by Joshua Frank

The Foundation for Interdisciplinary Research and Education Promoting Animal Welfare (FIREPAW)

Abstract: Human companion animal overpopulation is a problem of human creation, with significant human costs, and that can only be addressed through human action. A model was constructed to understand the dynamics of canine overpopulation and the effectiveness of various policy options for reducing euthanasia. The model includes economic and ecological factors in human and dog populations. According to the model, a "no-kill" society is an achievable goal at an acceptable human cost. Spay/neuter programs and increasing adoptions were both found to be very effective options. However, spay/neuter policies need to be evaluated over a very long time horizon since full impact may not be achieved for thirty years or more. In addition, spay/neuter can be effective even if it only effects a small portion of the human population. Adoption and spay/neuter programs were found to work well in combination, and to continue being effective as society approaches no-kill dynamics.

Key words:

Human companion animal overpopulation is a problem of human creation, with significant human costs, and that can only be addressed through human action. In many respects, companion animals lie in an unusual gray area between the human world and the natural environment. Legally and economically, these animals are property and a tradable "good" and therefore lie within the realm of industrialized human society (though the relationship between companion animals and humans precedes industrialization by many millennium). However, at the same time, companion animals are also a connection between human society and the natural environment.

In fact, one of the attractions of companion animals may be the connection it gives humans to the natural world. Hirschman (1994) searched for "emergent themes" in the human-animal relationship. One theme found relates to "wildness". Owners seem to want some aspect of nature or wildness in their companion animal. However, most humans do not want too much wildness; animals that were too wild were often given up.

The possibility that companion animals serve the human need to connect with nature is consistent with the biophilia hypothesis (Wilson, 1984), which theorizes that contact with other species and the natural world is essential for humans to maintain their mental health.

Regardless of why humans choose to live with companion animals, it is clear that human value their animal companions very highly. Studies repeatedly have shown that the vast majority of people consider their companion animals to be "family members" (for example, Friedmann et al 1984, and Hirschman 1994) and are very attached to their animal companions (Ory & Goldberg, 1984). Frank (2001) found that most dog owners stated they would not trade their companion animal even if offered sums of money of a million dollars or more and promised that the animal would be well cared for. Since these animals have a high value to many humans, their welfare is of significant human concern.

In addition, humans have a certain responsibility for the welfare of companion animals. Dogs, the focus of this study, have been bred for thousands of years to serve our needs. They have therefore ceased being truly "wild" animals and instead became dependent on humans for survival. As the creators of a species dependent on humans, we have a certain responsibility for that specie's welfare. Humans also have a responsibility for addressing dog overpopulation since they are in a sense the perpetuators of the problem. Pet store suppliers, commercial breeders, and private owners (or "backyard breeders") intentionally produce millions of animals every year to meet public demand. Millions of consumers initially decide to purchase or adopt a dog, only to later abandon that animal because it is inconvenient or no longer suits their needs. Millions more choose not to spay or neuter their dog. Therefore, it is human actions and inaction that perpetuate dog overpopulation and creates the need for the human-made "solution" of euthanasia.

Although the estimates vary, there is no doubt that millions of dogs and cats are put to death every year in the United States. Arkow (1994) extrapolates data from nine states to come up with a national estimate of 8.3 million animals sheltered and 5.7 million euthanized. Rowan (1992) reports that the number of animals being euthanized is 5-6 million. Mackie (1992) estimates 7 to 15 million animals euthanized, Thornton (1991) estimates 16 million, and Carter (1990) estimates 13 to 17 million.

Focusing specifically on dog overpopulation there are multiple costs to human society. According to Rowan (1992) shelters spend approximately $1 billion every year to deal with unwanted companion animals. Baetz (1992), estimates that $500 million is paid each year for animal control by United States cities and counties. Other costs include dog bites which result in the death of 20 Americans and 585,000 injuries a year (Pediatrics, 1994). According to Beck, Loring, & Lockwood (1975) the reported bite rate in urban areas from all dogs (strays and owned) is 0.45%. However, according to Jones & Beck (1984), a high percentage of animal bites go unreported to authorities. There are other unexpected costs. Carding (1969) found that 6 percent of all automobile accidents and 1.2% of accidents involving death or injury to humans involved dogs.

Beyond these physical costs there are the psychological costs suffered by humans sympathetic to the plight of animals. According to Jasper & Nelkin (1992), 20% of Americans have contributed money to an animal protection organization, and 10-15 million Americans belong to at least one animal welfare group. Congress also receives more letters about animal welfare than any other topic (Fox, 1990).

But if animals are assumed to have interests independent of any human sympathy, the greatest cost is the impact on the animals themselves. This is a somewhat controversial assumption, but a growing number of philosophers and scientists are positing its validity including Singer (1975) and Regan (1986).

