c_migration.Rmd

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# Predicting Seasonal Migration

The presence of seasonal migration in a species’ life history can obviously alter distribution greatly. As a species alternates between foraging, breeding, calving or migratory behaviors response to the environmental is likely to vary. Accounting for these spatial and behavioral disparities is commonly done by building separate seasonal models to represent the different of habitats [@redfern_techniques_2006]. Migrations however can last up to 4 months over 20,000 km distances in the case of the grey whale. Models describing them as present over the entire range during that period would be insufficient for planning purposes. The general timing and broad locales are often available in natural history and scientific literature. Surprisingly I could not find a single species distribution model for cetaceans that explicitly includes migration.

Most papers which discuss migration and species distribution modeling are modeling the long term shift in distribution, typically poleward, imposed by climate change [@guisan_predicting_2005; @robinson_pushing_2011], and not the seasonal migrations common to megafauna. Mechanistic species distribution models have been suggested [@kearney_mechanistic_2009; @robinson_pushing_2011] but are complicated with energy and mass balance equations using parameters often difficult attain. Complex Markov models have been used with bird data to model bird migrations and trajectories [@sheldon_collective_2007]. 

A simpler method is possible and desirable for easily providing marine stakeholders and the general public (e.g. through OBIS-SEAMAP[^obis-seamap] or GROMS[^groms]) with a best guess view of what whales are where when. In its simplest form, separate models would be fit from observations separated out seasonally and spatially to distinguish the breeding, foraging and 2 migrating habitats. For the migratory habitat, time would be included as an interaction term for all environmental variables. Another variable could be introduced which measures distance along the axis of the median path, or straight line from the centroids of the breeding and foraging grounds. A significant fit for the interaction with this linear predictor would provide a clear description of where the whale is expected to be on its journey. Using the distance from this median line should give an idea of how widely dispersed the animals are along the way. If using a GAM then to model this interaction term, then it would be a bivariate smoother which could expand and contract along the axis. Compositing these models together could then provide a simple time-varying habitat model incorporating migratory movement.

[^obis-seamap]: http://seamap.env.duke.edu
[^groms]: http://groms.gbif.org

I propose to do this with the North Atlantic right whale (_Eubalaena glacialis_) since data is easily obtained through OBIS-SEAMAP over the entire species range and existing datasets are available for habitat in the Gulf of Maine foraging grounds [@best_online_2012; @departmentofthenavydon_navy_2007] and calving grounds off Florida [@good_spatial_2008], as well as comparison with migratory model based on telemetry data [@schick_striking_2009].

Kenney et al. [-@kenney_migration_2001] conceptualized a hierarchical sensory model for right whales to hone in on prey and navigate between summer foraging grounds in the Gulf of Maine and winter calving grounds off Florida, but fell short of postulating specific cues to initiate migration. Past years of observations and environmental data could be mined to explore a more specific environmental cue than date. This would enable predictions of the onset of migration. Other unmeasurable factors, such as satiation or hunger, are likely candidates, perhaps not inferable by environmental proxy.