On the Augmentation of Ring Recovery Data with Field Information

1. It is well-known that the Cormack-Seber model (Cormack 1970; Seber 1971) for ring-recovery data from birds ringed as nestlings does not provide unique maximum-likelihood estimates of the parameters without the addition of a constraint. Lakhani & Newton (1983) pointed out that the use of a constraint might yield misleading estimates. Unique estimates do result from the addition of separate information on one of the parameters; Lakhani (1987) suggested the possibility of the survival of first-year birds being based on observed deaths of radio-marked birds. 2. We show here that the estimate of the survival probability for first-year birds, obtained from radio-marked birds alone, may not correspond to the overall maximum-likelihood estimate of this probability. 3. We explain how such a discrepancy may arise, and show that, in this case, one of the other parameters in the model is estimated on a boundary to the parameter space, i.e. is either 0 or 1. 4. A small simulation study is carried out to explore the implications of this finding for the bias of the parameter estimators. We see that if the radio-marking does not affect first-year survival, then the most serious bias is for the survival probability phi(k), where k is the number of years' duration of the ringing study. For other parameters, bias will be lower, and possibly of the order of 10%, though this depends on the size of the radio-tracking study. This bias might well be less than the possibly unknown bias in the absence of any augmentation, as claimed by Lakhani (1987). 5. If radio-marked birds experience a reduced probability of survival then more serious bias may extend to all parameters. In this situation, bias increases as the size of the radio-tracking study increases. 6. When a discrepancy of the kind described in (2) above arises, repeating the radio-tracking experiment is advisable only if survival is not expected to be impaired by radio-marking, and if a large radio-marking experiment may be carried out. 7. Lakhani (1987, 1990) has suggested further improvements to the simple radio-tracking scheme examined here. Morgan & Freeman (1989) have discussed a model with first-year variation in survival rates which allows the estimation of model parameters, without the need of any constraints. The possibility of combining this modelling development with further field information is discussed.