Although millions of dollars are currently being spent to reduce the number of animals euthanized, there has been little rigorous scientific analysis to direct these efforts down the most fruitful paths. This study builds a mathematical population flow model that includes both economic and ecological factors in human and dog populations to understand population dynamics and to analyze the effectiveness of various policy options that can be used to reduce dog overpopulation resulting in euthanasia.

Figure 1: Diagram of dog population flow dynamics model

A generalized population flow model was constructed to be flexible enough to apply to any region and to incorporate the impact of policy options. The model was then

calibrated based on information obtained for one particular region.

The above diagram shows the ecological-economic model that is used here. The diagram shows all stocks (labeled "P" followed by a numeral for a population of animals) and all flows ("S" represents supply lines to the consumer pet market, "B" represents animal births, "D" represents deaths, "A" represents abandoned animals, and "T" represents other transfers).

The change in each population is defined by simply adding the flows in and out of the population with the starting values calibrated based on the results of a survey of the Capital Region of New York State. Each flow equation is defined mathematically and also calibrated based on survey data and prior research results. The table below gives the equations and values used for all model parameters. Populations are defined in the table by their change, with starting values based upon the survey results for the Capital Region. Births in the owned population and stray populations are defined ecologically (by a birth rate, the spay/neuter rate and the population size) while in the pet store and breeder population they are assumed to be managed to match the level of demand. The model implicitly assumes that there is some "supply push" from the stray population in that the number of strays adopted is a function of how many strays there are out there. In addition, while the demand for dogs from other sources goes down when stray adoptions go up, this decrease only partially compensates for the increase in stray adoptions.

Using the inputs described above, a base case model was created. The graph below shows the population over time for the base model.

As shown, the population sizes are stable over time. The graph below shows the flows into and out of P1, the population of "owned" animals for the base model. These flows are also stable in the base model. It should be noted that not only is the population size set to be approximately the estimated size from the survey, but also the flows approximate the levels found in the data. Approximately 5,500 dogs go to shelters each year in the model. The size of each supply source (S2-S5) is also based on the survey findings. The estimated shelter adoption rate (S2) from the survey (about 2900) is close to the amount estimated from surveying local shelters (2600). S2 in the model is between these two estimates.

Since this model includes many parameters which must be estimated based on incomplete information, the sensitivity of the model to these assumptions was tested. The table below gives the elasticity of death rates in the model to various parameters using both a 10 year and a 100 year time horizon. An elasticity of one indicates that a one percent change in the parameter results in a one percent increase in the death rate. The model is insensitive to most parameters, with only 3 of 36 parameters/time horizons having an elasticity (in absolute value terms) of one or more. By far the most sensitive parameter in the model is the spay/neuter rate, with a one percent increase in the spay/neuter rate decreasing the death rate by 14 percent using the longer time horizon. Fortunately, the most uncertain variables (such as the dynamics of the stray population) tend to have low sensitivities, while the more sensitive variables tend to have more reliable data available. It is also quite clear from these sensitivities that the time period used can have a large impact on model results (half of the parameter elasticities change sign when the time period is extended).

The primary purpose of the model is to test the effects of various potential policy alternatives or "treatments" on dog euthanasia rates. Possible treatments that can be used to reduce euthanasia of dogs include low cost spay/neuter programs, public relations programs to encourage spay/neuter behavior, public relations programs to encourage consumers to adopt animals rather than buying animals from sources that increase supply, financial incentives for adopting/taxes on purchases from other dog sources, improved marketing to increase shelter adoptions, public relations programs to encourage "responsible" ownership (i.e. discouraging abandonment and animal abuse/neglect even if it means discouraging some of these people from owning pets), and increasing shelter space.

There has been some controversy regarding low-cost spay/neuter programs. While some experts believe increasing spay/neuter rates is the key to long-term population control, others, particularly in the veterinary community, argue that low-cost spay/neuter programs are ineffective.

The percentage of licensed dogs sterilized jumped from slightly more than 5% to around 50% in Los Angeles however, the sterilization rate has dropped slightly since then to 48%. During the same period, the number of dogs impounded by the shelter also dropped dramatically. Rush (1985) attributes the improvement to low-cost sterilization and differential licensing (i.e. charging more for licenses for non-sterilized animals). However, Rowan & Williams (1987) present a possible alternative interpretation relating to changing demographics in the city leading to a decline in dog ownership. Their logic may explain some of the drop in licensing, but it does not explain the change in sterilization figures. The authors argue that the clinic was not responsible for most of the change in sterilization figures since they estimate that 8,000 out of approximately 75,000 sterilizations were performed by the clinic and the rest by veterinarians. However, their estimates of the total number sterilized are based on a probably inaccurate assumption that dogs switching owners or going into shelters are licensed in the same proportion as dogs in general. The authors also cite a study by Grayhavens (1984) as support for the view that a licensing drive did not increase the number of animals spayed and neutered. However, their logic is faulty here, confusing the number of dogs spayed/neutered with the percentage. The authors state that since the number of dogs licensed went up 48% but the percent altered only went up 4%, spay/neuter behavior was not effective. However, the study says just the opposite if one assumes that the marginal owner (the ones affected by the drive) had a lower spay/neuter percentage than owners who normally license their dogs. The authors do also cite evidence from shelter statistics between 1980 and 1985 indicating that differential licensing programs were correlated with a reduction in animals handled.

