Strengthening with the discrete-go out, population-top hierarchical model of McClintock ainsi que al

Way processes model

( 2013 ), we developed a six-state Chinese Sites dating app 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_n,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_n,t ? , where We indicates “hauled from ice,” S indicates “sleeping at the water,” L denotes “hauled out on house,” M denotes “mid-liquids foraging,” B denotes “benthic foraging,” and you may T denotes “transportation,” in line with the mutual guidance across the the studies avenues. Since the an effective heuristic instance of the path processes model really works, suppose a specific 6-h date action shown an initial step size, almost no time spent plunge lower than 4 meters, 100% dead date, and no dives toward water flooring; in the event that sea frost security was >0% and you may house defense was 0%, it’s possible to fairly anticipate your pet is actually hauled from ice during this period action (condition I; Desk step one).

Notes

• These studies avenues integrated horizontal trajectory (“step size” and you will “directional effort”), the fresh new proportion of your time invested dive below 4 yards (“dive”), this new proportion of energy invested deceased (“dry”), additionally the number of benthic dives (“benthic”) throughout the for each 6-h go out action. The new design integrated environment analysis to the ratio out-of water ice and you can belongings shelter inside the twenty-five ? twenty-five km grid telephone(s) with which has the start and prevent places each go out step (“ice” and you may “land”), as well as bathymetry investigation to spot benthic dives. Empty entries suggest zero a good priori matchmaking was in fact presumed on the model.

For horizontal movement, we assumed step length with state-specific mean step length parameter a_letter,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_letter,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_letter,t, d_letter,t, e_letter,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_letter,t and l_n,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).