Way 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”; 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 on ice,” S indicates “asleep at the sea,” L indicates “hauled from belongings,” M indicates “mid-liquid foraging,” B indicates “benthic foraging,” and you may T indicates “transportation,” according to the shared pointers across the all the data channels. While the a good heuristic exemplory case of how course procedure model works, guess a specific six-h go out step showed a preliminary action length, no time invested plunge less than 4 m, 100% inactive date, and no dives toward water flooring; in the event that sea freeze safety is >0% and you will house shelter are 0%, one could relatively anticipate your pet try hauled from ice during sex hookup sites Raleigh this time action (county We; Desk 1).
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- These investigation streams incorporated lateral trajectory (“step size” and you will “directional time and effort”), the brand new ratio of time spent diving below cuatro m (“dive”), brand new ratio of your energy spent inactive (“dry”), while the quantity of benthic dives (“benthic”) throughout the for every single six-h big date action. The model integrated environmental study for the ratio out of water frost and you can residential property defense in twenty five ? twenty five kilometres grid cellphone(s) with the beginning and you will end places for each and every date step (“ice” and “land”), plus bathymetry investigation to identify benthic dives. Empty records indicate zero a beneficial priori matchmaking have been thought about model.
For horizontal movement, we assumed step length with state-specific mean step length parameter an,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 < rletter,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, 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, cletter,t and ln,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).