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Integrated Evaluation of the Efficiency of Diverse Strategies of Regulating Stray Animal Numbers in Urban Ecosystems

by Ye.A.Ilyinsky

Candidate of Biology, Biologist,
Moscow Peoples Friendship University of Russia, 2011 72 p.

Introduction;
Part 1. Model of the Factors Impacting Animal Population Numbers for Diverse Ecosystems;

Part 2. Adaptation of Stray Animals to Human Effect and to Interspecific Relations;

Part 3. Procedure of Assessing Population Parameters in Applying Various Strategies for Regulating Stray Animal Numbers;

Part 4. Appraising the results of the Neutering Strategy Regulating Stray Animal Numbers in Moscow;

Part 5. Pattern of Animals Pain-Sense Modalities Resulting from Various Strategies for Regulating Stray Animal Numbers;

Part 6. Causes for Cruelty as a Result of Applying Strategies for Regulating Stray Animal Numbers;

Conclusion;

Tables

able 1. Table of Dynamic Population Characteristics (000 individuals) in the absence of a Strategy for Regulating Stray Animal Numbers;

able 2. Table of Dynamic Population Characteristics (000 individuals), Using a Sterilization Strategy, with a parameter of 20% of Females in the Population Being Sterilized;

able 3 . Table of Dynamic Population Characteristics (000 individuals), Using a Sterilization Strategy, with 40% of Females in the Population Being Sterilized;

able 4 . Table of Dynamic Population Characteristics (000 individuals), Using a Sterilization Strategy, with a parameter of 80% of Females in the Population Being Sterilized;

able 5. Table of Dynamic Population Characteristics (000 individuals), Using a Strategy of Non-return Trapping with Consistent Annual Removal of 20; 12; 7; 5; 2,5; 1,25; 0,61 (000 individuals), Respectively;

able 6. Number of Citizens Injured by Stray Dogs (number of humans bitten by stray dogs) in Moscow during 2008-2010;

able 7. Table of Evaluating Humaneness of Animal Numbers Reduction Methods;

able 8. Pattern of Animals Pain-Sense Modalities Observed when Various Methods of Animal Numbers Reduction are Applied;

able 9. Comparative Characteristics of the Causes of Cruelty towards Animals and Causes for Such Cruelty, Depending on the level of Engineering and Technology Development.

Introduction.

       The problem of stray animals dogs and cats, has become a serious factor of adverse impact on the environment in the cities of Russia from the second half of the 1990s, when the consequences of an unreasonably high growth of commercial dog and cat breeding began to take toll. Industrialized countries of Europe and the rest of the world had faced the problem of stray animals 30 years earlier than Russia, on average, and in most countries the problem was solved successfully [24].
      As I noted in the earlier published survey [13], the roots of this problem are in the economic area because the society, having seen that commercial breeding of cats and dogs promised handsome profits, placed these animal species in the classical pattern goods-money-goods. Overproduction of goods is an inevitable satellite and attribute of the emerging capitalism, all indications of which were in evidence from the early 1990s in Russia, and, in order to preserve high value of the goods, capitalists are ready to destroy surplus of goods. The dogs and cats proved no exception: overproduction of these resulted in a mass of stray animals in the streets that nobody wanted and that had become homeless against their will: subsequent generations of these animals give birth to feral cats and dogs in the streets.
      Therefore, successful solution of the problem of stray animals shall be based on the state-devised economic measures of curbing overproduction of dogs and cats and equalizing supply of and demand for the animals in the situation of commercial breeding and of unwanted arrival of the brood from owned animals. Economic measures of this nature exist in the legislation of most countries that solved the problem of stray dogs and cats successfully and which, as I had been demonstrated earlier [13], are solved by introducing a three-link system of measures: (1) mandatory registration of all dogs and cats with identification marking (chipping, etc.) and assigning each animal to a particular owner, (2) differentiated taxation of the dog and cat owners (when in case of neutered animal ownership the tax is reduced substantially), (3) administrative liability and high penalties for animals appearing outdoors without the owner (this leads to the growing number of stray animals and results from abandoning animals or breaking by the owner the rules of animal care). The study of the world experience of handling the problem of stray animals indicates no state law aimed at improving the position of pets in no country of the world will ever be a success unless it includes the aforesaid three-link system of measures.
      However, the above economic measures are preventive actions. In addition to preventive actions, it is also necessary to introduce a system of measures applicable to dogs and cats that already became stray, i.e. the strategy of regulating the numbers of stray animals should be optimized. This paper deals with such complex issue as elaborating a criterion for evaluating and choosing the best strategy to regulate stray animal numbers. Until quite recently, the matter of search for complex criteria to compare the effectiveness of diverse strategies for regulating stray animal numbers has remained unsettled.
      The problem is that while comparing various strategies of regulating stray animal numbers, not only quantitative parameters of the population of the species being regulated should be taken into consideration, but also such crucial qualitative parameter as humaneness of the applied strategy.
       This paper presents exactly such a complex criterion, along with a procedure of comparing diverse strategies to regulate stray animal numbers by this criterion. In particular, by criterion elaborated, a most typical for practice case for comparing two alternative strategies for regulating stray animal numbers is considered: a strategy of trapping, neutering and releasing stray animals in original environments, hereinafter neutering strategy, and a strategy of non-return trapping of stray animals for state (municipal) animal shelters, hereinafter strategy of non-return trapping.

Part 1.

Model of the Factors Impacting Animal Population Numbers for Diverse Ecosystems

       There are some studies available [7, 23], where some regularities of changing animal numbers indicators, identified in natural ecosystems, are transferred to urban anthropogenic ecosystems. However, such an approach fails to take into account the principal distinction of an anthropogenic urban ecosystem from the natural one, which renders incorrect a mere transfer of mechanisms responsible for the functioning of these fundamentally dissimilar types of ecosystems. This principal distinction consists in fundamentally different factors affecting animals in natural and in urban anthropogenic ecosystems. The natural ecosystems are dominated by a bioresource macro-factor governing population regulation, when the major population parameters, including population numbers, are regulated in accordance with bioresources available to the population, the most important of these being environment-forming conditions (climate, landscape, shelters), food base and population density of predators that are after the species being regulated. Urban anthropogenic ecosystems, however, are dominated by a human macro-factor that governs population regulation, when basic population parameters, including its numbers, are regulated in compliance with the requirements and objectives of the human socium and exist subject to the purpose assigned to the urban areas. Thus, in urban ecosystems, the numbers of the population of a particular species are not in a proportional equilibrium with available bioresources, but are dependent on the usefulness of population existence to human socium in a specific territory. Therefore, there frequently emerge situations in a city, when there are sufficient bioresources required for the existence of a particular animal species, yet population numbers are definitely low and are not adequate to the resources due to the human regulatory activity.
       Indeed, the influencing factor model, or impacting model, in any ecosystem that determines population density of animals of a certain species in a territory shall, generally, be determined by the following main factors (their significance listed in decreasing order):
       (1) adequacy of environment-forming conditions for ion;
       (2) human effect;
       (3) density of natural food base distribution;
       (4) population density of predators that limit the numbers of a species;
       (5) population density of animals of competitor species (that pretend to an equal food and territorial resource);
       (6) population density of conspecifics.

