Spatial habitat grid

Our model is a full-annual-cycle population model {hostetler2015full} that tracks groups of bat surviving through four seasons: breeding season/summer, fall migration, non-breeding/winter, and spring migration. 
Our state variables are groups of bats that use a specific maternity colony/breeding site and hibernaculum/non-breeding site.
Bats are also accounted for by life stages (juveniles/first-year breeders versus adults) and seasonal habitats (breeding versus non-breeding) during each year, 
This leads to four states variable (here depicted in vector notation): 
the population of juveniles during the non-breeding season,
the population of adults during the non-breeding season, 
the population of juveniles during the breeding season,  and
the population of adults during the breeding season, 
Each vector's elements depict a specific migratory pathway, e.g.,  is comprised of elements, {non-breeding sites}, {breeding sites}The variables may be summed by either breeding site or non-breeding site to calculate the total population using a specific geographic location.
Within our code, we account for this using an index column for breeding sites and an index column for non-breeding sides within the data table.
Our choice of state variables caused the time step (i.e. \(t\)) to be 1 year.
However, we recorded the population of each group during the breeding and non-breeding season as an artifact of our state-variable choice.
We choose these state variables partially for their biological information and partially to simplify programming.
We ran our simulation for 30 years because the USFWS currently issues Indiana Bat take permits for 30 years. 
Our model covers the range of the Indiana Bat, which is approximately the eastern half of the contiguous United States (Figure \ref{fig:BatInput}).
The boundaries of our range was based upon the United States boundary, the NatureServe Range map, and observations of the species. 
The maximum migration distance was 500-km, which was based upon field observations reported in the literature \citep{gardner2002seasonal, winhold2006aspects}.
The landscape was covered with approximately 33,000, 6475-ha grid cells and the grid size was based upon management considerations.
The U.S.~Fish and Wildlife Service considers a 2.5 mile radius around a known maternity colony to be its summer habitat range and all of the hibernaculum within a 2.5 miles radius to be a single management unit.
Hence the choice of 5-by-5 square grids (25 miles\(^2\) or 6475 ha).
Each group of bats within the model has a summer and winter grid cell as well as a  pathway connecting the cells. 
It is possible for a group to be in the cell for both seasons, but improbable for females (which we modeled). 
The straight line between summer and winter cells were buffered with different distances (1-km, 2-km, 10-km, 20-km, 100-km, and 200-km) as part of the turbine sensitivity and uncertainty analysis.
We dropped the largest two buffer sizes during the model development processes because they were biologically unrealistic and including them caused all populations to go extinct all of the time.
Note a 1-km buffer would be a 2-km wide path.
An example of two pathways are included in Figure \ref{fig:BatPath}.
The buffers accounts for bats not migrating in a straight line.
If we had precise locations for all summer maternity colonies, other approaches such as Circuitscape \citep{hanks2013circuit} could have been used to model migration routes and this would have reduced migration uncertainty.

Tags: bats, eastern-united-states, population-matrix-model, united-states, usgs-581e0b46e4b0dee4cc982537, white-nose-syndrome
Organization: Department of the Interior