Fractional Time Intervals

[Nuttallia]

Hi everyone,

I'm using mark recapture data collected at 5 and 7 month time intervals. I am interested in calcuating annual survival so I adjusted the time intervals from 5 and 7 months to yearly fractions (i.e. 0.417 and 0.583).

Upon doing this my survival rates decreased by 1.4-2 times that of the monthly estimates (i.e. the montly estimate raised to the power of 5 or 7) and my standard errors tripled. Is this because MARK does not know how to interprete fractional intervals? If not, does anyone know how to calculate the SE for the estimates that are raised to the power of 5/7 to get annual estimates?

Any help or suggestions would be greatly appreciated.

Thanks in advance,
Sarah

[cooch]

Hi everyone,

I'm using mark recapture data collected at 5 and 7 month time intervals. I am interested in calcuating annual survival so I adjusted the time intervals from 5 and 7 months to yearly fractions (i.e. 0.417 and 0.583).

Its important to understand what tweaking the time intervals does in MARK. Suppose you had put in the number of months: 5, 7, 5, 7,...

What MARK does is calculate the Lth root of the estimate value over that parameter. So, for example, if for a 5 month interval the probability of survivng from start to end is 0.7738, then MARK would report the 5th root of this, which is 0.95. And, this value would be the estimated monthly survival rate. What MARK is doing is trying to transform the estimates suchthat they all have the same interval. The only way it can do this is to the the Lth root of the estimate.

If you had used 5, 7, 5, 7, you could have taken your estimates of monthly survival for each part of each year, and then used the products of them to determine the annual estimate.

Alternatively, if you use 0.41667 and 0.5833 as you did (MARK handles that just fine), instead of monthly estimates, you'd get estimates of annual survival - but (and this is where you need to be careful), you'd get annual estimates based on the survival over the two different parts of the season, and they mght not be the same (i.e., MARK would estimate annual survival based on first 5 months, then another estimate of annual survival for next 7 months, and so on...).

If you want annual survival, then all you really need to do is take that data from one particular point of the year, and build your encounter history that way. Estimation of survival is not dependent on when you start the calendar (e.g., Jan -> Jan estimates will be the same as April -> April estimates). But, you have data at two times of the year. Having data at two discrete times of the year lets you partition annual survival among seasons, which is potentially much more interesting than grinding out annual survival. I'd suggest using 5, 7, 5, 7..., and then look at whether or not there is evidence of seasonal variation in estimated monthly survival. This is straightforward. Imagine 3 years of data (real years, sampled twice each year). A time dependent PIM would look like

Code: Select all

1 2 3 4 5 6
  2 3 4 5 6
    3 4 5 6
      4 5 6
        5 6
          6


The key is remembering that 1, 3, 5 form a set (say, first 5 months of each of the three years), and that 2, 4, 6 for another set (say, second 7 months of each of the three years). If you didn't think there was annual vairation in monthly survival, but that monthly survival varied between seasons (within years) you would compare

Code: Select all

1 2 1 2 1 2
  2 1 2 1 2
    1 2 1 2
      2 1 2
        1 2
          2


with

Code: Select all

1 1 1 1 1 1
  1 1 1 1 1
    1 1 1 1
      1 1 1
          1
          1


The former PIM allows for seasonal variation in monthly survival, whereas the latter PIM constrains them to be the same.

This sort of approach, with some care, will let you partition annual survival into seasonal components, which is invariably a good thing.

[bacollier]

All,
I have a question along the same lines as the quote at bottom so I stuck it in here rather than begin a new thread.

What about the situation where captures at the beginning of a study occur in the middle of a biologically relevent sampling interval. For example, if the biologically relevant seasons are Nov-March (5 months), April-July (4), Aug-Oct (3) with inital capture at the beginning of the study on 1 Feb. Can you set the time interval for the initial occassion to be 2 months (or some fraction) but then use 5 when specifying this interval for the rest of the analysis?

But, if this is ok, how could annual survival be estimated?

Thanks,
bac


Quoted from earlier Response: "If you want annual survival, then all you really need to do is take that data from one particular point of the year, and build your encounter history that way. Estimation of survival is not dependent on when you start the calendar (e.g., Jan -> Jan estimates will be the same as April -> April estimates). But, you have data at two times of the year. Having data at two discrete times of the year lets you partition annual survival among seasons, which is potentially much more interesting than grinding out annual survival. I'd suggest using 5, 7, 5, 7..., and then look at whether or not there is evidence of seasonal variation in estimated monthly survival. This is straightforward."