       In this case, in natural ecosystems factor (2) human effect is usually insignificant, and in most cases this factor may be ignored.
       Let us consider now what main factors impact stray dog distribution density in urban conditions, i.e. in an anthropogenic ecosystem. For greater part of city territory and for most stray dogs, the effect of factors (3), (4), (5) may be ignored.
       As a matter of fact, observations indicate that except the woods and some hard-to-reach areas that occupy maximum 10% of city territory, the food base for stray dogs features virtually uniform distribution over the city area and is actually more than adequate thanks to factor (2) human effect.
       This factor manifests itself in systematic feeding of stray dogs by the so-called dog guardians and in a haphazard, but plentiful feeding of the dogs by people of all descriptions, especially near catering facilities or dustbins, where humans leave food wastes in an open form specially for dogs. Stray dogs are fat and overfed. Heaps of food waste leftovers uneaten by dogs are left to be consumed by rats and crows!
       Besides, there are no stronger predators in the city that would limit population density of stray dogs, and no rival species of animals to compete for territory and food resource. Rats and crows are not competitors but rather dogs commensals [14]. Homeless cats are unable to stage perceptible competition for stray dogs, either.
       Thus, there remain only these factors of the impact model for an urban system: (1) conformance of environment-forming conditions for life, (2) human effect and (6) the population density of conspecifics.
       Some surveys [7, 23], dealing with procedures of stray dog inventory, to enhance statistical accuracy of appraisals offer a method of urban environment stratification. In an urban area, they distinguish certain zones (strata) of roughly identical environment -forming conditions for the life of stray dogs; these zones have specific environment -forming constant values. Within a stratum, average statistic indicators of a population, including population density of the animals of a species being studied, vary insignificantly. For example, they set apart an industrial area, a residential construction area, a zone adjoining railway lines, a zone of major rivers and other more specificated zones. However, it is obvious that in the conditions of a megapolis the aforesaid zones are strictly anthropogenic areas, i.e. entirely developed or improved by man, and are designed to attain particular objectives of human socium and, accordingly, may change radically under the influence of man. Thus, factors (1) and (6) are also determined by the human effect.
       In this way, given the adopted model of affecting factors in the range of real indicators of an urban population, it is fair enough to consider as the prevalent factor in an urban ecosystem, factor (2) human effect, which may be subdivided into (a), (b), (c), (d):
       - deliberate human effect with a view to:
                     () enlarging the stray dog population; and
                     (b) decreasing the stray dog population;
       - unintentional human effect leading to:
                     (c) enlargement of the stray dog population; and
                     (d) decrease of the stray dog population.
       Let us ponder over this factor at some length.
      (a) Deliberate human effect to enlarge the dog population consists in the so-called street guardianship of stray dogs by the people, which results in a situation of an unrestricted food resource for stray dogs in an urban anthropogenic ecosystem. This makes the following assertion inapplicable to stray dogs: A population invariably responds to abnormally high mortality by higher rates of reproduction; this assertion was put forward by some researchers at the end of the 1990s [7, 23]. It is important to note that this particular postulate was fundamental in adopting the dog sterilization strategy in Moscow as the postulate was believed correct for stray dogs, and on the strength of this they believed there existed a certain law governing self-regulation of the population numbers in urban ecosystems. The above postulate applicable to natural ecosystems was proved by some scientists [8], who demonstrated there existed an inverse linear relationship between the birthrate and population numbers (vide Fig. 2). When an animal population of a species decreases, the females and younglings get a larger food base as the number of food competitors declines, whereby breeding power of females increases and a higher percentage of the brood survives. However, if part of the stray dog population in anthropogenic ecosystem is trapped, the food volume per individual will be the same, i.e. excessive; hence, there are no prerequisites for an extra rate of increase of the remaining part of the population.
      (b) Deliberate human effect to reduce the stray dog population in the RF is set forth in measures aimed at regulating stray dog numbers (Ordinance of the RSFSR Council of Ministers No 449 dated 23.09.1980 (with amendments dated 29.10.1992) On Regulating the Management of Dogs and Cats in the Cities and other Human Settlements of the RSFSR), since stray dogs constitute a factor posing a hazard to human life and health and has a detrimental impact on ecology. As a result of this, we see the density of stray dog population in an urban ecosystem to be mainly determined by the attitude of authorities of varying levels, by the performance of dog trapping services as well as the attitude of population towards dogs dewelling in the streets. Here, there exist three major strategies of regulating stray dog numbers:
      - non-return trapping strategy;
      - neutering strategy;
      - absence of regulatory strategy.

      Although on a practical level occasional trapping of the most problematic individuals or dog packs in response to peoples complaints and secret (shadow) destruction of stray dogs by people locally (at a production facility, in a yard) are practiced as methods of deliberate human effect on a population, such methods shall be regarded as the absence of the regulating strategy, because it indicates there is no consistent scheme of actions carried out by the authorities from a single center, leading to the forecast change of urban population indicators.
      (c) Unintentional human effect leading to enlargement of the stray dog population consists in population replacement with discarded pet dogs or their unwanted offspring as well as in food wastes left accessible to stray dogs in the streets.
      Unfortunately, legislation of the RF is not as advanced as that of most EU countries, USA, Canada and other industrialized states, where animals are subject to mandatory registration and measures intended to restrict the breeding of dogs and cats by their owners are set forth. RF citizens have no responsibility for abandoning of a pet animal or its unwanted brood. As a result of the unlimited and uncontrolled flow of animals that find their way to the urban environment from the population of pet dogs and pet cats, which, is by more than an order of magnitude larger than the stray animal population, there emerges the so-called problem of dog and cat overproduction. Thus, the problem of the lack of legislative control of the pet-dog and pet-cat population, combined with the problem of optimum approach to regulating the numbers of animals that became stray, produces the unresolved problem of the growing stray dog and cat population.
      As for the availability of food wastes, there is a number of published survey results, indicating that the presence of open dustbins leads to a certain extra source of food resources for stray dogs. The volume and quality of these resources, however, are incomparable with the volume and quality of food made available to stray dogs by their guardians. Therefore, it is precarious to say that unavailability of dustbins to stray animals will help to resolve the problem.
      (d) Unintentional human effect to reduce the stray dog population consists in stray dogs dying due to industrious economic or other human activity in the city, under the vehicles wheels, etc.

Part 2.

