Strengthening towards discrete-big date, population-peak hierarchical brand of McClintock ainsi que al
Way processes 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 ? , where I indicates “hauled on frost,” S denotes “sleep at sea,” L denotes “hauled from homes,” Yards indicates “mid-h2o foraging,” B indicates “benthic foraging,” and T denotes “transit,” according to research by the combined advice around the most of the analysis channels. While the a good heuristic exemplory case of how the movement techniques design work, guess a specific six-h go out step exhibited a preliminary action duration, almost no time spent dive less than cuatro m, 100% inactive big date, with no dives to the water floor; if the ocean ice protection was >0% and you can home cover try 0%, one can relatively assume the pet try hauled on frost during this period action (county We; Dining table step one).
Notes
- These investigation avenues included lateral trajectory (“step length” and you will “directional time and effort”), the new ratio of time invested plunge less than cuatro m (“dive”), brand new proportion of your time spent dead (“dry”), plus the number of benthic dives (“benthic”) throughout for every 6-h day action. The fresh model included environment studies towards proportion out-of ocean ice and you may property safeguards for the twenty-five ? 25 kilometres grid mobile(s) which has the beginning and you will end locations for every go out step (“ice” and you can “land”), also bathymetry research to recognize benthic dives. Blank records indicate zero an excellent priori relationships was indeed believed about model.
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 https://datingranking.net/catholic-dating/, 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 wn,t, dn,t, eletter,t, cletter,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, 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).