Other evidence on the sterilization issue includes a study of Colorado Springs by Arkow (1985). The presence of a sterilization program in that community was correlated with a significant decline in the number and percentage of the total pet population handled by the shelter.

Schneider (1975) argues that low-cost neutering services are not a good solution and instead advocates that controlling demand is the key to reducing the excess dog population. However, his conclusion is partially based on the high turnover rate found for animals in the study area. In addition, older animals were found to have higher spay rates (but of course this is logically inevitable since once an animal is spayed it stays spayed, unless spayed animals die at a higher rate). From these facts Schneider concludes that owners are reluctant to spay animals because they may not stay long in the household. The flaw in this logic (other than its weak factual basis) is that owners who are reluctant to spay/neuter animals for this reason may be particularly sensitive to the price of the procedure since they allegedly are making a probability-based cost-benefit calculation.

According to MacKay (1993), "the belief that cost is an important barrier to sterilization has never really been borne out in any major survey" (p. 920). Yet a page earlier, the author states that comparison shopping has made the surgery unprofitable for veterinarians, which would seem to imply that consumers are very price sensitive for this service. Even if we accept the author's claim that no major survey has shown that cost affects sterilization rate, he does not cite any evidence showing the opposite is true, and in the absence of evidence it would appear to be reasonable to assume that cost plays some role. The author also estimates that 95% of sterilizations are done by private practice veterinarians.

Hodge (1976) cites the decrease in pet reproduction during the early 1970's as evidence that low-cost spay-neuter programs work, although he also gives credit to enforcement and education programs. He also points out that sterilization can reduce behavioral problems which are a major cause of pet abandonment.

Beck (1983) also concludes that there is little evidence that people use spaying programs, citing statistical evidence from Beck (1974) and Modern Veterinary Practice (1973a, 1973b), so therefore he concludes that spay and neuter programs are "much ado about nothing".

Clearly, expert opinion remains divided regarding the importance of sterilization. More rigorous analysis needs to be done on this topic. More empirical analysis is also needed, however it is important to model the theoretical impact of a sterilization program, something which has not yet been done in the literature on this topic. The model created here allows us to do just that. The graph below shows how the euthanasia rate changes as the spay/neuter rate is increased. To make the percentages easier to interpret, the spay/neuter rate is shown in terms of the percentage of the population that does not spay/neuter their dog. As the graph indicates, a reduction of 46.8% in the percentage of dog owners who do not spay/neuter their animal will result in a region with dynamics similar to the New York State Capital Region being able to sustainably maintain a no-kill policy. In other words, if about half of the people who do not spay/neuter their animal could be convinced to change this behavior, such a region could become "no kill" for the dog population. It should be noted that the euthanasia rate used here is the long-term steady-state value. This steady state can take a surprisingly long period of time to achieve. Time-scale issues will be discussed in more detail later.

The solid line charts the actual data while the dotted line is a straight line with the same starting and end points. In economic terminology, the straight line indicates constant returns as treatment level increases. As indicated, the actual data lies below the straight line. This demonstrates that increasing spay/neuter levels shows diminishing returns. In other words, as more and more people spay and neuter their animal, additional increases in the spay/neuter rate show less benefit. Changes to the spay/neuter rate near the top of the curve show about twice as much benefit as the same amount of change near the bottom of the curve. However, even as society approaches "no-kill" dynamics near the bottom of the curve, changes to the spay/neuter rate still have a powerful impact

The chart above does not give the full picture regarding the effects of spay/neuter programs since the time dimension is not included and since the time element is not included. The graph below gives a better understanding of the change in death rates over time. This graph shows not only the change in the euthanasia rate (D3), but also the effect of the spay/neuter rate on the death rate of strays (D2) and owned dogs (D1). As indicated, even after more than 20 years, the full impact of a one-time permanent increase in the spay/neuter rate is still being felt. In fact, though the chart does not extend this far, it takes approximately forty years for the death rate to stabilize at its new level. A decrease of 27 percent in percentage of people not spaying/neutering their animal is used in this chart. This percentage was used because 27 percent of people surveyed who did not spay/neuter their animal said they would do so at a lower price. Therefore, this chart gives the potential impact of a subsidized spay/neuter program. This is a potential two-thirds reduction in the number of animals euthanized from a program giving financial incentives to spay/neuter dogs.

