Experimentally derived likelihoods for light‐based geolocation

Summary Electronic tags have revolutionised animal movement studies, but the reliability of subsequent ecological inference hinges on being able to quantify uncertainty in location estimates. Light-based geolocation, which uses the time series of light intensity during twilight events, remains the only viable technology for many species (e.g. fish and small birds) despite its limited accuracy. Modern approaches to movement modelling, such as Kalman filters and gridded hidden Markov models, require a valid likelihood for each observed twilight. It is difficult to directly construct such a likelihood (i.e. the probability density of the light data during a twilight period) given any location on the globe, because of complicated autocorrelation structures and non-standard statistical distributions. We therefore use data from moored tags at known locations to construct a transformation that turns a simple one-dimensional statistic into a quantity with the properties of a log-likelihood. The result is a set of calibration splines that can be used with light data from a similar tag deployed on a real animal: for each twilight, the one-dimensional statistic is calculated for any location (e.g. on a grid of, or all possible, locations) and then transformed into a likelihood using the calibration splines. The likelihoods can then be input to any state-space model to estimate a track. We show an example track from a grid-based hidden Markov model applied to light data from a tag deployed on a southern bluefin tuna. This approach to light-based geolocation provides the flexibility to integrate movement and behaviour modelling in a novel way. The likelihood surfaces from our approach can be used in any state-space model of animal movement and behaviour, irrespective of whether estimation is by maximum-likelihood or Bayesian methods. Our approach is primarily aimed at users interested in developing and fitting their own state-space models to explore biological hypotheses about animal behaviour.

[1]  Karen Evans,et al.  Reproductive Schedules in Southern Bluefin Tuna: Are Current Assumptions Appropriate? , 2012, PloS one.

[2]  Roger D. Hill,et al.  Geolocation by Light Level , 2001 .

[3]  Chris Wilcox.  Defining regional connections in southwestern Pacific broadbill swordfish , 2014 .

[4]  Kevin C. Weng,et al.  Validation of geolocation estimates based on light level and sea surface temperature from electronic tags , 2004 .

[5]  David W. Welch,et al.  Ability of Archival Tags to Provide Estimates of Geographical Position Based on Light Intensity , 2001 .

[6]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[7]  J. D. Metcalfe.  Summary Report of a Workshop on Daylight Measurements for Geolocation in Animal Telemetry , 2001 .

[8]  Michael D. Sumner,et al.  Bayesian Estimation of Animal Movement from Archival and Satellite Tags , 2009, PloS one.

[9]  Scott A. Shaffer,et al.  State‐space framework for estimating measurement error from double‐tagging telemetry experiments , 2012 .

[10]  Henrik Madsen,et al.  Estimating animal behavior and residency from movement data , 2011 .

[11]  Karen Evans,et al.  Recent advances in bio-logging science: Technologies and methods for understanding animal behaviour and physiology and their environments , 2013 .

[12]  Brent S. Stewart,et al.  DOCUMENTING MIGRATIONS OF NORTHERN ELEPHANT SEALS USING DAY LENGTH , 1992 .

[13]  S. S. Wilks.  The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses , 1938 .

[14]  Henrik Madsen,et al.  Geolocation of North Sea cod (Gadus morhua) using hidden Markov models and behavioural switching , 2008 .

[15]  S. Wood.  Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models , 2011 .

[16]  Henrik Madsen,et al.  Geolocating Fish Using Hidden Markov Models and Data Storage Tags , 2009 .

[17]  David W. Welch,et al.  An assessment of light-based geoposition estimates from archival tags , 1999 .

[18]  Anders Nielsen,et al.  Improving light-based geolocation by including sea surface temperature , 2006 .

[19]  Aevar Petersen,et al.  Tracking of Arctic terns Sterna paradisaea reveals longest animal migration , 2010, Proceedings of the National Academy of Sciences.

[20]  Martin Wæver Pedersen,et al.  State-space models for bio-loggers: A methodological road map , 2013 .

[21]  Toby A Patterson,et al.  Classifying movement behaviour in relation to environmental conditions using hidden Markov models. , 2009, The Journal of animal ecology.

[22]  Philip A. Ekstrom,et al.  An advance in geolocation by light , 2004 .

[23]  Anders Nielsen,et al.  State–space model for light-based tracking of marine animals , 2007 .