Adaptation of Stray Animals to Human effect and to Interspecific Relations

      We should also dwell on comparative appraisal of the ability of stray dogs and cats to adapt in an urban environment to human effect as well as to relations with other animal species, and on the role of this adaptation in the survival of the stray animal population.
      Some authors [7, 23] noted the emergence of the types of single stray dogs and packs that differed by survival strategies. Significant impact of a specific zone of stray dog ion (industrial zone, residential construction area, wooded zone, etc.) on peculiarities of their behavior. For example, there noted cases of recurrent behavior of single individuals of stray dogs: crossing the carriage-way using a pedestrian crossing at a green traffic light or underground train runs, or trips using a surface transport, each time with exit at a particular stop.
      In paper [12] observations are described, indicating a high degree of dogs learning ability, both within a pack, and between packs, regarding the hunting for stray cats. If a pack adopts an individual with hunting habits, after a while the entire pack becomes a zealous exterminator of cats. Similarly, neighboring packs assimilate the experience of hunting for stray cats; in this case, situations are known when packs unite or temporary groups of single individuals are formed for collective hunting for stray cats. Such observations were made in winter, and in some cases of collective hunting for cats imprints left on the snow clearly indicated that, hunting over, the temporary group of dogs falls apart and subsequent routes of individuals do not coincide. The above observations indicate a rather high degree of stray dog population adaptation to human effect and to interspecific relations in an urban environment.
      Observations of a stray cat population indicate that in conditions of neighborhood with stray dogs, stray cats are subject to a most cruel extermination by packs of dogs. This being so, unlike interspecific relations predators/victims in natural ecosystems, in an urban enironment, stray dogs do not eat the cats they kill, because dogs have other, more energy-wise lucrative channels of getting the food (usually, through the guardians). Thus, interspecific relations between stray dogs and stray cats may be described as predation (of dogs) without consuming the victims (cats). According to the data of observations conducted for more than 5 years in some districts of Moscow, it is noted that the stray cat population in the course of 2 years is half-regenerated; it should be noted that out of each 10 gone cats, 9 cats are the victims of stray dogs, meaning that in 90%of the cases, stray dogs are the cause of death of cats. In addition to this, low stress resistance of stray cats is noted.
      While observing behavior of stray and pet-cats [12], we succeeded in identifying two special forms of cat behavior, called phenomenon of stress-caused psychical inadequacy (hereinafter, briefly PSCPI): a rapid form of PSCPI and long-lasting form of PSCPI.
      A rapid form of PSCPI more often than not manifests itself in a state of panic, loss of orientation, Capgras paranoia, inadequate appraisal of the choice of a safe place, and may become the cause of death (e.g. from dogs, under the vehicle wheels, due to a fall).
      Owing to the experience of permanent contacts with cats, behavior of stray dogs evolutionizes as follows: the dogs seem to realize that cats have a rather low resource of neuropsychic resistance. If a cat, running away from the dogs, manages to jump somewhere or, by a miracle, hide itself (up on a tree, under a car, or on a structure element), the dogs start barking loudly and keep the cat in a state of shock for some time. In a few minutes, some cats lose psychic control, grow panicky and usually try to run for life, i.e. they may well jump right into the dogs paws, this way going to their doom. In this manner, being in an extreme situation, then cats behavior becomes inadequate, which is proved by the cat moving from a safe hide-out to a place that spells danger to it.
      The long-lasting form of PSCPI is manifest largely in the states of depression, apathy, characterized by absolute indifference that sometimes end in death.
      The phenomenon of utter psychic stress is very common with home-bred pet cats that never left their home and all of a sudden found themselves outdoors (e.g. as a result of falling from the balcony). Once outdoors, the cats lose orientation completely, get Capgras paranoia, do not respond to the owners voice. Cats stress may be so strong that they can sit motionless for weeks at the same place having hid in a shelter of opportunity (most frequently, a basement) until they die of hunger (lapsing into a long-lasting form of PSCPI).
      The following phenomenon observed in Moscow today is also not uncommon: if a cat running away from the dogs, succeeds in finding a shelter (up on a tree, in a basement) and is sitting there quietly until the attack is over, the cat has a very strong stress. In the process, the cat may spend several days in the shelter, lapsing into a long-lasting form of PSCPI. This phenomenon has grown to be really wide-scale in Moscow: a cat driven by the dogs up a tree, at times to its top at the height of 15 m and more, will not climb down for several days, being in a state of PSCPI. Calls of animal rescuers to bring down cats driven by the dogs up the trees in spring and summer of 2010 were registered in Moscow virtually every day, there being up to 5 such calls a day. When the excessive stress caused by dog attack was too strong for the resources of neuro-psychic rehabilitation of a cat, the long-lasting form of PSCPI ends with death there and then.
      Let us consider this example of a situation when a cat survived but lapsed into a long-lasting form of PSCPI. The cat having lived in the street for several years, would come up to the people of its own free will, would often sit and go for a walk in an open space, it never hid itself. Then, after a pack of stray dogs settled in the yard, there followed a series of attacks. As a result, the cat stopped leaving the basement, but was trapped and brought in a home. Subsequent behavior of the cat may be described as absolute apathy. For moths, it would sit, having hid in the same shelter, virtually motionless, although there was no threat to it in the apartment. It was not until the cat made sure there was nobody in the room that it would come up to the food left for it. If the entrance to the shelter was closed, e.g. by a sheet of newspaper, it even did not try to get out of for several days to come up to the food and water, obviously thinking it was blocked and doomed.
      There were cases when a few days before they were destroyed by dogs, stray cats exhibited strange behavior, not typical of them. A cat that nearly every day was the object of dogs attacks suddenly began to enter the house front door and meow loudly for some reason, which it never did before. The cat was healthy and was not hungry. The door to the street at that moment was left open and one could hear the pack of dogs barking as if from afar. In a few days the cat died an excruciating death from the said pack of dogs. The cat had been a good mixer and cheerful. Apparently, it was unable to hide in the basement all its life, going out for food alone.
      The most adroit and lively cats that were subject to dozens of dogs attacks, escaping unhurt, demonstrated a phenomenon reminiscent of a suicide. In a situation, where these cats clearly were able to run away from the dogs, they unexpectedly stopped to resist (or lost orientation?), and the dogs killed them. It is possible that these cats simply were tired of struggling and living in permanent fear. Such behavior may be regarded as a variety of the long-lasting form of PSCPI.
      On the basis of the aforesaid observations, one can draw the following conclusion: a population of stray cats dwelling side by side with a stray dog population, is unable to adapt itself to such life due to a permanent high stress caused by dog-induced harassment.
      The result of a very low stress resistance and inability to adapt to permanent psychic commotions they experience in the course of dwelling outdoors is also reduced immunity against the background of stress, which leads to viral and infectious diseases in a large number of stray cats. A crucial factor of activation of viruses existing in an organism and transition of a disease to a pathological form is not always the presence of infection proper, but reduced immunity, which is known to be produced by a stress. Observations indicate that the organism of stray cats is incapable of struggling with the commenced disease on its own, and that without medicamental aid the cats shall be doomed. Besides, stray cat population shows a very high mortality due to infection in the nurtured broods of kittens as well as a phenomenon of the females refusing to feed the entire brood of kittens.
      Our conclusion that a population of stray cats is unable to survive, when dwelling side by side with a stray dog population is confirmed by the well-known concept of ecological strategies of population survival advanced by a number of authors [35]. Pursuant to this concept, successful survival and reproduction of a species is possible either through improving the adaptability of individuals and their competitiveness (C-strategy) or through intensification of reproduction (r-strategy), which recompenses a high death-rate of individuals and in critical cases makes it possible to restore the numbers quickly.
      The point is that cats and dogs, according to the aforesaid concept, belong under the C-type strategy of survival, because both the cat and dog population in a routine mode maintain the numbers of their populations by adapting to the environment (unlike the populations of rats, that, to a greater extent, are adapted by r-strategy). As was noted above, stray dogs cope with the task easily and get adapted to an urban anthropogenic environment quickly, most stray dogs getting adapted to human effect, too. However, this again occurs in a routine mode only when there are no total trappings by man and in the absence of stronger predators, e.g. wolves. Thus, some surveys [2, 25] indicate that as soon as a stray dog population begins to contact a wolf population (however small) closely, stray dogs are unable to get adapted to such a neighborhood and are forced to migrate, distancing their dwelling territory from the wolves. However, there are no wolves in an urban environment.
      Roughly, the same applies to a population of stray cats in an urban environment. Stray cats are unable to get adapted to the neighboring much stronger predators stray dogs, not only due to physical destruction by stray dogs, but essentially because of the permanent stress produced by daily harassment on the part of stray dogs. When daily stress is beyond the permissible threshold of routine adaptation of individuals, after which there follow the aforesaid stages of cats psychic deviations (PSCPI), we can observe a mass phenomenon when females stop feeding their offspring.
      Yet, unlike relations between stray dogs and wolves, where dogs have the opportunity to move their territory away from the wolves habitat, cats in an urban environment have no such opportunity, for they dwell in a rather small area that usually comprises several yards and basements of the neighboring buildings. And even if cats were capable of migrating over long distances, they would have nowhere to go, because in Moscow dogs spread across the entire city territory and hunt for stray cats everywhere. For this reason, the population of stray cats in the conditions of confined neighborhood with the stray dog population virtually becomes the dogs hostage and is doomed, which is confirmed by our observations.
      The nature of interspecific relations of the type of predation without consuming the victim is noted by researchers [14] in interspecific relations between stray dogs and not only cats, but also with representatives of numerous species of wild terrestrial urban fauna. Extermination by stray dogs of numerous valuable species of wildlife is a phenomenon that has long been known and is noted in the works of many authors [1, 2, 3, 4, 6, 9, 10, 14, 18, 19, 20, 21, 25, 26, 27, 31, 32, 33]. Work [14] lists 40 species of wild terrestrial fauna subject to predatory pressure by stray dogs. The official document of Moscow Government titled Moscow Red Data Book lists 6 species of animals, their numbers limited due to harassment on the part of stray dogs.
      The relatively recently published works [29] disproves the assumption advanced by some biologists earlier, regarding a substantial impact of stray dogs on rat population numbers. The said survey is conclusive because a statistically significant group of stray dogs were subjected to paunch openings which indicated the absence of rat consumption by the dogs.