If we take the average cost of a spay/neuter procedure to be approximately $100 (Preece & Chamberlin, 1993), according to the survey results, the spay/neuter rate increases approximately linearly as the price of the procedure is reduced. From this information, and regional demographic information, the impact per dollar spent on a spay/neuter program can be calculated. Two cost efficiency measures are calculated in the table below. The "minimum" measure gives the percentage improvement in the euthanasia rate per thousand dollars spent per year assuming the cost of the program is at its minimum. The minimum cost assumes that the number of people using the spay/neuter program is exactly equal to the number of households in the marginal spay/neuter population. The "maximum" measure assumes that all consumers who have the option switch to the low-cost program increasing the financial burden on that program. The studies on spay/neuter programs previously cited indicate that most people still prefer to go to traditional full-cost veterinarians for their spay/neuter procedure even when subsidized spay/neuter programs are available. Therefore, the actual cost of these programs may be closer to the minimum value.

Table 3: Percent change in average annual euthanasia rate per $1,000 spent

An alternative method for increasing spay/neuter rates besides financial incentives is to conduct an public information to educate/encourage the public to spay/neuter their animal. Media campaigns for similar causes have been very effective at times on other issues. One obvious example of a successful public relations effort is the campaign by animal rights organizations to discourage the public from wearing clothing made with animal fur. Since the results of such a campaign can vary greatly, the cost effectiveness cannot be estimated with great precision. However, we can arrive at a rough approximation. The information on the first three lines of the table below is adopted from Ad Resource (2000).

A conservative assumption would be that an effective campaign will need to use a mixture of media rather than simply the most cost effective medium. A further conservative assumption used here is that the campaign reaches residents at random rather than being focused on a particular population. A well-targeted campaign may be able to reduce costs further by focusing on likely dog-owners who may not spay/neuter their animal. Using these assumptions, the cost effectiveness for an education campaign appears to be in roughly the same range of the low-cost spay/neuter program. It should be noted that the cost of a subsidized spay/neuter program must be paid every year while a one-time education program could have long-lasting effects. Below is the cost effectiveness of an education program assuming different frequencies of the campaign.

Table 5: Percent change in average annual euthanasia rate per $1,000 spent

A second method for reducing euthanasia rates is to increase the adoption rate. It is important to recognize that adoption rates can be increased from two possible sources which have quite different long-term impacts. One way to increase adoption is through substitution of sources (i.e. people who would otherwise purchase their dog from a different source). The other source of increased adoptions is the "marginal consumer", people who would not have purchased a dog at all if they had not been encouraged to adopt. The graph below gives the impact of increasing adoptions through substitution. If the adoption rate increases 90% through substitution, the region can become sustainably "no-kill". The graph also shows approximately constant returns to scale, with the dotted straight line appearing almost directly below the data points. Once again, the euthanasia rate used here is the steady state value.

As the graph below indicates, the results for increasing adoption by new dog owners is dramatically different than the results for increasing adoption by substitution of sources. Using the euthanasia rate 100 years after treatment, the adoption rate would have to increase 656% using new dog owners to eliminate all euthanasia (compared to an increase of 90% for substitution of sources). Also in this case, three data series are shown. This is because the impact of the treatment is quite different depending on what time period is considered.

Looking at the impact one year after treatment, euthanasia reaches zero when the adoption rate is increased close to 100%. However, looking at euthanasia after 30 years or after 100 years, the effort required to reach "no kill" increases dramatically. Intuitively, this is because the number of pet owners has increased due to the higher adoption rate, which causes more abandonment and reverses much of the benefits of the increased adoptions. It should also be noted that returns to scale are close to constant.

There are several methods that could be utilized to increase adoption rates. The first is to educate the public in the same way that one would with a spay/neuter education campaign. Many consumers make their animal purchase decision without an awareness of the impact buying from a breeder or pet store versus adopting an unwanted animal has on the dog population. Making the public aware of the impact of their choice could have a powerful impact. A second approach that can be taken through the media is to focus on marketing the product rather than on an altruistic message. This can be done by aggressively advertising animals for adoption, both through the media and through events and appearances. A third method of encouraging adoption is through financial incentives. Theoretically this could be through subsidies for adoption or taxes on dogs from other sources. However, there are problems with reducing the price of adopted dogs. First, lower purchase prices have been associated with higher abandonment rates (Patronek et al, 1996). Second, dogs that are too cheap or free can be purchased for illicit purposes such as to resell for research or for other abusive uses. In addition, subsidies require funding while taxes can generate public funds. Therefore, the mechanism most often discussed for financial incentives is taxes rather than subsidies.

