`library(simlandr)`

An important property of the states in a landscape is their stability, characterized by the barrier height between these states and other adjacent states. `simlandr`

also provides tools to calculate the barrier heights from landscapes.

You can use the general function `calculate_barrier()`

to calculate the barrier for most landscapes. There are also specific `calculate_barrier_*()`

functions available. The output of these functions is a `barrier object.

The `barrier`

objects contain the potential function and the position of both states and the saddle point. For 3D landscapes, the lowest elevation path (LEP) is also provided. `barrier`

s can also be calculated for landscapes from multiple simulations. In this case, remember to set `individual_landscape = TRUE`

in landscape construction functions.

The local minimums are searched in a square space around a given point. The point with the lowest potential value in the given region is set as the position of the stable state. If all the potential values in the region are equal to `Umax`

(which represents ~`Inf`

), the barrier calculation functions will expand the searching area automatically. Use `expand = FALSE`

to disable this feature.

For landscapes from multiple simulations, the searching regions for their starting and ending points can be different. `simlandr`

provides `make_barrier_grid_2d()`

and `make_barrier_grid_3d()`

functions to help you put these settings into a data frame with the correct format.

The `barrier`

objects also provide a `ggplot`

geom object that can be added to the landscape plots to show the starting (white), end (white), and saddle (red) points, as well as the LEP (white line, only for 3d landscapes). Use `get_geom(b)`

to access those geoms.

Below are examples of different barrier calculations. See the help documents of those functions for further details.

Prepare data sets and landscapes (see `vignette("landscape")`

)

```
<- sim_fun_test(
single_test par1 = list(var1 = 1),
par2 = list(var2 = 1, var3 = 0)
)
<- make_2d_density(single_test, x = "out1", from = -2, to = 2, adjust = 1)
l_single_2d <- make_3d_static(single_test, x = "out1", y = "out2", lims = c(-3, 3, -3, 3), h = 0.01, kde_fun = "ks")
l_single_3d #> Calculating the smooth distribution...
#> Done!
#> Making the plot...
#> Done!
#> Making the 2d plot...
#> Done!
<- new_var_set()
batch_test <- batch_test %>%
batch_test add_var("par2", "var3", 0, 0.5, 0.1)
<- make_var_grid(batch_test)
batch_test_grid <- batch_simulation(batch_test_grid, sim_fun_test,
batch_test_result default_list = list(
par1 = list(var1 = 0),
par2 = list(var2 = 0, var3 = 0)
),bigmemory = FALSE
)<- new_var_set()
batch_test2 <- batch_test2 %>%
batch_test2 add_var("par1", "var1", -0.2, 0.2, 0.2) %>%
add_var("par2", "var2", -0.2, 0.2, 0.2)
<- make_var_grid(batch_test2)
batch_test_grid2 <- batch_simulation(batch_test_grid2, sim_fun_test,
batch_test_result2 default_list = list(
par1 = list(var1 = 0),
par2 = list(var2 = 0, var3 = 0)
),bigmemory = FALSE
)
<- make_2d_matrix(batch_test_result2, x = "out1", rows = "var1", cols = "var2", from = -1, to = 1, adjust = 0.1, individual_landscape = TRUE)
l_batch_2d_m2 #> Making the plot...
#> Done!
<- make_3d_matrix(batch_test_result2, x = "out1", y = "out2", rows = "var1", cols = "var2", lims = c(-3, 3, -3, 3), h = 0.001, kde_fun = "ks", Umax = 10, individual_landscape = TRUE)
l_batch_3d_m2 #> Making the 2d plot...
#> Done!
<- make_3d_animation(batch_test_result, x = "out1", y = "out2", fr = "var3", Umax = 20, lims = c(-3, 3, -3, 3), h = 0.002, individual_landscape = TRUE)
l_batch_3d_a #> Wrangling data...
#> Done!
#> Making the plot...
#> Done!
#> Making the 2d plot...
#> Done!
#> Making the 3d matrix...
#> Making the 2d plot...
#> Done!
#> Done!
```

Frequently used parameters for the family of barrier functions:

`start_location_value`

,`end_location_value`

: the initial position (in value) for searching the start/end point; `start_r`

,`end_r`

: the searching (L1) radius for searching the start/end point.

```
<- calculate_barrier_2d(l_single_2d, start_location_value = -2, end_location_value = 2, start_r = 0.3, end_r = 0.3)
b_single_2d
$local_min_start
b_single_2d#> $U
#> [1] 1.722065
#>
#> $location
#> x_index x_value
#> 1 -2
$local_min_end
b_single_2d#> $U
#> [1] 1.723732
#>
#> $location
#> x_index x_value
#> 512 2
$saddle_point
b_single_2d#> $U
#> [1] 2.167971
#>
#> $location
#> x_index x_value
#> 267.00000000 0.08219178
get_barrier_height(b_single_2d)
#> delta_U_start delta_U_end
#> 0.4459061 0.4442392
plot(l_single_2d) + get_geom(b_single_2d)
```

```
<- calculate_barrier_3d(l_single_3d, start_location_value = c(-2.5, -2), end_location_value = c(2.5, 0), start_r = 0.3, end_r = 0.3)
b_single_3d plot(l_single_3d, 2) + get_geom(b_single_3d)
```

```
<- calculate_barrier_2d_batch(l_batch_2d_m2, start_location_value = -0.35, end_location_value = 0.35, start_r = 0.34, end_r = 0.34)
b_batch_2d_m2 plot(l_batch_2d_m2) + get_geom(b_batch_2d_m2)
```

```
<- calculate_barrier_3d_batch(l_batch_3d_m2, start_location_value = c(-1, -1), end_location_value = c(1, 1), start_r = 0.3, end_r = 0.3)
b_batch_3d_m2 #> The U in this range is too high. Searching range expanded...
#> r = c(0.691959798994974,0.691959798994974)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.752261306532662,0.752261306532662)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.691959798994974,0.691959798994974)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.691959798994974,0.691959798994974)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.601507537688441,0.601507537688441)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.571356783919597,0.571356783919597)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.752261306532662,0.752261306532662)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.752261306532662,0.752261306532662)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.903015075376882,0.903015075376882)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.903015075376882,0.903015075376882)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.752261306532662,0.752261306532662)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.752261306532662,0.752261306532662)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.691959798994974,0.691959798994974)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.631658291457285,0.631658291457285)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.691959798994974,0.691959798994974)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.691959798994974,0.691959798994974)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.631658291457285,0.631658291457285)
#> The U in this range is too high. Searching range expanded...
#> r = c(0.691959798994974,0.691959798994974)
plot(l_batch_3d_m2) + get_geom(b_batch_3d_m2)
```

```
<- calculate_barrier(l_batch_3d_a, start_location_value = c(0,0), end_location_value = c(2, 1), start_r = 0.3, end_r = 0.6)
b_batch_3d_a #> The U in this range is too high. Searching range expanded...
#> r = c(1.83618090452261,1.83618090452261)
#> The U in this range is too high. Searching range expanded...
#> r = c(1.41407035175879,1.41407035175879)
#> The U in this range is too high. Searching range expanded...
#> r = c(1.02211055276382,1.02211055276382)
plot(l_batch_3d_a, 3) + get_geom(b_batch_3d_a)
```

```
## This barrier calculation doesn't find proper local minimums for several landscapes. Specify the searching parameters per landscape manually.
## First, print a template of the data format.
make_barrier_grid_3d(batch_test_grid, start_location_value = c(0,0), end_location_value = c(2, 1), start_r = 0.3, end_r = 0.6, print_template = TRUE)
#> structure(list(start_location_value = list(c(0, 0), c(0, 0),
#> c(0, 0), c(0, 0), c(0, 0), c(0, 0)), start_r = list(c(0.3,
#> 0.3), c(0.3, 0.3), c(0.3, 0.3), c(0.3, 0.3), c(0.3, 0.3), c(0.3,
#> 0.3)), end_location_value = list(c(2, 1), c(2, 1), c(2, 1), c(2,
#> 1), c(2, 1), c(2, 1)), end_r = list(c(0.6, 0.6), c(0.6, 0.6),
#> c(0.6, 0.6), c(0.6, 0.6), c(0.6, 0.6), c(0.6, 0.6))), row.names = c(NA,
#> -6L), class = c("var_grid", "data.frame"))
#> var_list var3 start_location_value start_r end_location_value end_r
#> 1 0 0.0 0, 0 0.3, 0.3 2, 1 0.6, 0.6
#> 2 0.1 0.1 0, 0 0.3, 0.3 2, 1 0.6, 0.6
#> 3 0.2 0.2 0, 0 0.3, 0.3 2, 1 0.6, 0.6
#> 4 0.3 0.3 0, 0 0.3, 0.3 2, 1 0.6, 0.6
#> 5 0.4 0.4 0, 0 0.3, 0.3 2, 1 0.6, 0.6
#> 6 0.5 0.5 0, 0 0.3, 0.3 2, 1 0.6, 0.6
## Then, modify the parameters as you want, and send this `barrier_grid` to the barrier calculation function.
<- calculate_barrier_3d_batch(
b_batch_3d_a
l_batch_3d_a,make_barrier_grid_3d(batch_test_grid,
df =
structure(list(start_location_value = list(
c(0, 0), c(0, 0),
c(0, 0), c(0, 0), c(0, 0), c(0, 0)
start_r = list(c(
), 0.1,
0.1
c(0.2, 0.2), c(0.2, 0.2), c(0.3, 0.3), c(0.3, 0.3), c(
), 0.3,
0.3
end_location_value = list(c(0, 0), c(
)), 1,
0.5
c(1, 0.5), c(1.8, 0.8), c(2, 1), c(2, 1)), end_r = c(
), 0.6, 0.6,
0.6, 0.6, 0.6, 0.6
row.names = c(NA, -6L), class = c(
)), "var_grid",
"data.frame"
))
)
)plot(l_batch_3d_a, 3) + get_geom(b_batch_3d_a)
#> geom_path: Each group consists of only one observation. Do you need to adjust
#> the group aesthetic?
```

```
## Now it works well.
```