Part 3.

Procedure for Assessing Population Parameters in Applying Various Strategies for Regulating Stray Animal Numbers.

      Indicators of Environmental Biocapacity
      There are known works [8], in which it is demonstrated that the growth of population numbers in the natural ecosystem takes the form of an S-shaped curve that reaches its maximum at a certain point C, corresponding to population saturation (vide Fig. 1). An indication of point C attainment shall be a condition: mortality (decrease) of the population is equal to birth-rate (increment) in the population. Thus, point C shall be an indication of natural biocapacity of the environment, at which saturation of the population reaches an equilibrium with bioresources of the ecosystem in case of the dominant bioresource impact model (no human effect). In this case, the basic mechanism of point C emergence is seen clearly. The said mechanism is associated with lack of bioresources needed for continued growth of the population, but essentially with lack of the food bioresource. In other words, while the population grows, it simply eats out the food bioresource, which causes a slow-down of the reproduction processes, because females (according to the genetically-determined law) give birth to as many broods as they are capable of nurturing [34].


Figure 1.

      However, as was noted above, there are always ample bioresources with respect to animal species under consideration dogs and cats in an anthropogenic urban ecosystem. Therefore, a surplus of the food base for our case rejects totally the mechanism of point C emergence, observed in natural ecosystems.
      It may be said that surplus of the food changes the type of the so-called r-curve that describes intensity of reproduction r in the population, depending on numbers of the population [8], which for a natural ecosystem drops in a linear fashion, when the population grows as shown in Fig. 2. In the case of an anthropogenic urban ecosystem for the population of stray animals this dependence is some averaged constant, as shown by a dot-and-dash line in Fig. 2, and does not depend on population numbers (in the range of actual numbers of the population).


Figure 2.

      It is also obvious that in the natural and anthropogenic ecosystems there act different mechanisms of diminution for populations of the species under consideration (dogs and cats). It was demonstrated in the researcher works [8] that in the natural ecosystems the population survival curve, depending on the age spectrum of individuals, may be of three types (vide Fig.3): the 1st type is typical of predators and highly-developed mammals, well-adapted to the environment, hardly, if at all, susceptible to the impact of larger predators. Most individuals of the 1st type live until old age average maximum of biological age of life and die a natural death, which it is correct to refer to as natural diminution of the population. Now, the 2nd type characterizes proportional mortality of the population age-wise, i.e. proportional age-wise diminution. And, finally, the 3rd type characterizes the unusually high mortality (diminution) in the younger age groups. The curve of wildlife dog species (canine) population survival and of cats (feline) in the natural ecosystems lies between the 1st and 2nd type, as shown in Fig. 3 by a dot line.
      According to observations carried out in the conditions of an anthropogenic urban ecosystem: () diminution of population individuals aged prior to sexual maturity equals 75% for kittens [12] and 78% for puppets [5]; and (b) average longevity of individuals in the population of stray dogs and cats equals, at best, 5-20% of average maximum biological age of life of these species. Thus, observations demonstrate [12] that average longevity of stray cats is 1 year, which equals 5% of average maximum biological age of life for the feline species of 20 years. For stray dogs, according to researcher observations [22, 24], the average age of life is 2-3 years, which makes not more than 20%, given the average maximum biological age of life for the dogs equals 15 years. Thus, in an urban habitat, the survival curve for the population of dogs and cats, depending on the age spectrum of individuals drops abruptly in the area of 1-3 years, i.e. it looks very much like the 3rd type, as shown in Fig. 3 by a dot-and-dash line. At the same time, most stray animals literally die, therefore it seems incorrect to refer to this process as natural diminution; rather, it should be assessed as man-induced diminution. For example, the cause for mass death of stray cats killed by stray dogs in Moscow in 2003-2009 was the neutering strategy, a dominant factor of human effect.


Figure 3.

      When considering an anthropogenic urban ecosystem, it is worthwhile talking about the emergence of the lower and upper limits of the environmental biocapacity.
      The upper and lower limits of the environmental biocapacity are the limits that determine the extreme (threshold) values of population numbers, at which the applied strategy of numbers regulation has no dominant impact any longer, and other man-induced factors start impacting the population numbers. However, the point to which population numbers will tend (strictly speaking, the sign of population numbers gradient) shall be fully determined exactly by the strategy of human macro-factor in the impact model. It will be shown below that if the applied strategy of stray animal numbers regulation is aimed at reducing the population, the population seeks within the limit to reach the lower limit of the environmental biocapacity. If the applied strategy of numbers regulation is aimed at enlarging the population, the population tends toward the upper limit of the environmental biocapacity.
      Yet, not posing the labor-intensive task of searching for strictly optimum strategies, we shall term suboptimal (progressive, the best) such strategies of regulating population numbers that will tend population numbers parameters toward the lower limit of the environmental biocapacity. Conversely, we shall term nonoptimal (regressive, the worst) such strategies of regulating the numbers that will tend parameters of population numbers toward the upper limit of the environmental biocapacity.
      For example, if nothing is done to trap and neuter part of the stray dog population for a number of years (as was the case in Moscow from 2001 to 2002), theoretically, estimates of the population may be quite high (vide Table 1). However, the actual numbers of stray dogs all the same will be limited and will equal the upper limit of the environmental biocapacity, because the population numbers will be curbed (this is sometimes incorrectly termed natural diminution) under human effect. Thus, in the absence of and even despite prohibited centralized trapping in 2007-2008, there began to emerge in Moscow, like mushroom growth, private services for shadow commercial trapping; uncontrolled regulation of stray dog numbers by population, mostly by poisonings, increased. A similar situation was observed in Moscow after 2003, when after applying the neutering strategy the percentage of neutered females in the packs of dogs was approximately 20%, and because the non-neutered females could not help reproducing, theoretical estimates of population numbers were rather high (vide Table 2). However, as Moscow inventory figures indicated [7, 23], the numbers remained at the level of 25 thousand, which is an eloquent testimony that the entire increment of the population was neutralized by human factor. The difference between population numbers in 1999 (21 thousand individuals) and in 2006 (25 thousand individuals) is small and virtually lies in the range of net inaccuracy of the population numbers estimates.
      On the contrary, if we apply the super-effective strategy of total preemptive trappings, even in such a case the population numbers shall not be zero, but shall tend toward the lower limit of the environmental biocapacity. The value of the lower limit of the environmental biocapacity shall be impacted by the issues unresolved legislatively: absence of control of breeding and situation in the area of overproduction of dogs causing concern; absence of differentiated taxation of animal owners; absence of mandatory registration and microchipping; failure, on a large scale, to heed the rules of dog management not only by natural, but also by legal persons at the car parks, in garages, in industrial zones and to observe some other social factors. The existence in the city of areas for selling and buying animals on animal markets and near the metro stations is conducive to a situation where representatives of a group of persons dealing in a particular business, the so-called scalpers collect unwanted puppets and kittens from the local population in these areas in order to receive money allegedly for accommodating the animals, later the same people plant boxes with these kittens in residential blocks.
      In theory, evaluation of the lower and upper limits of the environmental biocapacity is a rather complex math problem. We do not formulate such a problem in this paper. Here, we deal with the backbone of the notions and reasons for emergence of the upper and lower limits of the environmental biocapacity.
      With the accuracy sufficient for comparing various strategies, using the criterion suggested in the paper, let us take the values of the upper and lower limits found empirically on the basis of observing the population of stray dogs in 1999-2006 in Moscow.
      Taking into consideration and comparing the data on stray dog inventory in 1999 [23] and in 2006 [7], we note with good reason that stray dog numbers virtually did not change during the said 8 years. This enables us to regard the figure of numbers of 25 thousand individuals as the upper limit of the environmental biocapacity. Let us take into account that during the aforesaid time interval the neutering strategy was applied, which, as follows from Table 2-4, is a nonoptimal strategy of regulating the numbers and leads to an increase of the population numbers, i.e. tending the parameters of population numbers toward the upper limit of the environmental biocapacity.
      In the absence of experimental data that make it possible to judge the lower limit of the habitat biocapacity, let us assume that this limit should be at least by an order of magnitude smaller that the upper limit of the environmental biocapacity and should be equal to 2.5 thousand individuals.
      It is significant that the concept of the upper and lower limits of the environmental biocapacity is applicable to any area of an anthropogenic ecosystem, i.e. to any human settlement as human effect inevitably disturbs natural processes and actuates the mechanism of emergence of these limits. However, in practice, numerical value of the upper and lower limits of the environmental biocapacity may differ in different cities and human settlements, depending on numerous parameters of a specific anthropogenic ecosystem, and, besides, parameters of an anthropogenic ecosystem may, in turn, vary significantly within an interval of several years. Therefore, the values of the upper and lower limits of the environmental biocapacity are only true of the city of Moscow and, strictly speaking, only of a specific time interval, when estimates of population numbers were obtained in the city inventory data [7, 23]. At the same time, let us note once again that errors in assessing these limits do not affect the result of criteria application, since they equally and on the same side contribute to the strategies under consideration, therefore the effect of errors in assessing the upper and lower limits of the environmental biocapacity are recompensed in the comparison procedure.
      Furthermore, let us consider a procedure of obtaining numerical estimates for an area of population parameters implemented in practice, a procedure reflecting the criterion content (quantitative components). Criterion calculations boil down to two stages. At the first stage, the type of strategy applied is determined (nonoptimal or suboptimal), and on that basis a judgment is passed regarding strategy categorization (applicable or inapplicable). At the second stage, population diminution is determined (annual and total).