An alternative to taxes would be restrictions on the breeding market that act to limit this source of supply. Many animal shelters are proposing legislation to ban or restrict the breeding of companion animals in their communities and states (Rowan, 1992). This is opposed by animal breeders, since it directly impacts on their livelihood. Strand (1993) presents the breeder's perspective on this issue, arguing that breeders make significant contributions to animal welfare causes and help advance the case of animal welfare. However, in the same article, the author makes some statements that some animal welfare advocates would find quite suspect, including advocating that all deaf Dalmatians be euthanized.

If breeding restrictions act to limit this source of supply, the social impact is similar but not identical to a tax on breeding. Because the social impact of a tax can be more readily analyzed, the impact of a tax is used as one option as well as a proxy for other options restricting supply. If we use the same average response rate as for a spay/neuter campaign, the table below gives the change in the euthanasia rate per $1,000 spent on an adoption campaign that assumes substitution and otherwise using the same assumptions and time period as in the prior table.

Table 6: Percent change in average annual euthanasia rate per $1,000 spent

As shown, the cost efficiency of the adoption program is somewhat lower than that of the spay/neuter campaign, particularly over time horizons of 30 years or longer. However this may not actually be the case. All the campaigns are assumed here to have the same response rate. However, in reality these campaigns will have varying response rates. It is quite possible that the public would be more responsive to an adoption campaign. There are a number of reasons for this. Although there is still misinformation and ignorance about spaying/neutering animals, the public is generally more aware of the importance of spaying/neutering than they are aware of the connection between their animal purchase choices and euthanasia rates. In addition, while the spay/neuter choice is usually well thought out, dog purchases are sometimes impulse decisions, which may be more easily affected through marketing efforts. It is quite possible for the response rates to differ enough to make an adoption campaign more cost efficient than a spay/neuter campaign. It should also be noted that though a public education campaign promoting adoption and a marketing campaign focusing on the product are quite distinct in practice, for purposes of the theoretical model, the results are identical since the same response rate is assumed.

The cost of the third option to promote adoption, financial incentives, can be estimated using the economic concept of producer and consumer surplus. Based on the results of the survey, a tax that brings the purchase price of a dog to $1,500 could change the behavior of 38% of the relevant population so that they purchase their next animal from a shelter. However, over a $1,000 tax is very high and most likely politically unfeasible. If we instead assume an after tax purchase price of $700, this would change the behavior of 24.7% of the relevant population (assuming actual behavior corresponds with reported behavior). According to the survey results, the average purchase price of a dog from a breeder was $412 and the average purchase price of a dog from a pet store was $474. Taking a weighted average of these gives an average purchase price of $427 which implies a tax of $273 per dog.

The benefit in terms of improved animal welfare can be calculated from the model. However, a more difficult question is the cost of this tax. There is no direct cost to the program (assuming administrative costs are low) since revenue is actually generated from the tax. However, there is a social cost in lost consumer surplus and lost producer surplus. Generally, speaking, the consumer surplus represents the utility consumer's receive from a good in excess of its price, while the producer surplus represents the profit received by the supplier of a good above the cost of production (for further discussion of the concepts of producer and consumer surplus see Hicks, 1941). Theoretically, the size of the producer and consumer surplus should take into account any negative economic effects of reducing or eliminating sales of dogs from breeders and pet stores.

The graph below is adopted from the data in the survey results section indicating how many people would switch to adopting dogs if the price of animals from other sources increased. The graph below converts the data into a standard demand curve so that the consumer surplus can be determined. In addition to the downsloping demand curve segment shown, a flat line indicating the amount of the tax is shown. The lost consumer surplus is the area between points ABC. Approximating this area as a triangle gives a lost consumer surplus of $80,020. Other consumers outside of this triangular area do lose money from the tax, but the loss for these other consumers is a transfer rather than a deadweight loss.

Figure 8: Consumer surplus lost from a tax on dogs from non-shelter sources

Calculating the lost producer surplus is a more difficult matter since we do not have the data to construct a supply curve. In fact, there really is no way with the data currently available to accurately estimate producer surplus. For lack of a better method to estimate this value, producer surplus will be assumed to be approximately equal to consumer surplus, giving a very rough deadweight loss estimate for the tax program of $160,000.

Since the result of this treatment is qualitatively the same as the public education program to increase adoption (i.e. both programs hopefully would cause people to substitute adoptions for other dog purchases), the cost effectiveness of these two programs can be compared directly without recreating the welfare impacts of this treatment. The cost of the public education program is estimated to be approximately $25.56 per adoption generated while the social cost of the tax is only $9.91 per adoption generated. On the surface, the tax appears more efficient, however this assumes that the administrative costs of the tax are minimal, that it is enforceable, and that it is politically feasible.

