Violation of Instantaneous Sampling?! HELP!

[foxfire235]

Hello,

After multiple years of marking animals and collecting recapture data, we now realize our animal's principle source of mortality occurs during the sampling period. We have a rather long sampling period of April through May, and we have run tests using Multi State models and found differences in survival rates of animals tagged during the early season versus the late season. So my question is... How do we correct for this? It seems to be a clear violation of instantaneous sampling. How should we incorporate this in our estimates of survival rates?

Many Thanks!

[gwhite]

One way that I have handled this problem in the past is to code an individual covariate for the number of days into the annual interval that the animal was marked. So, assume that you start marking on April 1 each year. The individual covariate gives the number of days that the marked animal should have "deducted" from the annual interval during its first year. You have to model the first year's survival of each newly marked animal as a function of this individual covariate (meaning the first diagonel of the survival PIM). If you are seeing significant mortality during the marking period, then you will get a very positive effect from the individual covariate model, i.e., survival will increase with increasing values of the individual covariate.

This approach requires that there is little individual heterogeneity of survival rates or else you will get a slightly biased estimate of survival. Typically I don't figure there is much heterogeneity of survival rates because natural selection removes the lower portion of this distribution. Howerver, if there is some compensating reproduction to increase fitness of the low survival animals, then you may get a slightly biased estimate of annual survival.

Gary

[ganghis]

The answer to whether sampling mortality biases survival estimates really depends on the underlying hazard functions for survival and capture during the sampling period. If they more or less stay constant from year to year (i.e. the main mortality pressure doesn't change from the beginning of April to the end of May in consecutive years, and capture effort/probability remains similar from year to year), there should be minimal bias. The unfortunate problem is that there is seldom a way to test for whether these underlying conditions apply. One thing I would suggest is to plot the distribution of first captures (the first time an animal is captured/recaptured within the sampling period), and see if the expected time to first capture varies from year to year. While somewhat ad hoc, these plots should allow you to compare the relative length of survival intervals (i.e. the time interval between expected time to first capture was 12.4 months for one year and 11.8 for the next, etc.) and thus to get some idea of possible biases.


Cheers, Paul Conn

[foxfire235]

Excellent suggestions gentlmen, thank you. Paul - We know that there is a large difference in mortality when we have a wet or dry winter. The mortality, however, remains constant through these two types of "season", and since we can model the survival rates around these differences our estiamates should be unbiased.