First stage of calculations:
determining the type of chosen strategy (nonoptimal or suboptimal).

       Point : Calculation of the tables of the population dynamic indicators for the conditions when there are no limitations for population behavior on the observation interval: the upper limit of the environmental biocapacity is equal to infinity, the lower limit of the environmental biocapacity is equal to zero.
      At the first stage of calculations, it is necessary to deduce a formula that would reflect to the maximum extent possible behavior of a numbers control strategy (i.e. maximum sensitive to the strategies applied, to evaluate the dynamics of parameters change for some isolated population on the observation interval of everal years; parameters under which there are no factors limiting the population. Thus, it is necessary to make a theoretical calculation for the condition, when the upper limit of the environmental biocapacity is equal to infinity, and the lower limit is equal to zero.
      The case of an isolated population, i.e. a population where animals are not replaced during the observed interval of years, is taken to adapt, to the maximum extent possible, the formula for the comparison of various strategies and obtain the result of comparing the diverse strategies without any other external impacts. It was noted above that in reality the urban population each year is replaced by pets due to the emerging new litter of pet animals, which animals constitute factors of unintentional human effect on population enlargement and contribute to increasing the absolute values of the upper and lower limits of the environmental biocapacity (in generally-accepted definitions). However, here we took into account that: () the aforesaid process of annual arrival of pet animals from their owners does not depend on the applied strategy of numbers regulation (using the definitions formulated in the Introduction) at all, as the process is fully regulated by legislative measures aimed at regulating the birthrate and curbing the breeding; this we mentioned in the Introduction, to the point of complete termination of the process of arrival of pet animals from the owner (minimization of the process to the values that may be ignored), and (b) the process of changing population parameters, resulting from the application of the numbers regulation strategy and the process of arrival of new pet animals from the owners are superposed independently from one another. Thus, at the end of the day, introducing in the formula of extra superposition of the micropopulations annually emerging from the owners with subsequent due consideration of their birthrate will only make the mathematical part of the criterion much more complicated, yet will add the unneeded extra noise to the formula component relating specifically to the comparison of strategies.
      Thus, with the assumptions made, the numbers of the population at the end of the i-th year, whatever the strategy and combination of strategies, shall generally be calculated as

Ni = (Ni-1 - Ni rem) (1 + Kp Kunneuter Ksex)                                                         (1)

      where
      Ni-1 population numbers at the end of previous i-th year,
      Ni rem numbers of individuals (males and females) removed from the population at the beginning of the i-th year,
      Kp average number of puppets given birth to by a female during a year,
      Kunneuter ratio of non-neutered females in total female numbers,
      Ksex sex ratio equal to the ratio of male and female numbers,

      Then population numbers at the end of the observation interval i = 1...Y years may be computed as the sum Σi i = 1...Y years

NΣ = Σi (N i-1 - Ni rem) (1 + Kp Kunneuter Ksex) = Σi Ni-1 - Ni rem + Ni p                             (2)

      where Ni p = Kp Kunneuter Ksex (Ni-1 - Ni rem) puppets litter numbers for the i-th year.
      We shall estimate population increment for the i-th year as

Ni Δ = Ni - Ni-1                                                                                                                           (3)


      Furthermore, on the basis of equations (1)-(3) we shall build up the values of tables of the population dynamic indicators.
      Below, examples for 3 most typical cases of applied strategies are given, and in Tables 1 5 the corresponding tables of the population dynamic indicators are cited.
      Since the table of the population dynamic indicators has one universal format, Tables 1-5 feature some intermediate or partially non-used parameters of the population that do not appear in an explicit form in formulas (1)-(3), such as:
      Ni fem - total number of females by the end of the i-th year;
      Ni neuter - numbers of neutered females by the end of the i-th year;
      Ni for neuter - numbers of females subject to neutering in the current i-th year;
      Ni unneuter - numbers of non-neutered females by the end of the i-th year;
      Ni p fem - number of females from the puppets of an annual litter in the i-the year.
       The aforesaid indicators are easily calculated from parameters listed in formulas (1) (3).

Point B: Calculation of annual and total diminution of the population on the observation interval: upper limit of the environmental biocapacity and lower limit of the environmental biocapacity have finite other-than zero values.

       The case of nonoptimal strategies:
       If as a result of applying the numbers regulation strategy, population increment is positive Ni Δ > 0 on the observation interval i = 1...Y years, i.e. population numbers tend toward the upper limit of the environmental biocapacity N lmt upper, such strategy shall be termed nonoptimal. Annual diminution for such a strategy shall be determined as

Ni dim+ = Ni - N lmt upper                                                                                                         (4)


      providing that Ni > N lmt upper, i.e. beginning from the year when population numbers Ni exceed the upper limit of the environmental biocapacity N lmt upper .
      Diminution of the population during the interval of nonoptimal strategy application i = 1...Y years shall equal

N dim+ Σ = Σi Ni dim+                                                                                                         (5)


      Considering that parameters of annual population increment do not change too much in the process, it may be assumed that

Ni dim+ = const = N dim+ ,                                                                                              (6)
N dim+ Σ = Y N dim+                                                                                                         (7)


      It may be said that in the case of nonoptimal strategies we deal with a lawn mowing effect, when the entire increment of the population resulting from the applied strategy that grew beyond the upper limit of the environmental biocapacity, is mown each year, turning into an annual diminution of the population.
      We shall group nonoptimal strategies with the class of inapplicable (non-recommended for application) in practice because these strategies in the area of implemented values of population parameters (e.g. % of neutered females in the population for neutering strategy) do not decrease annual diminution of the population and do not diminish the population numbers.