One final approach a public education campaign could take is to focus on reducing abandonment rather than adoptions or spay/neuter behavior. The campaign would educate people regarding the serious decision involved in taking on a pet, make more tangible the suffering and death caused by animal abandonment, and encourage people not to take on dog ownership unless they understand the costs, responsibilities, and time involved in responsible dog ownership.

The graph below indicates the reduction in the abandonment rate required to reach a no-kill level. A campaign to encourage dog purchasers to be responsible and think hard before making a purchase may actually reduce dog purchase rates as well as abandonment rates. However, in this graph, abandonment was assumed to be reduced without changing the number of dogs purchased. As in the previous graph, because of widely varying effects over different time horizons, the euthanasia rate is shown for 1 year, 30 years, and 100 years.

As indicated, the abandonment rate must be reduced about 70% to stop euthanasia in one year. However, abandonment rates must be reduced 96% to keep the euthanasia level at zero for 100 years. But the most interesting part of the graph is the shape of the curve as the time horizon changes. At a 100-year horizon, euthanasia sharply goes up before it declines. This is due to a sharp dog population increase that occurs under the assumptions used in this treatment. It was assumed under this treatment that birth rates (per dog), pet purchases, and adoptions remain stable even though abandonment rates go down. Therefore, the dog population increases and the number of dogs abandoned increases in some cases even though the abandonment rate goes down.

Using the same general assumptions as used in the spay/neuter and adoption campaigns already discussed, the table below gives the cost efficiency of a campaign stressing responsible ownership/guardianship in order to reduce abandonment.

Table 7: Cost-Effectiveness of reducing abandonment

As shown, this type of campaign is generally less cost-efficient than the other options already discussed. However, two caveats must be stressed. First, as previously mentioned, all types of campaigns are assumed to have the same response rate. Since a generic campaign response rate has been assumed here, the actual relative cost-efficiency may be higher or lower depending on the public's responsiveness to this type of campaign. Second, it should be noted that a campaign to encourage responsible ownership may have other positive effects outside of changing the euthanasia. Such a campaign may improve the quality of life for dogs in addition to improving euthanasia rates.

Although we have analyzed the effect of a variety of treatments individually, an interesting and important question is what effect combining treatments has on euthanasia rates (i.e. are there synergies or possibly reduced effectiveness when combined). This question can be answered by using the economic concept of a production possibilities frontier (PPF). A PPF curve shows all the combinations of two inputs that can be used to achieve a certain level of output. PPF curves were created for different pairs of treatments. A goal of reducing euthanasia by 50% over a 30-year horizon was chosen to calculate the PPF.

The graph below shows the PPF curve for different levels of improvements in spay/neuter rate and adoption rates.

The axis for adoption indicates the percent increase in the adoption rate from its starting level. Adoption is assumed to be through substitution in all the PPF curves. The spay/neuter axis indicates the percentage decrease in the number of people not spaying/neutering their dog. The dotted curve is a straight line, while the actual data (solid curve) plots slightly below this line, indicating that less resources are required in combination than when the two treatments are done separately. In other words, there are some synergies when the two treatments are done in combination.

However, the other two PPF curves show the opposite situation. The curve below shows spay/neuter combined with reduced abandonment.

The abandonment axis indicates the percentage reduction in abandonment rates. For the sake of consistency with the prior "no kill" simulation, it was once again assumed that abandonment rates were reduced without affecting other model variables. The curve lies above the straight dotted line, indicating that more resources are required when the two treatments are done in combination than when they are done separately. Somehow, these two treatments hamper each other's effectiveness.

The final PPF curve below shows abandonment and adoption treatments in combination. Once again, the actual data lies above the dotted line indicating that these two treatments also hamper each other's effectiveness when combined.

Often, fairly long time horizons have been utilized here to address the question of sustainability and long-term steady state. However, a very important question to a community or organization that decides to spend a large amount of money on an effort to address the surplus dog population problem is how long they need to wait for the treatment to show full effectiveness. Once again using the simple goal of reducing euthanasia rates, the following graph shows how the euthanasia rate changes over time for various treatments. The level of each treatment is chosen to create a 50% reduction in euthanasia rates (compared to the before-treatment rate) after 30 years.

The chart shows that the spay/neuter treatment benefits occur gradually, and stabilize given this level of treatment after about forty years. Increasing adoption rates through substitution shows immediate and permanent benefits, with only a slight change over time. Adoption by adding new dog owners also shows immediate benefits. However, this benefit decreases over time as the dog population rises. Eventually, the benefit appears to stabilize at a new reduced level. Decreasing abandonment rates also shows immediate benefits if it is assumed that this variable can be changed in isolation. However, these benefits disappear as the dog population rises. On the other hand, if we assume that abandonment can only be reduced by deterring likely abandoners from purchasing dogs and we assume two dog purchasers must be deterred to eliminate one abandonment, then the abandonment treatment has exactly the opposite pattern over time. Initially, the euthanasia rate is high (this is due to adoptions going down along with other sources of animal supply). However, this euthanasia rate goes down rapidly, and eventually becomes the lowest of all treatments on the graph.

