per year).

Loss et al (2014) used a similar procedure, except that they had data from 11 cities (including Calgary and Toronto), which they modeled using a negative binomial distribution. From this procedure, they obtain an mortality rate of 24.3 birds per building (95% CI: 5–76), or roughly 2.5x the value reported by Machtans et al. (2013). They report a total mortality in the 95% confidence interval of 104,000 and 1.6 million birds (median ~508,000) for a mean of 20,900 tall buildings in the US. Both tall building estimates again use distributions that admit either few or no zeroes. There is again a question of whether it is appropriate to apply a correction factor to buildings that may in reality cause no mortality.

Methods of Estimating Bird-Window Collision Frequency

There are two main types of data used to estimate bird-window collisions. Carcass recovery studies are conducted onsite. For example, Klem (1989) placed several clear window panes about a meter above the ground in rural Illinois. To account for non-lethal collisions, a strike was also registered if “or a feather, body smudge, or blood smear was found on the glass” (p. 608). The windows were checked “daily,” though the time of day was not specified.

Survey studies ask respondents to recall collisions. Bayne et al. (2012)‘s had University of Alberta conservation biology students recruit respondents by distributing a pamphlet about the survey around the metropolitan Edmonton area, as well as on social media. Individuals who opted into the survey were asked how many birds had collided with a window in their current home in the past year, and whether they survived or died. There were also items about plausible covariates of collision risk, such as having a bird-feeder in the yard. Self-reported zip codes were used to determine the urbanicity of the neighborhood.

Due to their labor-intensive nature, carcass recovery studies are only conducted on fairly small scales, sometimes just one or two buildings. Researchers also need to get permission from property owners to search the property; if willingness to comply is correlated with the rate of collisions, then the selection of buildings will be biased, even if the original selection of respondents was based on random sampling. Surveys are a low-cost way to measure collisions at a large, diverse range of buildings.

A benefit of the carcass recovery approach, though, is that the detection probability for that location can be directly estimated. Carcass detectability is imperfect for a number of reasons. For one, scavengers may remove the carcass before observers get to it. The rate at which scavengers remove carcasses can be estimated by placing carcasses in an area and observing how long it takes for them to disappear. Similarly, the probability that observers will detect a carcass that is still there can be estimated by randomly distributing carcasses around the study area and seeing how many of them observers find (Hagar et al., 2013). Note that, even for a single location, there is no single detection probability, because it may vary by time of day or year. Unfortunately, Riding & Loss (2018) note that detection is rarely assessed in carcass detection studies.

For survey studies asking respondents to report bird strikes retrospectively, detection rates should be lower because residents were not necessarily looking for them. Kummer et al. (2016) used a prospective approach in Edmonton, asking respondents to search for evidence of collisions on their own. Compared to Bayne et al. (2012), Kummer et al.’s sample reported over three times as many bird strikes. Interestingly, the number of strikes that were actually fatal was in closer agreement, and slightly lower in the prospective approach. The authors hypothesize that, “participants in the standardized searches were more likely to take note of things like body smudges, collision noises, and feathers or blood on the window once they were told these were evidence of a bird-window collision. When participants were asked survey questions, this type of evidence was likely more difficult to recall than finding a dead or injured bird and may explain the differences” (p. 5).

Random sampling is also very rare. The best available data on mortality associated with tall buildings comes from citizen science organizations. We might expect citizen science efforts to arise in locations that are experiencing bird mortality rates large enough to inspire a response. Cities that are located within flyways and next to large waterbodies where migrants may stage before attempting a crossing during poor weather conditions, such as Toronto, may experience higher mortality rates than differently situated cities (Evans Ogden 1996). Loss et al. (2014) also note that most data collection focuses sampling effort on migration periods.

Once a general area has been selected, there is also a risk that only buildings that are known to be problematic will be monitored. We only found one study that seems to have used random sampling in order to estimate heterogeneity in bird collisions (Hager et al., 2013). Among 20 buildings in Rock Island Country, Illinois, they found no fatalities at 50% of the buildings. Using covariates of collision risk, they modeled a highly heterogeneous spatial distribution of bird deaths with overall median 2.6 (range 0.3 – 52.1). Kummer et al., (2016) points out an analogous risk for survey studies:

participants with an interest in birds and a pre-established window collision issue may have been more likely to answer a series of questions relating to bird-window collisions than those who had not previously observed such an event. Such biases could result in collision and mortality estimates that are much higher than what actually occurs. (p. 2).

