Analysis of animal movement using opportunistic individual identifications: Application to sperm whales

Data sets in which animals are identified individually in different places and times may contain considerable information on movements. However, if th e probability that an animal is reidentified depends on its movement patter n, then standard methods of analyzing movement are not applicable. I show t hat modifications of maximum likelihood methods, in which the identificatio ns themselves establish the spatial and temporal distribution of effort, ca n be used to derive movement parameters in three situations: (1) Identifica tions in one location allow calculation of the "lagged identification rate" (the probability of reidentification after various time lags) as well as e stimation of residence times inside, and outside, the study area. (2) When more than one study area is sampled, it is possible to derive lagged identi fication rates between them and to estimate movement rates between areas an d other population parameters. (3) Movements through continuous space can b e described by diffusion rates (rates of population spread), and plots of s quared displacement against time lag. To simplify computation, and to permi t the analysis of large data sets, summed nonindependent log-likelihoods ca n be maximized in place of the true log-likelihood to obtain approximately unbiased parameter estimates, and binomial, multinomial, or hypergeometric models can be approximated by the Poisson distribution. The first and third of the techniques were verified using simulated data, and all were applied to a 13-yr data set of identifications of sperm whales in the South Pacifi c Ocean. Residence times in waters close to the Galapagos Islands were of t he order of 8 d, but during the study period there was a substantial net mo vement out of the Galapagos region and into waters of the coastal eastern t ropical Pacific. Diffusion rates of sperm whales were similar to 700 km(2)/ d over time scales from 1 to 100 d but decreased considerably over time sca les of years, indicating displacements of similar to 50 km/d within home ra nges spanning similar to 1000 km. Although giving relatively imprecise esti mates of movement parameters compared to more standard methods, the techniq ues considered here should be particularly useful when examining animal mov ements over long time scales.