       The case of suboptimal strategies:
      If as a result of applying the population regulation strategy population increment is negative Ni Δ < 0 on the observation interval of i = 1...Y years, i.e. population numbers tend toward the lower limit of the environmental biocapacity N lmt lower, such strategy shall be termed suboptimal. For such a strategy annual diminution of the population for the i-th year

Ni dim- = Ni - Ni-1 = Ni Δ                                                                                                         (8)


      with the proviso that Ni > N lmt lower, i.e. on the observation interval, when population numbers Ni exceed the lower limit of the environmental biocapacity N lmt lower .
      Population diminution on the interval of the application of the suboptimal strategy i = 1...Y yers shall be equal to

N dim- Σ = Σi Ni dim- = Σi Ni Δ                                                                                                   (9)


      From Table. 5 it follows that it is possible to choose such parameters of removal rom the habitat implemented in practice, when annual increment for a suboptimal strategy on the observation interval of several years decreases year after year. For this reason, formula (9) is exactly the formula for calculating population diminution N dim- Σ for suboptimal strategies on the observation interval of i = 1...Y years.
      However, beginning from the year when population numbers, decreasing each year as a result of applying the suboptimal strategy, reach the level of the lower limit of the habitat biocapacity, application of the suboptimal strategy shall no longer lead to a negative increment. Thus, for the suboptimal strategy, population number will always tend towards the lower limit of the environmental biocapacity.
      Wee shall group suboptimal strategies with a class of applicable (recommended for application) in practice, since these strategies in the area of implemented values of population parameters (e.g. volumes of withdrawal from the habitat for a strategy of non-return trapping) shall reduce population numbers and reduce annual diminution of the population.
      Conclusion drawn from this criterion: with an acuracy of the assumptions made it can be argued that when a nonoptimal strategy is used, population numbers shall always be determined by the upper limit of the environmental biocapacity. At the same time, while using a suboptimal strategy within a fairly long interval of observations, population numbers shall be determined by the lower limit of the environmental biocapacity.
      This theoretical deduction makes it possible to substantiate the quantitative part of a complex criterion of evaluating the efficiency of a particular strategy. For this kind of evaluation it is possible to use:
      () rough criterion applicable or inapplicable the strategy based on the deduction as to whether the strategy is suboptimal or nonoptimal, and
      (b) accurate criterion for comparing diverse suboptimal strategies, which amounts to estimating the number of years for reaching the lower limit of the environmental biocapacity.

Second stage of assessments:
estimating population diminution.


      At the second stager of calculation, for nonoptimal strategies we introduce in formulas (6), (7) in calculations the real value of the upper limit of the environmental biocapacity, obtained experimentally on the basis of observations and then estimate annual diminution. In our case, the value of the upper limit of the environmental biocapacity (valid for the urban ecosystem of Moscow) is equal to 25 thousand individuals based on 8-year long observations of population numbers change.
      Thus, by the condition that if the chosen strategy is nonoptimaland then population numbers should tend towards the upper limit of the environmental biocapacity, let us take a certain reasonable time interval, for which population increment will be compensated. For example, for convenience of calculations, let us assume the compensation interval equal to 1 year.
      Then, for the case of using nonoptimal strategies of numbers control (such as neutering, when annual population increment is positive, which follows from Tables 1 4, it may be crudely believed that the part of population, which will annually produce population increment in excess of the upper limit of the environmental biocapacity, is transformed during the compensation interval into population diminution. As a consequence, population diminution during several years of the observation interval will be equal to annual diminution (6), multiplied by the number of years of the observation interval and will be calculated by formula (7).
      For the case of applying suboptimal strategies (such as non-return trapping, when annual increment is negative, which follows from Table 5), annual increment shall be compensated by removalal of part of the population for animal shelters and constitutes annual diminution (8). At the same time, population numbers tend towards the lower limit of the environmental biocapacity, which we assumed equal to 2.5 thousand individuals. In this case, combined diminution on the interval of observations shall be calculated by formula (9).
      The dutiful reader will note that formulas used for calculating population diminution take into consideration only population increments preconditioned by strategy application, but ignore, for example, diminutions as a result of diseases of stray dogs, from natural ageing of the population, death from the impact of aggressive environment of the megapolis, death caused by humans, etc. Nevertheless, we took into account that in practice annual diminution from the above factors amounts to several per cent of the population numbers. Whereas annual variation of population numbers, determined by a strategy of control pursuant to Table 1-5 are over 50% of population numbers. By this means, should one simply ignore diminution from the aforesaid factors as values by an order of magnitude smaller compared with diminution calculated by the above formulas, one will really not mare a gross error.
      Besides, it should be noted once again that the calculations are approximate , and their purpose is comparison of the strategies, therefore mistakes and assumptions made make an equal contribution and affect equally all strategies being compared, hence, as a result their impact is deleted.
      According to the criterion, formulas (1)-(3) may be used to examine various strategies and combinations of strategies, draw up tables of dynamic indicators of a population on any interval of observations and determine nonoptimality or suboptimality of strategies. Formulas for the calculation of annual diminution (6), (8) in these cases are also valid.
      To exemplify application of the criterion (quantitative component), let us take 3 most illustrative cases for the practice:
      () No strategy (on the entire interval of observation);
      (B) Neutering strategy (on the entire interval of observation);
      (C) Strategy of non-return trapping (on the entire interval of observation).
      Let us make calculations for particular basic parameters of population: sex ratio of males and females = 1, minimum number of puppets littered by the female during a year = 4 individuals, 2 male and 2 female individuals. A minimum number is taken to determine the lower limit of reproduction, the 4 puppets are not the average number of littered puppets in the brood, but the average number of puppets that survived and reached the age of adolescence [7, 23]. With such an approach, the subsequent calculations of estimated diminution do not include diminution of puppets at an early age (deaths resulting from infections, parasitogenic diseases and inviability of weak individuals).
      As they do, population parameters are not taken arbitrarily, but only those that have a practical meaning and are attainable in reality, i.e. are in the area of real solutions.

      Case : No strategy.
      At the first stage pursuant to formulas (1)-(3), we determine population parameters and fill out Table 1 of dynamic indicators of the population. From the results of Table 1 it follows that in the absence of any strategy, annual increment of population numbers is positive, hence, the absence of strategy is a special case of nonoptimal strategy. On the strength of this we come to the conclusion that population numbers will tend towards the upper limit of the habitat biocapacity, and annual diminution of the population will be calculated by formula (6).
      At the second stage by inserting the value of the upper limit of the habitat biocapacity in formula (6), we calculate annual diminution of the population and total population diminution (7) on the chosen interval of observation.

      Case B: Neutering strategy.
      At the first stage, for a number of values implemented in practice - 20%, 40%, 80% of neutered females in the population, according to formulas (1)-(3) we determine population parameters and fill out Tables 2-4. From the results of Tables 2-4 it follows that when the neutering strategy with chosen parameters is applied, annual increment of population numbers is positive. Consequently, the neutering strategy is nonoptimal. On the basis of this, we draw a conclusion that population numbers will tend towards the upper limit of the habitat biocapacity, whereas annual diminution of the population is calculated by formula (6).
      The dutiful reader will ask a reasonable question: why is there no table of dynamic indicators of the population for the strategy parameter of 100% of neutered females? The answer is this. The task formulated in this paper is to elaborate a practically useful criterion for work in the area of strategies really admissible in practice. Therefore, we do not go deep into the area of mathematical research with abstract value, trying to adhere to our real goal - find and show the strategies that are really applicable and can be implemented in practice.
      Even the parameter of 80% of neutered females in a population is recommended in the strategy manuals as a top mark which ideally one can only strive for, although on a practical level the mark is hardly attainable. For example, there exist data that in India and Greece, - the few countries where the neutering strategy is carried out at the state level and is heavily financed from the state budget, they managed, during the 12-15 years of the neutering strategy campaign, to raise percentage of neutered females to 50% only, and the dynamics of this parameter in those countries is actually nil. And the fact that in Moscow, during the5 years of the neutering strategy campaign they only succeeded in raising the percentage of neutered females in the population to 20% [7] is indicative of the same.
      Therefore, we group the neutering strategy with a class of in applicable in practice as no strategy parameters (% of neutered females) have been found among those that can be implemented, so that the neutering strategy should reduce he population numbers and its annual diminution. At the second stage, by inserting the value of the upper limit of the environmental biocapacity in formula (6), we calculate annual diminution of the population and total diminution of the population (7) on the chosen interval of observation.
      Assessments appearing in Table 2 correspond to the actual situation in Moscow, when during the 7-year interval of the neutering strategy application from 2002 to 2009, the numbers of stray dogs were not lower than the upper limit of biocapacity of 25 thousand individuals, and at the same time percentage of neutered females never exceeded 20% [7]. From this it follows that during the period of 7 years, a population of at least 40 thousand individuals was destroyed (meaning that, based on all-city records [7, 23], 80% of females remained unneutered and these were to litter at least 40 thousand puppets a year, at the same time population numbers never increased, hence minimum 40 thousand individuals were destroyed each). In all, during the 7-year interval of the neutering strategy application the number of individuals disposed of amounted to no less than 280 thousand.

