Open-Population Mark-Recapture Models - Introduction to Ecological Sampling - page 109

TABLE 8.4
Data Collected from a Bird-Banding Experiment with Releases for k Yea r s
and Recov eries of Dead Animals for l Yea r s

Recoveries of Dead Animals in Year

Year of
Release

Number
Released

Total
Recovered 1 2 3 . . . l

1 N 1 a 11 a 12 a 13 . . . a 1 l R 1

2 N 2 a 22 a 23 . . . a 2 l R 2

3 N 3 a 33 . . . a 3 l R 3

⋮ ⋮ ⋱ ⋮ ⋮

k N k a kl R k

C j , year total C 1 C 2 C 3 . . . C l

adults. Survival and recovery results can either be constant or vary with the
age class or the year. Estimates from the models cannot in general be cal-
culated explicitly. Instead, the numerical solution of equations is required,
using appropriate computer software.
Although it is not realistic to review the many models that have been pro-
posed for the recovery of dead animals, it is instructive to consider one model
in some detail to understand the nature of the modeling process. The model
chosen is the first one discussed by Brownie et al . (1985, p. 15).
Suppose that batches of birds are banded in years 1, 2, . . . , k , and records
of recoveries are available for years 2, 3, . . . , k , k + 1, . . . , l . Then, the basic data
can be displayed as shown in Table 8.4. Thus, N i birds are released in year
i , a ij of these are recovered dead (or their bands are recovered) in year j , and
N i - R i are never recovered. If the survival rate for all birds in year j is S j , and
the probability of recovering a bird that dies in that year (or its band) is f j ,
then the probabilities shown in Table 8.5 apply. For example, the probability
that one of the birds released in year 2 is recovered dead in year 4 is S 2 S 3 f 4 .

TABLE 8.5
Probabilities Associated with the Recovery Histories Shown in Table 8.4

Recoveries of Dead Animals in Year

Year of
Release

Number
Released

Probability
Recovered 1 2 3 . . . l

f 1 S 1 f 2 S 1 S 2 f 3 . . . S 1 . . . S l -1 f l θ 1
2 N 2 f 2 S 2 f 3 . . . S 2 . . . S l -1 f l θ 2
3 N 3 f 3 . . . S 3 . . . S l -1 f l θ 3
⋮ ⋮ ⋱ ⋮ ⋮
k N k S k . . . S l -1 f l θ k
Note: The recovery probability θ i is the sum of the recovery probabilities for years i to l
given in row i of the table, 1 ≤ i ≤ k . For example θ 3 is the sum of the recovery prob-
abilities for years 3 to 1 as shown in row three of the table.

1 N 1