Building for the distinct-day, population-level hierarchical model of McClintock et al

Building for the distinct-day, population-level hierarchical model of McClintock et al

Path 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 indicates “hauled out on ice,” S indicates “asleep at ocean,” L indicates “hauled from property,” Meters denotes “mid-h2o foraging,” B denotes “benthic foraging,” and you can T indicates “transit,” in accordance with the combined guidance all over the analysis streams. As an excellent heuristic exemplory instance of the way the direction processes design work, guess a particular 6-h go out action presented a short step duration, little time invested dive below 4 yards, 100% lifeless go out, without dives for the sea floor; if ocean frost safety try >0% and you can home coverage are 0%, you can reasonably expect the animal are hauled from ice during this time period action (condition We; Table 1).

Cards

  • These types of study channels integrated lateral trajectory (“step size” and you will “directional dedication”), the newest proportion of your energy spent plunge below cuatro m (“dive”), this new proportion of your energy spent deceased (“dry”), additionally the number of benthic dives (“benthic”) during the each six-h big date action. This new design included ecological data towards ratio out of sea ice and you will residential property protection within the twenty five ? twenty five km grid mobile(s) that contains first and you may prevent cities per date step (“ice” and “land”), plus bathymetry data to understand benthic dives. Empty records indicate no a great priori relationship was indeed believed in the design.

For horizontal movement, we assumed step length with state-specific mean step length parameter aletter,z > 0 and shape parameter bn,z > 0 for . For bearing, we assumed , which is a wrapped Cauchy distribution with state-specific directional persistence parameter ?1 < rn,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 , Rate My Date dating app 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 wletter,t, dn,t, eletter,t, cn,t, and lletter,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 lletter,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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