The results here demonstrate that there are several cost-effective methods of reducing dog overpopulation. Which method is most cost-effective depends in part on the time horizon used. However, it appears that spay/neuter campaigns may be the most powerful over long time horizons. Cost effectiveness numbers are shown here because allows a common unit for the comparison of programs. It must be noted however that these cost-effectiveness numbers are rough estimates at best. They are best interpreted as level-of-magnitude estimates of costs rather than precise forecasts since public responsiveness and a number of other key variables are not known with certainty. Well-monitored pilot programs would be the ideal method for testing these costs. This research provides valuable information to such programs by giving information on what programs are likely to be most effective.

The research here also provides valuable information for evaluating such programs. For example, since spay/neuter programs can take over thirty years to reach full effectiveness, actual efforts to measure the full-effectiveness of such programs often will underestimate the long-term impact. Spay/neuter evaluations must be done with very long lags or at least done in such a way as to extrapolate future impacts.

The results here also counter the arguments made by some veterinarians that spay/neuter programs are ineffective because it is contended that they only reach a small percentage of the population. In fact, because of the powerful impact of birth rates on population dynamics, even a small change in birth rates can make a dramatic difference in long-term euthanasia rates.

Despite the caveats regarding cost measures being approximate, they still do give a rough idea of what it would take to get to a "no-kill" society on a regional basis. Comparing these numbers to community willingness-to-pay measures for the Capital Region in New York (Frank, 2001), the costs are generally a level of magnitude lower than society's willingness to pay at least for this region. Therefore, even with rough numbers it is safe to say that "no-kill" is achievable for a cost acceptable to society. Or in other words, if we view dog overpopulation from purely a human perspective, the benefits for humans of reducing dog overpopulation outweigh the costs to humans of reducing dog overpopulation.
Although these estimates still rely on a number of assumptions, the non-monetary measures of what it takes to reach no-kill from the model are known with a higher degree of certainty. For example, knowing that it takes a 47 percent change in the number of people who do not spay/neuter their dogs or a 90 percent increase in the adoption rate to reach no-kill for a region with certain demographic characteristics can benefit decision-makers by improving long-term planning and goal-setting for a campaign aimed at reducing companion animal overpopulation.

As more and more humans express concern regarding dog overpopulation and increasing numbers of non-profit organizations work to achieve a no-kill society, it is important to understand how various programs interact and how their effectiveness changes over time. On this front, it appears that increasing adoption or spay/neuter rates fares better than focusing on reducing abandonment. In fact, it is encouraging to note that adoption and spay/neuter programs appear to work better when done together.

The results here also highlight the importance of issues that often are not considered. When setting goals or measuring results, time-scale is key and must be given careful consideration. When planning adoption programs, in terms of long-term animal population dynamics, who adopts makes a difference. In addition, if efforts are made to discourage abandonment, reducing abandonment rates without reducing birth rates can actually lead to more euthanasia long-term due to a growth in the animal population.

In order to draw realistic conclusions from the model, data from a particular U.S. region was obtained. However, this does not imply that the results here cannot be generalized to the communities across the United States or internationally. Although the precise quantitative parameters will of course vary, many of the qualitative conclusions of this study are applicable to a wide range of communities.

Dog overpopulation is a human problem, with human costs and deriving from human sources. The dynamics of the problem also depend primarily on human behavior and population dynamics. It also is a problem that can only be addressed through human solutions. However, the good news is that there are adequate and cost-effective solutions, and these solutions have more human benefits than human costs.

Ad Resource, 2000. "Do-It-Yourself Media Buying, Part III", 12/6/200, (available online

at http://adres.internet.com/feature/article/0,,8961_527721,00.html).

Arkow, P. S. 1985. Animal control, birth control and community education: impacts on

Colorado Springs pet population. Proceedings of a Workshop on Animal Control,

Wilson, A. K. & Rowan, A. N. (eds.) pp. 30-48, Tufts Center for Animals, Boston.

Arkow, P., 1994. "A New Look at Pet 'Overpopulation'", Anthrozoos, 7(3)202-205.

Baetz, A. 1992. "Why We Need Animal Control", 1992 First National Urban Animal

Management Conference, Brisbane.

Beck, A. M. 1983. "Animals in the City," in New Perspectives on our Lives with

Companion Animals, Katcher, A H & Beck, A M (eds), University of Pennsylvania

Press, Philadelphia.

Beck, A. M. 1973. The Ecology of Stray Dogs: A Study of Free-Ranging Urban

Animals, York Press, Baltimore.

