Not two different approaches, instead, I'd suggest 'two different hypotheses'. In the MARK help file below the example data,
The last variable (an individual covariate) in this example is the age of the nest at the time it was first found -- 4 days old for the first nest. ...[next record in the example] The age of this nest was 11 days when it was found on day 18.
In this example, as you pointed out, each nest is aged according to the day the first egg was laid.
From the MARK Book (page 17-15),
We want to build a model that contains each nest’s age on each day of the nesting
season. Fortunately, we have the covariate AgeDay1, which you may recall tells us the age of the nest
on the 1st day of the nesting season (a negative value for most of the nests!).
Here the reference point for each nest is
1st day of the nesting season rather than, in the MARK Help File,
the day that the first egg was laid.
In my view, neither of these are right or wrong, they're just implying different hypotheses. In the example from the MARK Help File, the prediction being tested is
nest success is a function of days since the first egg was laid in that nest. In the MARK Book, the prediction being tested is
nest success is a function of when the nest was initiated (first egg laid) relative to the beginning of the nesting season.
For the former prediction, perhaps (a competing hypothesis) predators are more likely to locate a nest as days progress into incubation. And the latter, perhaps the arrival of a nest egg predator occurs late in the incubation period...and so late nesting pairs, relative to the start of incubation, have a higher risk of losing their eggs.
andre