Normatividad Internacional

All methods developed throughout Chapters 2–5, along with that proposed in the previous section, rely on the assumption that cue-producing individuals do not move throughout the duration of the survey. This allows them to be associated with just one single location within the survey region. While this is appropriate for many anurans (e.g., A. lightfooti) and some songbirds (e.g., S. aurocapilla), there is current interest in the use of cue-based SECR approaches to estimate densities of species belonging to taxa for which this does not hold. Examples include cetaceans (e.g., B. acutorostrata, P. macrocephalus, the har- bour porpoise Phocoena phocoena) and microbats (e.g., the northern long-eared batMyotis septentrionalis). Methods that account for intercue movement of individuals are required in order to relax this assumption and therefore obtain appropriate estimates of animal density in these cases. However, it is worth noting that (ironically) the more animals move between the production of cues, the less of a concern this becomes; for example, if intercue movement is so great that the location at which one cue is produced does not provide any information

about the next, then these locations can be considered independent. The methods that suitably estimate animal density with stationary animals can then instead be directly used to estimate cue density.

Standard DS methods also assume that individuals remain stationary. Animal move- ment can cause substantial bias in density estimates obtained from both point-transect and line-transect surveys, particularly at higher animal speeds (Glennie, Buckland, & Thomas, 2015; Prieto, Thomas, & Marques, in prep.), and so this is also possibly the case for current cue-based SECR estimates. DS methodology to account for movement on such surveys, however, does not yet exist.

SECR methods for dealing with issues pertaining to the movement of animal home- range centres across sampling occasions have recently been proposed (Ergon & Gardner, 2014; Royle, Fuller, & Sutherland, 2016). Modelled movement behaviours include tran- sience (whereby individuals’ home-range centres move between each sampling occasion) anddispersal (whereby individuals may be associated with the same home-range centre for a number of sampling occasions, before undertaking a single movement). The spatial scale of dispersal is usually greater than that of transience. Interestingly, Royle et al. (2016) found (via simulation) that models that did not account for these movement effects nevertheless estimated density with minimal bias.

On SECR surveys for which these movement behaviours have been developed, each cap- ture history is associated with a particular individual and a particular sampling occasion. On cue-based SECR surveys, on the other hand, each capture history is associated with a particular individual and, specifically, a particularcue it has produced. Once this compari- son between sampling occasions and cues has been made, similarities between movement of home-range centres in standard SECR and movement of individuals in cue-based SECR are obvious: for example, echolocating species typically move around in between the emission of cues (cf. transience), while others (e.g., songbirds) may produce a number of cues at one location before moving to another (cf. dispersal). Indeed, similar models to those that have been proposed to account for transience and dispersal could potentially be used for intercue movement in cue-based analyses.

There is one considerable complication that precludes the direct application of these models to cue-based data. On standard SECR surveys, if a previously detected individual is not detected on one particular occasion, then a capture history of 0m is observed; thus

it is known when a previously detected individual has evaded detection. On cue-based SECR surveys, however, it is not known when a produced cue remains undetected, and so a capture history isnot observed when a previously detected individual has evaded detection.

This is problematic as it is difficult to determine the plausible range of intercue movement when not all cues generate observed data. For example, if a considerable length of time has elapsed between the detections of two cues attributed to the same individual, then it is plausible that either (i) it produced a number of cues that remained undetected by virtue of having moved away from the detector array, or (ii) it remained in the proximity of the detector array, but did not produce any cues in the intervening period.

In order for a ML approach to infer which is more likely given the data at hand, it is thus necessary not only to integrate over the latent locations at which the two detected cues were produced—but additionally all possible paths the individual may have travelled between them, presenting a substantial computational obstacle. This can potentially be minimised by assuming a Markovian movement model—the resulting dependence structure between an individual’s locations over the course of a survey allows a high-dimensional integral to be broken down into a series of lower-dimensional integrals, hence increasing efficiency; see Rue and Held (2005). Alternatively, a Bayesian approach could instead sample over plausible latent locations and their connecting paths.

The likelihood derived in the previous section (Equation (7.1)) provides a means of incorporating animal movement. The final term within the integrand needs to be extended to the joint PDF f(Xi;γ,ζ), where Xi holds the locations at which all ni detected cues

were produced. The integral for the ith detected individual must be evaluated jointly over all such locations and thus has dimension 2ni. The term within the product should then

condition on xij, the location at which the jth detected cue was produced by the ith

detected individual. Calculation of the PMF of the random variableni|Xi remains unclear,

and depends on the individual’s travelled path—the longer this has the individual in the proximity of the detector array, the larger its expectation.