      Case C: Non-return trapping strategy.
      At the first stage, for a number of practicable values of consistent annual withdrawal of population (non-return trapping for animal shelters) 20,000, 12,000, 7000, 5000, 2,500, 1,250, 0,61 thousand according to formulas (1) (3) we determine population parameters and fill out Table 5. From the results of Table 5 it follows that in the case of the strategy of non-return trapping, applying the chosen parameters, annual increment of the population numbers is negative. Hence, the strategy in question is a suboptimal strategy. On the strength of this, we deduce that population numbers will tend towards the lower limit of the population, while annual diminution of the population is calculated by formula (8).
      At the second stage, using formulas (8),(9) we calculate the respective annual diminution of the population and total diminution of the population on the chosen interval of observation, taking the value of the lower limit of the environmental biocapacity equal to 2.5 thousand individuals.
      Thus, it can be roughly believed that on the 7-year interval of applying the strategy of non-return trapping, the numbers of stray dogs will tend towards the lower limit of the environmental biocapacity. It also follows from Table 5 that the numbers of individuals that should be withdrawn for animal shelters will, during the first three years be diminishing annually by approximately 60%.
      The data given in Tables 1-5 for the 2-year period of observation are presented in Fig. 4, where the lower and upper limits of the environmental biocapacity are shown, too.


Figure 4.


      In this manner, we have obtained a procedure for quantity estimates the first component of the criterion. And have given real examples of using the quantitative component of the criterion to compare the actually used strategies of regulating the population numbers.

Part 4.

Appraising the Results of the Neutering Strategy Used to Regulate Stray Animal Numbers in Moscow


      In May of 2009 the neutering strategy in Moscow was terminated; it lasted from 2002 to 2009 (7 years), and the strategy of non-return trapping of stray dogs for municipal animal shelters specially set up for the purpose got under way.
      To appraise the results of changing the strategy The Center for Animal Welfare Legal Protection carried out a questionnaire survey of Moscow prefectures, requesting statistics on the number of citizens who had been hurt by stray dogs from 2005 to 2010 (with a breakdown by six-month periods so as to assess the dynamics). To compare the efficiency of the neutering strategy (2002 June of 2009) and the strategy of non-return trapping (June of 2009 2010) based on the criterion of the number of citizens who had got hurt by stray dogs on the basis of the data made available by Moscow, we took the data for 2008 (the last year of the neutering strategy) and for 2010 (strategy of non-return trapping for animal shelters).
      Because the prefectures provided their data for the second half of 2010 only for the period from the beginning of the year to September 30, 2010, to fill out the missing estimate of the number of the hurt citizens for the remaining period of October-December of 2010, we used a method of linear approximation, when the number of citizens hurt during the period October-December of 2010 was taken on the basis of the number of citizens bitten for the previous interval of the same duration.
      Analysis of the results appearing in Table 6 clearly indicates the dynamics of the decreasing number of those hurt by stray dogs after the cancellation of the neutering strategy in all administrative districts (AD) of Moscow presented in the table.
      For example, in 7 AD of Moscow and in the Sviblovo Council of the North-Eastern District that made available information on the bitten citizens, the number of those hurt by stray dogs was halved on the average:
      Sviblovo Council of the North-Eastern AD a 3-fold reduction;
      North-Western AD a 2.6-fold reduction;
      South-Eastern AD, Northern AD, Western AD, Zelenogradskii AD halved, on the average ;
      Central AD, North-Eastern AD 1.4-fold.
      I regret the Eastern AD, South-Western AD and Southern AD failed to submit data on the citizens bitten by stray dogs, alleging circumstances of all kinds.
      The results of Table 6 evidence the following:
      1. The numbers of the of stray dog population in the streets of Moscow have been halved proportionally on the average compared with 2008.
      2. Utter worthlessness of arguments put forward early in the 1990s, saying that the stray dog population has its own mechanisms of biological self-regulation and if the trapping of stray dogs is commenced in the city, the urban stray dog population will allegedly restore itself quickly because purportedly there will occur an explosion of reproduction and the packs of stray dogs being trapped will give way to other packs of dogs (this time more aggressive!) from the city environs. As can be seen from the data in Table 6 (as well as on the basis of observations during 2008-2010), the packs of stray dogs trapped in Moscow are definitely not replaced by any feral dogs from Moscow environs. Again one can see on the city green lawns homeless cats, peacefully playing and even sleeping, which was unthinkable during the period of the neutering strategy campaign from 2002 to 2009 due to cats being killed by stray dogs, and which is a further evidence of an abrupt reduction of the numbers of stray dogs in Moscow.
      3. By and large, harmfulness of the neutering strategy to the health of the citizens and a higher efficiency of the non-return trapping strategy compared with the neutering strategy.

Part 5.

Pattern of animals pain sense modalities, resulting from various strategies for regulating stray animal numbers.


      Among methods of regulating population numbers, birthrate curbing methods and methods of reducing the numbers should be marked out. Methods of curbing the birthrate include a neutering method, on which the neutering strategy is based. However, the neutering method does not reduce the numbers: it only prevents fertility because a neutered individual does not vanish from the urban environment. Besides, the numbers of stray animal population in the course of applying the neutering strategy get diminished not as a result of neutering strategy being used at all, but due to the combination of a number of factors working in the urban ecosystem that impact diminution of population numbers, such as interspecific extermination, unauthorized and secret methods of animal destruction practiced by the population and authorities, mortality caused by diseases ad human effect. In this way, below we shall discuss specific methods of population number diminution, with which neutering has nothing to do.
      Furthermore, we shall try to introduce in the criterion the qualitative component, i.e. humaneness of the strategy being applied on the scale of the entire ecosystem. To secure this, in Table 7 we classify all known and used methods of numbers diminution by the degree of humaneness, scale of application in urban practice and by certain application peculiarities. Marked out in bold type in Table 7 are reduction methods that are principal and most widely used in urban practice, and making the main contribution to the change of population numbers.
      Let us introduce the qualitative component of the criterion appraisal of humaneness of the strategy being applied as an evaluation of the combination of factors proportionate to animals pain sense modalities that accompany the use of a particular control strategy. In so doing, humaneness should be appraised on the sale of the entire ecosystem, including not only the species controlled by the strategy in question (e.g. stray dogs), but also the other animal species that represent the given ecosystem (stray cats, wildlife) that are impacted by the use of the strategy under consideration.
      From Table 7 it follows that all methods of numbers diminution have, one way or another, to do with direct impact on the animal, whereby there emerges a certain pattern of pain sense modalities, the pattern being subject to dynamic changes time-wise. Let us specificate in the time-wise dynamics of the onset of pain sense modalities the active and passive phases, where there emerges respectively, a primary and secondary pattern of pain and let us specificate the principal indicators of the pattern of pain sense modalities [15, 16, 28]:
      The active phase (phase of direct impact on the animal as a result of applying a method of numbers reduction):
      Indicators (direct and indirect) of the pattern of pain sense modalities:
      () Intensity, duration and nature of impact on the nerve endings of the skin integument, tissues and organs.
      (B) Area and volume of afflicted nerve endings of the skin integument, tissues and organs.
      Passive phase (phase of secondary pathology of the organs and tissues building up, leading to death):
      (C) Intensity, duration, nature and volumes of building up pathology of the organs and tissues.
      Next, we tablicize (Table 8) the pattern of animals pain sense modalities, when different methods of animal numbers diminution are applied.
      Analysis of the data appearing in Tables 7 and 8 evidences that the most cruel, from the standpoint of the pattern of pain sense modalities, are methods of reducing population numbers equated to sadistic methods, when the pattern of pain is unbearably-shocking, and in most cases the animal dies in the active phase from the pain shock. It follows from Table 8 that the method of reducing population numbers termed biting to death by predators is used on a large and mass scale in the ecosystem, when the neutering strategy is applied.
      Next, to streamline the criterion, we shall determine the rule of appraising humaneness of the strategy used to control population numbers. This rule is determined by the lowest degree of humaneness in respect of animals en masse in the ecosystem on the entire interval of observation, that is conditioned by the method of numbers reduction being applied or by methods of numbers reduction admissible and encouraged by the particular strategy of numbers control.
      For example, let us compare, by this criterion, the humaneness of applying the strategies of neutering and of non-return trapping. As was stated earlier, the neutering strategy is nonoptimal, it does not educe the stray dog population numbers, and during its application, population numbers, irrespective of the observation interval, will be tending towards the upper limit of the environmental biocapacity. This strategy allows cohabitation of the population of stray dogs, stray cats and wildlife, which admits on a large scale the method of biting to death by predators since stray dogs, in conditions of uncontrolled habitation, become the dominant predator on the scale of an urban ecosystem and exterminate stray cats and wildlife on a mass scale. Thus, according to Tables 7 and 8, humaneness of the neutering strategy is equivalent to the use of sadistic methods of reducing the number of the animal population on the scale of an urban ecosystem despite the fact that the neutering strategy in respect of stray dogs allows the neutering method only and prohibits reduction of population numbers.
      The non-return trapping strategy is suboptimal, as it reduces the stray dog population numbers throughout the observation interval; the numbers in this will be tending towards the lower limit of the environmental biocapacity and also reduces to zero the application of the method of biting cats to death by predators and minimizes the existence in the ecosystem of the method of biting to death by predators, admitting the method only on natural territories inhabited by wildlife, which is not of a mass, cruel or extermination nature, including the protected species.
      Hence, the humaneness of applying the non-return trapping strategy will depend on the methods of reducing population numbers that are used during and after the application of the procedure of territorial redistribution of animals being trapped and that can be improved by man.