One possible way to minimize this bias in future studies would be to use probability sampling instead of opt-in methods. Alternatively, survey responses could be weighted by variables known to correlate with collision risk. For instance, if there were unbiased national estimates of what percentage of people live in apartments, opt-in survey could be weighted so that apartment residents influence the results in proportion to their national prevalence (Bayne et al., 2012, p. 590).

Recommendations For Coping with Uncertainty

General Considerations

We did not uncover estimates that are both unbiased and precise for any of the three populations. In this subsection, we explore five different ways stakeholders can respond to uncertainty. In the subsequent subsections, we speculate which course of action to pursue for urban pigeons, urban rats, and birds in window collisions. We caution that definitive guidance would require a more thorough analysis of the cost and efficacy of the interventions themselves.

First, stakeholders could treat the best available estimates as though they were accurate enough for decision-making purposes. This strategy is more defensible when there is data available for the area where the stakeholder would like to implement the intervention. It also makes sense when all of the available estimates are large enough for a given intervention to meet some minimal bar for cost-effectiveness (see Box 3). If the cost of helping a certain population is very low, for example, then the intervention can still be cost-effective even if a relatively small number of animals benefit.

Second, stakeholders could create a better Fermi estimate based on the available evidence, adjusting for all of the sources of bias we pointed to. This option is sensible when there is some high-quality evidence to draw upon, including about the most important covariates to model when extrapolating to the area where a proposed intervention would take place. It can also be worthwhile to try to revise previous Fermi estimates that involved dubious modeling decisions. Fermi estimates are less informative when the optimal decision is sensitive to small changes in the estimated population size. Machtans and Thogmartin (2014) describes the level of inaccuracy one can expect:

The overall error of the estimate is likely to be the square root of the number of terms in the equation multiplied by the standard deviation on the log scale of the individual term errors; thus, a 4-term estimate where each term is correct within a factor of 2 would have a likely range of 2^√4 or ¼ to 4x the real value…as long as there is no consistent bias in the error of the constituent terms. (p. 4).

Machtans and Thogmartin regard an estimate that is off by a factor of 4 as “acceptable accuracy,” (ibid) but some may be far too expensive under the most pessimistic assumptions that are plausible. It is also not always possible to bound inputs by a factor of two. For instance, the appropriate correction factor for imperfect detection of bird strikes could plausibly err in either direction by an order of magnitude. If there were four inputs that were all this noisy, then the margin of error would vary from .01x to 100x of the true parameter value.

Whether an imprecise estimate of population size actually undermines the utility of a cost-effectiveness analysis depends on stakeholders’ risk attitudes (for a primer on risk attitudes in wild animal welfare, see McAuliffe, 2023). “Risk-neutral” decision-makers treat the expected value as the key metric. It would not matter if there is a non-trivial chance that the intervention is not cost-effective, so long as it is when the expected value is treated as if it were the actual population size. “Risk-averse” decision-makers will generally only want to implement an intervention if it would be cost-effective even under pessimistic scenarios.

When population sizes are too uncertain to inform decision-making, stakeholders can fund or conduct original empirical research. This option is attractive when the research is cheap to conduct, and the opportunity to act on the results is not particularly time-sensitive. A practical barrier is that the available tools for measuring a certain animal population may not be particularly sensitive. It may be more strategic to allocate resources to improving the methods underlying population estimates before actually applying them.

Alternatively, a Fermi estimate might be accurate enough to show that the intervention does not meet the minimal bar for cost-effectiveness. Stakeholders should then pivot to exploring if there are other currently targetable populations which are abundant enough to help cost-effectively. If not, then they could invest in developing new interventions that can reach larger populations that can be targeted with extant interventions (for more details, see the Technical Ability section of McAuliffe, 2024).

Guidance for Urban Pigeons

Variation in pigeon population density appears too complex to boil down to a single factor like human population density. Yet, the logistical barriers to conducting high-quality studies of pigeon density seem minimal. We would recommend conducting distance sampling studies in areas where pigeon population control activities occur before deciding to intervene there. The effort required to generate a sufficiently precise estimate can be minimized by stratifying by landscape type. Tang et al. (2018) is a particularly rigorous study that future researchers can use to inform their methodological choices.

