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Course techniques model

( 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 (?_letter,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”; e_letter,t), the average proportion of sea ice cover , and the average proportion of land cover for each 6-h time step t = 1, …, T_n and individual n = 1, …, N. Our goal was to identify and estimate activity budgets to six distinct movement behavior states, z_letter,t ? , in which I indicates “hauled on ice,” S indicates “resting at water,” L indicates “hauled out on belongings,” M denotes “mid-water foraging,” B denotes “benthic foraging,” and you will T indicates “transit,” in accordance with the joint pointers round the all the studies channels. Once the an excellent heuristic exemplory instance of the movement techniques model performs, assume a certain 6-h time action exhibited a short step length, no time invested dive less than 4 meters, 100% lifeless day, with no dives towards ocean floor; if the water freeze safeguards try >0% and you can house safeguards is 0%, one could fairly predict the pet was hauled out on frost during this period step (state We; Table 1).

Cards

• These analysis streams integrated lateral trajectory (“action duration” and you will “directional efforts”), the fresh new ratio of time spent diving lower than cuatro meters (“dive”), the fresh new ratio of your time spent dead (“dry”), plus the number of benthic dives (“benthic”) during the each 6-h go out step. The fresh model included environmental analysis to your ratio from ocean frost and you can homes safety inside twenty five ? 25 kilometer grid cell(s) that contains the start and prevent metropolitan areas for every single time step (“ice” and you can “land”), along with bathymetry analysis to determine benthic dives. Blank entries indicate no a beneficial priori dating was assumed on model.

For horizontal movement, we assumed step length with state-specific mean step length parameter a_n,z > 0 and shape parameter b_letter,z > 0 for . For bearing, we assumed , which is a wrapped Cauchy distribution with state-specific directional persistence parameter ?1 < r_n,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 w_n,t, d_n,t, e_n,t, c_letter,t, and l_letter,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, e_letter,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, c_n,t and l_letter,t were calculated based on the average of the sea ice concentration and land cover Los Angeles free legit hookup sites 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).