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 the probability that an animal is reidentified depends on its movement pattern, then standard methods of analyzing movement are not applicable. I show that modifications of maximum likelihood methods, in which the identifications themselves establish the spatial and temporal distribution of effort, can be used to derive movement parameters in three situations: (1) Identifications in one location allow calculation of the "lagged identification rate" (the probability of reidentification after various time lags) as well as estimation of residence times inside, and outside, the study area. (2) When more than one study area is sampled, it is possible to derive lagged identification rates between them and to estimate movement rates between areas and other population parameters. (3) Movements through continuous space can be described by diffusion rates (rates of population spread), and plots of squared displacement against time lag. To simplify computation, and to permit the analysis of large data sets, summed nonindependent log-likelihoods can 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 Pacific Ocean. Residence times in waters close to the Galápagos Islands were of the order of 8 d, but during the study period there was a substantial net movement out of the Galápagos region and into waters of the coastal eastern tropical Pacific. Diffusion rates of sperm whales were ∼700 km²/d over time scales from 1 to 100 d but decreased considerably over time scales of years, indicating displacements of ∼50 km/d within home ranges spanning ∼1000 km. Although giving relatively imprecise estimates of movement parameters compared to more standard methods, the techniques considered here should be particularly useful when examining animal movements over long time scales.