Roaming dogs collected for vaccination and/or sterilisation may be permanently marked to distinguish them as having been through the intervention process and hence not be collected in the future. By carrying out a minimum of two counts of marked dogs over the first two years of the intervention their annual survival can be estimated. P, the probability of counting a surviving marked dog on a survey count, which in this case is a "nuisance parameter", is estimated along with annual survival S. Both are assumed to be constant over the period of the counts. One reason for estimating S is that it allows the total number of roaming dogs to be estimated from the fraction of dogs on the street that are marked. P would allow an estimate of total roaming dog population if unmarked dogs are counted along with marked dogs over the entire area, however using an estimate of S is more efficient. This is because the fraction of roaming dogs that are marked can be estimated cost-free over the whole area by equiping people involved in the collection process with event counters. Surveys designed to count numbers of marked dogs and estimate S can be conducted over a smaller area to reduce the effort required (to obtain comparable counts of marked dogs over time the counting surveys have to be carefully conducted to maintain constant survey effort - using event counters to measure the fraction of dogs on the street that are marked does not require any control or measurement of effort).
The "permanent_mark_survival" program that can be downloaded from this page allows for from two to four of such counting surveys. If two surveys are used they should be conducted at the end of the first and second year of intervention/marking, if four surveys are used they should be conducted every six months. The program accepts data from a "datafile.txt" file that expects on the first and second lines the daily rate of mark releases and the number of surveys conducted to count marked dogs. Subsequent lines hold the day number of the survey and the number of marked dogs counted, separated by a comma.
The mark release rate refers to marked dogs released within the area where the surveys are conducted. If this is not the total area (to limit the spatial extent of the required surveys) the rate of release of dogs into the surveyed area may not be constant, even if the total number of dogs marked per day is constant, because collection and release of dogs may focus on different areas over time. In that case if the "constant marking rate" checkbox is cleared the value entered for the daily release rate is ignored and the number of dogs released into the surveyed area each week read from the following lines (thus about 104 lines for weekly releases over two years).
If the textbox holding the path to the data file is cleared the program reverts to a simulation mode to allow the user to observe the performance of the S estimator. The way the simulation is run and the results interpreted is as descibed under the previous section refering to temporary marking of owned dogs. Deriving confidence limits on an estimate of S is also as described in that section.
The stochastic model for the number of surviving marked dogs seen on each survey assumes each has, independently, a probability P of being seen. In practise the fact that some dogs will be counted in groups means that he probabilities may not be independent and hence the width of the confidence interval underestimated. If necessay, the "variance:mean ratio" textbox, which is not used during the estimation if the "-1" default is retained, can be used to enter a value for that ratio derived by replicating the surveys.
Download the following files to the same temporary folder to try out the permanent_mark_survival program:
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