Buildiletterg toward discrete-date, population-height hierarchical brand of McClintock et al

Buildiletterg toward discrete-date, population-height hierarchical brand of McClintock et al

Direction techniques design

( 2013 ), we developed a six-state movement behavior model for bearded seals, where movement behavior states and associated movement parameters were estimated from seven data streams. These data streams included step length , bearing (?n,t), the proportion of time spent diving >4 m below the surface , the proportion of dry time , the number of dives to the sea floor (i.e., “benthic dives”; en,t), the average proportion of sea ice cover , and the average proportion of land cover for each 6-h time step t = 1, …, Tn and individual n = 1, …, N. Our goal was to identify and estimate activity budgets to six distinct movement behavior states, zletter,t ? , in which I denotes “hauled on frost,” S indicates “sleep on ocean,” L indicates “hauled out on homes,” Meters indicates “mid-h2o foraging,” B indicates “benthic foraging,” and T denotes “transit,” according to the combined suggestions around the most of the data channels. While the good heuristic exemplory case of how the path process design really works, assume a specific six-h date action presented an initial action duration, no time spent diving below 4 yards, 100% dead time, and no dives towards the ocean floors; if the ocean freeze safeguards are >0% and you will land shelter is 0%, one can relatively anticipate your pet is hauled on frost during this time period action (condition We; Dining table 1).


  • These types of analysis channels provided horizontal trajectory (“action length” and you will “directional effort”), the fresh proportion of time spent diving less than 4 m (“dive”), the newest proportion of your energy invested dead (“dry”), plus the level of benthic dives (“benthic”) throughout the for each and every six-h big date step. The fresh new model included environment study on ratio out of water ice and you may land coverage when you look at the 25 ? 25 kilometres grid cell(s) that features inception and you can stop places for each day step (“ice” and you may “land”), and bathymetry investigation to spot benthic dives. Blank records suggest zero good priori dating was basically believed on the design.

For horizontal movement, we assumed step length with state-specific mean step length parameter an,z > 0 and shape parameter bletter,z > 0 for . For bearing, we assumed , which is a wrapped Cauchy distribution with state-specific directional persistence parameter ?1 < rletter,z < 1. Based on bearded seal movement behavior, we expect average step length to be smaller for resting (states I, S, and L) and larger for transit. We also expect directional persistence to be largest for transit. As in McClintock et al. ( 2013 ), these expected relationships were reflected in prior constraints on the state-dependent parameters (see Table 1; Appendix S1 for full details).

Although movement behavior state assignment could be based solely on horizontal movement characteristics (e.g., Morales et al. 2004 , Jonsen et al. 2005 , McClintock et al. 2012 ), we wished to incorporate the additional information about behavior states provided by biotelemetry (i.e., dive activity) and environmental (i.e., bathymetry, land cover, and sea ice concentration) data. Assuming independence between data streams (but still conditional on state), we incorporated wn,t, dletter,t, eletter,t, cn,t, and ln,t into a joint conditional likelihood whereby each data stream contributes its own state-dependent component. While for simplicity we assume independence of data streams conditional on state, data streams such as proportion of dive and dry time could potentially be more realistically modeled using multivariate distributions that account for additional (state-dependent) correlations.

Although critical for identifying benthic foraging activity, eletter,t was not directly observable because the exact locations and depths of the seals during each 6-h time step were unknown. We therefore calculated the number of benthic foraging dives, defined as the number of dives to depth bins with endpoints that included the sea floor, based on the sea floor depths at the estimated start and end locations for each time step. Similarly, cletter,t and ln,t were calculated based on the average of the sea ice concentration and land cover values, respectively, for the start and end locations. We estimated start and end locations for each time step by combining our movement process model with an observation process model similar to Jonsen et al. ( 2005 ) extended for the Argos error ellipse (McClintock et al. 2015 ), but, importantly, we also imposed constraints on the predicted locations by prohibiting movements inland and to areas where the sea floor depth was shallower than the maximum observed dive depth for each time step (see Observation process model).

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