By McCrea, Rachel S.
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Additional info for Analysis of Capture-Recapture Data
T denotes the number of samples taken. • The ith row of the data matrix X, provides the capture history, xi of the ith individual; here 1 indicates capture and 0 indicates no capture. Thus X has N rows and T columns, and is only partially observed. D animals are captured at least once and by convention the last N − D rows of X contain only zeros. • Frequently several animals will share the same capture history and we write x ˜h for the number of animals with non-empty capture history h, occurring with probability sh .
For more discussion, see Fewster and Jupp (2009). 4 35 Model classes So far in this chapter we have encountered a range of models, for both individual capture histories and for frequencies of capture. A useful structure for models has been introduced by Otis et al. (1978): the binomial model with constant recapture probability is denoted by M0 ; model class Mt indicates that p varies with time; model class Mb indicates that there is a behavioural response to capture, and model class Mh denotes heterogeneity of capture, with diﬀerent values of p for diﬀerent individuals.
9), producing, say, N ˆc ≥ N ˆ , and Cormack and Jupp (1991) proved that the showed in general that N ˆc and N ˆ is of order 1; Fewster and Jupp (2009) extended diﬀerence between N this work to wider families of models. 1 under the binomial model, with constant recapture probability p, and 34 ESTIMATING THE SIZE OF CLOSED POPULATIONS ˆc and N ˆ of less than one individual. found a maximum discrepancy between N However, for a model in which p incorporated both heterogeneity and trap response they found that there could be large diﬀerences, and recommend the ˆ in this case; see also Chao and Hsu (2000).
Analysis of Capture-Recapture Data by McCrea, Rachel S.