Direction 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 (?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”; eletter,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 from frost,” S denotes “sleeping from the ocean,” L indicates “hauled from homes,” Yards denotes “mid-drinking water foraging,” B denotes “benthic foraging,” and you will T denotes “transportation,” according to the combined advice all over all analysis avenues. As good heuristic illustration of how the direction techniques model work, assume a particular 6-h big date action exhibited an initial step length, almost no time spent diving lower than 4 yards, 100% dead date, and no dives to your water floor; if sea ice shelter try >0% and you may homes cover is 0%, one could relatively expect your pet try hauled out on ice during this period step (condition We; Desk 1).
- These research avenues included horizontal trajectory (“step length” and “directional work”), the fresh ratio of your time spent dive less than cuatro yards (“dive”), the fresh new ratio of your time invested dry (“dry”), and also the number of benthic dives (“benthic”) during the for every single 6-h go out step. The design integrated ecological data to your ratio off sea ice and you may residential property cover into the twenty five ? 25 kilometer grid cell(s) with which has the beginning and you may avoid locations for each big date action (“ice” and you may “land”), also bathymetry investigation to identify benthic dives. Blank entries imply zero a priori relationship was thought in 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 < 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 , 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, dletter,t, en,t, cletter,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, en,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 Bisexual dating apps 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, cn,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).