Energy Landscapes With Enerscape

Energy landscapes are spatially explicit projections of the energy cost of travel (kcal or J) for an animal. In enerscape, energy landscapes depend on the body mass of the animal and the incline between locations, following the ARC model from Pontzer (2016): https://doi.org/10.1098/rsbl.2015.0935. For a general overview of energy landscapes, refer to Berti et al. (2021): https://doi.org/10.1111/2041-210X.13734.

library(terra)
#> terra 1.8.60
library(enerscape)

Enerscape comes with the default dataset sirente; this is a matrix with values the digital elevation model (DEM) for Monte Sirente in Central Italy:

data("sirente")
dem <- rast(
  sirente, 
  crs = "+proj=utm +zone=32 +datum=WGS84 +units=m +no_defs",
  extent = ext(879340, 885280, 4672880, 4676810)
)
plot(dem)

I provided the correct coordinate reference system (CRS) and the extent of the DEM; in most cases, this will already be present in downloaded raster layers.

Enerscape assumes that the coordinate system is in meters:

crs(dem, proj = TRUE)
#> [1] "+proj=utm +zone=32 +datum=WGS84 +units=m +no_defs"

You have to check this by yourself to make sure +units=m or enerscape results will not be meaningful. Enerscape checks if this is the case and returns a warning if +units does not match m, but it will still return its output.

The energy landscapes can be obtained with the enerscape() function. There are two mandatory inputs: dem, which is the SpatRaster of the DEM, and mass, which is the body mass of the animal (kg).

en <- enerscape(dem, 10, neigh = 4, unit = "kcal")
#> DEM is assumed to have planar CRS in meters.

Before visualizing it, it is worth nothing that, from my experience, energy landscape values are usually right-skewed, i.e. with most cells having low values and few cells having high values. In such cases, it is useful to log-transform energy landscape for visualization:

en_log <- log(en)
plot(en_log)
terra::contour(dem, add = TRUE, nlevels = 5)

en_log <- crop(en_log, ext(881306, 882853, 4674928, 4675984))
plot(en_log)
terra::contour(dem, add = TRUE, nlevels = 20)

Initialization files for Circuitscape/Omniscape

Circuitscape and Omniscape are circuit theory approaches to calculate connectivity in landscapes. The main idea of these two algorithm is that resistances in the landscape (e.g. due to energy costs) behave like resistances in electric circuit. For instance, parallel resistances will give a lower overall resistance than each of the individual resistances (https://en.wikipedia.org/wiki/Series_and_parallel_circuits#Resistance_units_2).

The major advantage of a circuit theory approach is that it consider all possible paths of travel, instead of focusing only on one, e.g. a least cost path. Circuity theory has, thus, more realistic assumptions on how animals behave and I preferred Circuitscape/Omniscape over least-cost path analysis. Following rgeos and rgdal, I rewrote the core of the package in C++, removing the dependency also on gdistance. In doing so, I also removed the function to calculate least-cost paths using the transition matrix approach from gdistance. If you want to use these functions, check older releases on enerscape (https://github.com/emilio-berti/enerscape/releases; until 0.1.3, included).

Currently, there are no implementations of Circuitscape/Omniscape in R. There are, however, two great Julia libraries that are extremely easy to use:

• Circuitscape.jl: https://www.juliapackages.com/p/circuitscape.
• Omniscape.jl: https://www.juliapackages.com/p/omniscape

Both are one-liners in Julia, e.g. run_omniscape("omniscape.ini"). The major obstacle in using these libraries is to create the initialization file (.ini).

# two random points
p <- spatSample(en, 2, xy = TRUE)[, c("x", "y")]
circuitscape_skeleton(en, path = tempdir(), points = p)

julia> using Circuitscape
julia> compute("circuitscape.ini")

[ Info: 2022-12-16 10:05:18 : Precision used: Double
[ Info: 2022-12-16 10:05:18 : Reading maps
[ Info: 2022-12-16 10:05:18 : Resistance/Conductance map has 231472 nodes
[ Info: 2022-12-16 10:05:21 : Solver used: AMG accelerated by CG
[ Info: 2022-12-16 10:05:22 : Graph has 231472 nodes, 2 focal points and 1 connected components
[ Info: 2022-12-16 10:05:22 : Total number of pair solves = 1
[ Info: 2022-12-16 10:05:24 : Time taken to construct preconditioner = 2.510170134 seconds
[ Info: 2022-12-16 10:05:24 : Time taken to construct local nodemap = 0.021110616 seconds
[ Info: 2022-12-16 10:05:27 : Solving pair 1 of 1
[ Info: 2022-12-16 10:05:27 : Time taken to solve linear system = 0.512068804 seconds
[ Info: 2022-12-16 10:05:28 : Time taken to calculate current maps = 0.82549585 seconds
[ Info: 2022-12-16 10:05:29 : Time taken to complete job = 11.5802219
3×3 Matrix{Float64}:
 0.0  1.0       2.0
 1.0  0.0       0.559379
 2.0  0.559379  0.0

omniscape_skeleton(en, path = tempdir(), radius = 10)

julia> using Oircuitscape
julia> run_omniscape("circuitscape.ini")

[ Info: Starting up Omniscape with 1 workers and double precision
[ Info: Using Circuitscape with the cg+amg solver...
[ Info: Solving moving window targets...
 days,Progress: 100%|                                | Time: 0:08:08
[ Info: Time taken to complete job: 490.2733 seconds
[ Info: Outputs written to /tmp/RtmpXZb2Hv//tmp/RtmpXZb2Hv/omniscape
(Union{Missing, Float64}[missing missing … missing missing; missing 3.4477693535486376 … 4.462051188132685 missing; … ; missing 10.365746449782868 … 4.186837622531591 missing; missing missing … missing missing], Union{Missing, Float64}[missing missing … missing missing; missing 0.652059842432581 … 0.743080786816455 missing; … ; missing 0.7753872880414857 … 0.7333620170587554 missing; missing missing … missing missing])

Energy Lanscapes for Walking People

As of enerscape 1.2 I implemented the energy cost model for walking people from Looney et al. (2019). This can be calculated using the humanscape() function. The arguments are the same as for enerscape(), except for an additional argument v, which is the walking speed (m/s). If v is not specified, it is assumed to be v = 1.39, which optimize the energy costs.

en <- lapply(
  seq(0.5, 2.5, by = .5),
  \(v) humanscape(dem, 10, v = v, neigh = 4, unit = "kcal")
)
#> DEM is assumed to have planar CRS in meters.
#> DEM is assumed to have planar CRS in meters.
#> DEM is assumed to have planar CRS in meters.
#> DEM is assumed to have planar CRS in meters.
#> DEM is assumed to have planar CRS in meters.
en <- rast(en)
names(en) <- paste0("v = ", seq(0.5, 2.5, by = .5))
en_log <- log(en)
panel(en_log, nc = 3)

Changelog

References

Pontzer, H. (2016). A unified theory for the energy cost of legged locomotion. Biology letters, 12(2), 20150935.

Berti, E., Davoli, M., Buitenwerf, R., Dyer, A., Hansen, O. L., Hirt, M., … & Vollrath, F. (2022). The r package enerscape: A general energy landscape framework for terrestrial movement ecology. Methods in Ecology and Evolution, 13(1), 60-67.

Looney, D. P., Santee, W. R., Hansen, E. O., Bonventre, P. J., Chalmers, C. R., & Potter, A. W. (2019). Estimating energy expenditure during level, uphill, and downhill walking. Med. Sci. Sports Exerc., 51(9), 1954-1960.