Beck, A. M., Loring, H., & Lockwood, R., 1975. "The ecology of dog bite injury in St.

Louis, Missouri", Public Health Reports, 90(3): 267-269.

Carding, A. H. 1969. "The Significance and Dynamics of Stray Dog Populations with

Special Reference to the U.K. and Japan." Journal of Small Animal Practice,

10(7):419-46

Carter, C. N., 1990. "Pet population control: Another decade without solutions?"

Journal of the American Veterinary Medical Association, 197:192-195.

Fox, M. W. 1990. Inhumane Society: The American Way of Exploiting Animals, St.

Martin's Press, New York.

Frank, J. 2001. "A new economic paradigm for addressing dog overpopulation and the

effectiveness of policy alternatives," Doctoral Dissertation, Rensselaer Polytechnic

Institute, Troy, NY.

Friedmann, E., Katcher, A. Eaton, M., & Berger, B., 1984. "Pet Ownership and

Psychological Status", in The Pet Connection: Its Influence on Our Health and Quality

of Life, Anderson, R. K., Hart, B. L., & Hart, L. A. (eds.) Center to Study Human-

Animal Relationships and Environments, Minneapolis.

Grayhavens, T., 1984. "The values of animal control", Community Animal Control,

May/June:8-9, 28-30.

J.R. Hicks. 1943. "The Four Consumer Surpluses," Review of Economic Studies 9, 31-

41.

Hirschman, E. C. 1994. "Consumers and Their Animal Companions", Journal of

Consumer Research, 20: 616-632.

Hodge, G. H. 1976. "The reign of dogs and cats' or contemporary concepts of animal

control", Management Information Service Report, Oct 8(10):1-20.

Jasper, J. M. & Nelkin, D. 1992. The Animal Rights Crusade: The Growth of a Moral

Protest, The Free Press, New York.

Jones, B. A. & Beck, A. M. 1984. "Unreported Dog Bite and Attitudes towards Dogs", in

The Pet Connection: Its Influence on Our Health and Quality of Life, Anderson, R. K.,

Hart, B. L., & Hart, L. A. (eds.) Center to Study Human-Animal Relationships and

Environments, Minneapolis.

MacKay, C. A., 1993. "Veterinary practitioners' role in pet overpopulation", Journal of

the American Veterinary Medical Association, 202(6):918-920.

Mackie, W. M. 1992. "It's time for early age neutering," Californian Veterinarian,

Nov/Dec:19-21.

Modern Veterinary Practice, 1973. "Spay Clinics: Boon or Boondoggle?" Staff Report,

Modern Veterinary Practice, March, pp. 23-29.

Modern Veterinary Practice, 1973. "Spay Clinics: The Other Side of the Story", Staff

Report, Modern Veterinary Practice, April, pp. 23-29.

Ory, M. G. & Goldberg, E. L., 1984. "An Epidemiological Study of Pet Ownership in

the Community", in The Pet Connection: Its Influence on Our Health and Quality of

Life, Anderson, R. K., Hart, B. L., & Hart, L. A. (eds.) Center to Study Human-Animal

Relationships and Environments, Minneapolis.

Pediatrics, 1994. 93:913-916.

Patronek, G. J., Glickman, L. T., Beck, A. M., McCabe, G. P. & Ecker, C., 1996. "Risk

factors for relinquishment of dogs to an animal shelter", Journal of the American

Veterinary Medical Association, 209(3):572-581.

Preece, R. & Chamberlain, L. 1993. Animal Welfare and Human Values, Wilfrid Laurier

University Press, Ontario.

Regan, T. 1983. The Case for Animal Rights, University of California Press, Berkeley.

Rowan, A. N., 1992. "Shelters and Pet Overpopulation: A Statistical Black Hole",

Anthrozoos, 5(3):140-143.

Rowan, A. N. & Williams, J. 1987. "The Success of Companion Animal Management

Programs: A Review, Anthrozoos, 1(2): 110-122.

Rush, R. I. 1985. "City of Los Angeles animal care and control", Proceedings of a

workshop on animal control, Wilson, A. K. & Rowan, A. N. (eds.) pp. 55-58, Tufts

Center for Animals, Boston.

Singer, P., 1975. Animal Liberation, The New York Review, New York.

Schneider, R. 1975. "Observations on the overpopulation of dogs and cats", Journal of

the American Veterinary Medical Association, 167:281-285.

Strand, P. L. 1993. "The pet owner and breeder's perspective on overpopulation", Animal

Welfare Forum, 202(6):921-928.

Thornton, G., 1991. "Veterinarians as members of the humane society", Journal of the

American Veterinary Medical Association, 198:1352-1354.

Wilson, E.O. 1984. Biophilia, Harvard University Press, Cambridge.