Part 6.

Causes for cruelty manifestation as a result of applying strategies for regulating stray animal numbers.


      The level of cruelty in applying any strategy of population numbers regulation on the minimum time interval of 10 years, which is used in engineering as an average interval for updating the existing technological capability shall be essentially determined by controllability of population numbers reduction methods used in the strategy and ability of the said methods to develop according to the state-of-the art in world engineering and technology. For example, if an urban ecosystem is dominated by predators stray dogs, which is inevitable in the case of the neutering strategy, extermination of stray cats and wildlife by stray dogs does not yield itself to monitoring and control by man. In this connection, the humaneness of the neutering strategy shall by no means depend on the human factor, shall never be controllable, but will always be determined and equal to the degree of cruelty of extermination of the urban fauna by stray dogs, i.e. only depend on interspecific relations between animals, and, respectively, will not be responsive to the improvement of the level of engineering and technology.
      However, in the case of non-return trapping for animal shelters, including the use of painless mercy killing (euthanasia), humaneness will always be controllable and will be determined by the level of engineering and technology development. In particular, development of new techniques, procedures and technologies of trapping, animal management in a shelter and painless mercy killing will, as time goes on, inevitably improve and advance humaneness of the non-return trapping strategy and, accordingly, reduce cruelty attending to that strategy. For comparative characteristics of the causes of cruelty towards animals manifestation and of the causes underlying dependence of cruelty on the level of development of engineering and technology, see Table 9.
      One of the reasons for cruelty manifestation is participation of socium in regulating animal numbers. It is thought that no proof is required in support of the contention that the more effective the applied strategy of numbers control, the weaker the manifestation of socium participation in regulating the population numbers. Here, too, comparison of the strategies is not in favor of neutering. The fact is that the growing population of stray dogs and biting cats to death by the dogs observed during the application of the neutering strategy have resulted in the following: () cruelty towards stray dogs as response of the socium, and extermination of stray dogs by the population using inhuman methods (poisonings, shootings); (b) withdrawal by citizens, out of pity, from the streets of stray cats (to a lesser degree, of dogs) and placement of these in own apartments, turning them into animal shelters, which, in 80% of the cases also leads to inhumaneness towards animals, because the owners of such shelters (especially if they are single and elderly citizens),with total indifference of society, aggressiveness and lack of understanding on the part of the people around them, first, suffer themselves, second, are unable to manage properly the animals they picked up in the street, often already ill and in need of serious treatment. These, quite adverse social phenomena, i.e. lynchings of stray dogs and apartment shelters by observations in Moscow from 2002 to 2009 became an inalienable part of the neutering strategy and the cause for these is application of the neutering strategy.
      However, when the strategy of non-return trapping is applied, no grounds for the aforesaid social phenomena emerge, since the population of stray animals gets really diminished.
      Thus, at the stage of appraising the criterions qualitative component there also exists (a) rough agorhithm only humaneness of the applied strategy is appraised in accordance with Tables 7 and 8, and (b) accurate algorithm as per Table 9 possibility of modifying the strategy in future is appraised, subject to advancement of engineering and technology.

Conclusion.


      An attempt has been made in this paper to develop a complex criterion for evaluating the effectiveness of applying a particular strategy to regulate stray animal numbers.
      Solution of the problem formulated in the paper has been found in the proposed two-component complex criterion which comprises the quantitative and qualitative components.
      To elaborate the criterion, the author carried out synthesis and analysis of some mathematical models of population behavior in an ecosystem; besides, pilot experimental data in the form of tables were systemized.
      The criterion includes:
      () in the quantitative part a procedure of a two-stage calculation based on the formulas and tables developed by the author, the outcome of the procedure may be a rough appraisal of applicability of a particular strategy of the type of applicable/inapplicable, and an accurate quantitative evaluation resulting from comparison of the strategies;
      (b) in the qualitative part a procedure of appraising humaneness of a strategy on the basis of the rule of appraising humaneness of the applied strategy developed by the author; the rule algorithm includes the use of a combination of tables obtained by the author on the strength of experimental data and observations.
      Thus, the criterion makes it possible to appraise and compare not only quantitative characteristics, but also humaneness indicators of the applied strategy of regulating the numbers. Besides, the criterion has forecasting properties as its qualitative part is supplemented with an additional procedure of evaluating dependence of the applied strategy on the level of development of engineering and technology, which evaluation is also made on the basis of the tables.
      By way of example of criterion work, the case of comparing the effectiveness of application of the most typical numbers regulation strategies is considered: the neutering strategy and non-return trapping strategy. By quantitative component of the criterion, the neutering strategy is inapplicable (nonoptimal), because according to this criterion it does not belong with a class of strategies that reduce the numbers and annual diminution of the population. By qualitative component of the criterion the neutering strategy is inapplicable, either, as it admits, on a mass scale, the use of inhumane methods, equated with sadistic by the pattern of pain sense modalities in animals; an example of such a method is biting to death by predators, when stray dogs en masse bite stray cats and wildlife. Besides, cruelty attendant to the neutering strategy which consists in a method of biting to death by predators, does not yield itself to monitoring on the part of the human factor, nor does it depend on the level of advancement of the world engineering and technology. Thus, by this criterion, the neutering strategy is absolutely inadmissible for application.
      Judging by the quantitative component criterion, the strategy of non-return trapping shall be applicable (suboptimum), because according to this criterion such a strategy belongs with a category of strategies that reduce the numbers and annual decrease of the population. By the qualitative component criterion, the strategy of non-return trapping shall be equally applicable since: (a) it does not suggest using lower class inhumane methods on a large scale that could be likened to sadistic ones by pain sense modalities experienced by animals, and (b) methods of the numbers reduction used in the case of the non-return trapping strategy shall be subject to control by human factor and shall be determined by state-of-the art of the worlds engineering and technology. Thus, by this criterion, the strategy of non-return trapping shall be recommended for use.

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