Population dynamics

What controls the number of dogs in a city? In a wildlife population we look for "density dependant" factors such as shortage of food or breeding sites to explain why a small population grows and a large population does not. Such factors may affect a dog population too but a less subtle mechanism is likely to be the main controlling factor. A city environment is unlikely to allow dogs to breed and raise many puppies unaided. Thus a population of stray dogs persists indefinitely only as a result of continual addition of puppies raised in a domestic environment and then abandoned. Its size will determined by the rate of survival of those young dogs - it will grow until the number of dogs that die each year equals the number abandoned plus the number that are born and raised on the streets.

The "sterilise.exe" program, which can be downloaded from this page, simulates this process by keeping track of dogs in the "domestic" and the "street" populations (a necessary simplification - some dogs may raise puppies in both the domestic environment and on the streets). It considers only females, on the assumption that there will always be an excess of males available for breeding. It assumes an initial equilibrium state, allows for dogs killed by any existing control programmes and then simulates the affect of starting a sterilisation programme. In particular it considers the number of dogs sterilised, their ages and the how the number of sterilisations is split between the domestic and street populations. It thus attempts to assess the size of programme required to reduce and control the size of the street population and the type of sterilisations that would be most affective.

Download the "sterilise.exe", "sterilise.ini" and "killed.txt" files to the same folder on your PC and double-click the "sterilise.exe" file. Maximise the window and click on the "run" button. The upper part of the screen is divided into boxes dealing with the domestic and street populations, a box for comparing the simulation results to a current survey of the street population and a box for defining the control measures.

Consider the parameters in the "street dogs" box. They set the the probability of survival from birth to age 1, the annual survival of adult females, the (whole number) ages at which a female can have her first and last litters, the probability she will have a litter at each age within that range and the average number of females per litter. The model thus assumes dogs breed once a year, which is again a simplification as dogs can breed more frequently. However the affect of that simplification can be offset by increasing the litter size. Females are assumed not to live more than 10 years. The probability of survival to age 1 should not exceed the indicated limit (which depends on the other parameters), to avoid the street population growing without the addition of abandoned dogs.

The parameters of the domestic population are assumed to be the same except that the probability of survival to age 1 is much larger. In the domestic population that probability is fixed as a function of the other parameters by assuming that the population would remain at constant size if no dogs wrere abandoned and 70% of the females were sterilised. The box to the right of the "street dogs" box displays this balancing level of first year survival and the corresponding doubling time of the population if none were sterilised - thus its intrinsic rate of increase under optimal conditions. It also shows expected lifespan at birth and age 1. Any of the parameters can be adjusted to give desired values for these diagnostics.

In the "owned dogs" box the scrollbar adjusts the number of females abandoned per year - the model assumes they are abandoned at age 1. The percentage of dogs not abandoned that are sterilised is set at the top of the box. These settings determine the constant size of the domestic population and number of female sterilisations per year - the number of sterilisations can be compared with data from vetinary clinics. The number of females abandoned per year combined with the parameters in the street dogs box determine the equilibrium size of the street population, which stays at that size until some control measures are introduced.

The "killed.txt" file contains data from Cairo on the number of female dogs killed per year. To use a different set of data replace the file with another using the same format, that is, "year , number of female dogs killed" (years in which no dogs were killed nead not be entered and the data need not be entered chronologically). These numbers are subtracted from the numbers at each age in the simulated street population in proportion to the number at that age. In the "control" box the range of years over which the subtractions take place is set - the range can be adjusted to investigate the effect of having increased or reduced the amount of control.

The red line on the plot shows the resulting trajectory of street population size and the "survey" box gives its present (year 2005) size, the reduction over the previous five years and the percentage of the population consisting of abandoned dogs (as opposed to dogs born and raised on the street). Those diagnostics can be compared with available survey data (marked variation in size and appearance of street dogs indicates that a high percentage of them are abandoned). Adjust the scrollbar in the "owned dogs" box to give the current estimate of the number of female street dogs. Adjust first year survival to adjust the reduction over the previous five years - decreasiing first year survival will require increasing the number of abandoned dogs in order to get back to the current estimate of the number of street dogs and give less reduction over the previous five years.

The horizontal and vertical scrollbars in the "control" box adjust the sterilsation effort from the specified start year and the relative effort expended in the domestic and street populations. The blue line on the plot shows the annual total number of sterilisations and the output in the "control" box the number of sterilsations of "owned" and "street" dogs in the first year (also shown as the percentage of unsterilised dogs in each population). The red line then shows the affect of the specified levels of sterilisation effort on the street population.

The "sterilise.ini" file holds the parameter settings from the most recent run. The version downloaded will display a possible scenario for the Cairo street dog population, with a roughly equal number of extra sterilisations in the street and domestic populations (about a 30% increase). To preserve current parameter settings save a copy of the "sterilise.ini" file before the next run.

The model simplifications should not invalidate its main conclusions. It shows why even a large cull of street dogs will not lead to a permanent reduction as the continued input of abandoned dogs leads to regrowth of the population. It also shows the benefit of targeting sterilisation effort at the domestic population, particularly if first year survival on the streets is very low - sterilising a female will have little affect on the population if she is in any case unlikely to raise a litter successfully. The eventual aim would be to raise the level of sterilisation in the domestic population to a point (around 70%?) at which the overall surplus is eliminated and a local surplus can be rehoused via temporary shelters. Any remaining street population would then die out within a few years.

LIST OF ADDITIONAL PROGRAMS

- Sterilisation rates required to stabilise a population
- A regression estimator for a roaming dog population
- An estimator for total roaming dogs in a city block using sight-resight data (allowing for possible emigration)
- An estimator for total roaming dogs in a city block using sight-resight data (allowing for possible heterogeneity)
- A program for using temporary marking of owned dogs to estimate numbers of owned and unowned dogs
- A program for using permanent marking of roaming dogs to estimate their survival
- Population dynamics

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