Time Intervals

Time Intervals specify the amount of time between encounter occasions (specified in the Initial Values Window), and their interpretation depends on the Data Type. The default is 1, as in 1 year, or 1 month. As an example of how to use this feature of Program Mark, suppose that 3 consecutive years of live trapping are conducted (with the first year capturing only only new or unmarked animals), then a year is missed, then 3 more consecutive years are conducted. Then, the time intervals for these 5 encounter occasions would be specified as

1 1 2 1 1

where the "2" indicates that the length of the time interval separating these 2 capture occasions is 2 years instead of 1 year like the remaining 4 intervals. The purpose of specifying the time intervals is to make the survival rates for each of the intervals comparable. Thus, the survival rate for all 5 of the above intervals will be an annual or 1 year rate, so that all can be constrained to be the same, even though the length of the time intervals to which they apply are not the same. The time interval is used as an exponent of the estimated survival rate to correct for the length of the time interval.

To explain in more detail, unequal time intervals between encounter occasions are handled by taking the length of the time interval as the exponent of the survival estimate for the interval, i.e., S(i)**L(i). For the typical case of equal time intervals, all unity, this function has no effect. However, suppose the second time interval is 2 increments in length, with the rest 1 increment. This function has the desired consequences: the survival estimates for each interval are comparable, but the iHHncreased span of time for the second interval is accommodated. Thus, models where the same survival rate applies to multiple intervals can be evaluated, even though survival intervals are of different length.

Time intervals are not allowed for the Closed Capture or Huggins Closed Captures models, because the time interval between encounters is assumed to be so small that no mortality or emigration is allowed. Effectively, the time interval is assumed to be zero.

For the Robust Design model, time intervals are used to specify which encounter occasions are grouped together to form the encounter sessions. The time intervals between the encounter occasions within a session have a length of zero, whereas the time intervals between sessions have a positive (>0) length. An example will make this clearer. Assume that animals are trapped for 15 separate times. The first year, animals are trapped for 2 days, the second year for 2 days, the third year for 4 days, the fourth year for 5 days, and the fifth year for 2 days. The number of encounter occasions would be specified as 15. The length of the time intervals would be specified as

0 1 0 1 0 0 0 1 0 0 0 0 1 0

That is, only 14 time intervals are needed, where the value 1 means that 1 year elapsed. This mechanism is flexible, but can be a bit tricky. Note that all sessions must have at least 2 occasions. Thus, you will never have 2 consecutive time intervals of length >0.