Even if there are no data available for a given city and no opportunities for collecting it, we can at least make an educated guess about whether it is likely to have a relatively large pigeon populations. We know that intentional bird feeding and the presence of old buildings are associated with greater pigeon abundance. We also know that the pigeon population grows the most during the warm months of the year (Giunchi et al. 2007). Collectively, these facts suggest that older cities that receive many tourists during the summer months are more likely to have high densities of pigeons. Not only does tourism increase population density, but tourists seem more likely to feed pigeons in cities, whereas locals are more likely to regard them as a nuisance (e.g., Rueda, 2018).

Guidance for Urban Rats

Marking animals is labor-intensive. Being trapped, handled, and marked likely also reduces rats’ welfare. Newer “resight” methods have the same underlying logic as mark-recapture studies, but reduce labor costs and are more welfare-friendly. For example, camera traps are baited stations that take a photo when an animal is detected (Weerakoon et al. 2014). To serve as a resight method, these photos are then analyzed to identify individuals and determine if recapture has occurred. DNA-based methods that rely on the capture of individual DNA in hair samples or feces could also be employed (e.g., DNA‐based mark–recapture based on hair snagging; see Boulanger et al., 2004). A potential concern with resight methods is that the technology to reliably distinguish between individuals may not be advanced enough (Augustine et al. 2018). However, a recent study with a small population of large rodents (marmots) compares mark-recapture and camera-trapping and suggests similar accuracy for population estimates (Forti et al., 2022).

Resight methods have hardly been used for urban rats, but likely would alleviate the labor costs that cause investigators to resort to methods that do not directly estimate the detection probability.⁷ de Cock et al. (2024) reports that they attempted to use camera traps to track urban rats, but that cameras were frequently stolen. They suggest that non-valuable objects like chew cards might be a suitable alternative, or ultrasonic recorders (which are valuable, but perhaps could be small enough to hide), might serve better. Studying whether any of these technologies could be reliable and practical enough to study urban rat populations could substantially reduce the barriers to conducting rigorous research.

Alternatively, it may make more sense to focus on investing in solutions that would help non-urban rats as well. Population control of rats is common in food processing and some agriculture settings (e.g., orchards) due to the abundance of food. Certain interventions to reform rodent pest control, such as bans on second-generation anticoagulant rodenticides, so far have only applied to municipal settings. The political will-power to extend these bans to the food supply chain does not exist (Elmore et al., 2023). In contrast, humane alternatives to current population control methods might be applicable to some commercial settings.

Guidance for Bird-Window Collisions

It might make a significant difference to bird strike estimates whether we assume that buildings that have no observed bird strikes in fact have any during an average year. Indeed, the greatest source of uncertainty in Loss et al (2014) was how much mortality occurs in low-rise buildings, where it seems most plausible that many buildings have none. Given widespread interest in helping birds, it may be possible to coordinate a cost-effective research effort to address this lacuna. For instance, a funder could offer a small pot of money to any urban university willing to recruit students to search for bird strikes at randomly selected buildings around the city.

In the meantime, the fact that spatial factors play such a large role in collision risk would enable researchers to create spatial risk maps that identify which areas have the highest relative risk (e.g., Buchan et al., 2022; Liechti et al., 2013). Window collisions were indirectly captured through mapping of light pollution and urbanization. Mapping window collision risk could be based on known covariates and knowledge about particular flyways, such as common stopover areas. Spatial risk maps would help determine where it would be cost-effective to intervene.

If it proves too difficult to improve the evidence base, we would suggest focusing on interventions that would incidentally help populations that are almost certainly highly abundant. For example, reducing light pollution will not make a major dent in reducing bird collisions, as the majority of collisions occur in residential areas, where artificial light at night is not the most relevant risk factor. Nevertheless, attraction to stationary, artificial light sources may cause 100 billion insect deaths per summer in Germany (Eisenbeis & Hänel, 2009). Reducing lighting in commercial buildings could therefore avert a large number of animal deaths, even though the nominal beneficiaries are not particularly numerous.

The intellectual content contained in this article, remains the exclusive property of Kim Cuddington. Unauthorized reproduction or public display of this article, in whole or in part, without explicit written permission from the author is strictly prohibited. Requests for permission to reuse or republish the content should be directed to Kim Cuddington.

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