Getting started with the oneimpact package in R • oneimpact

Introduction

Anthropogenic disturbance often takes place in landscapes already affected by infrastructure development and land use change, leading to cumulative impacts on biodiversity. Typically, the impact of a given type of infrastructure is determined by computing the distance to the nearest feature only, ignoring potential cumulative impacts of multiple features, which can lead to severe underestimations. The oneimpact package is a collection of tools and functions intended to aid the estimation of cumulative impacts in ecological studies and environmental impact assessments. Its main functions are related to the calculation of zone of influence (ZOI) metrics based both on the nearest influence only and the cumulative influence of multiple features of a given type of infrastructure. By calculating the ZOI of the nearest feature and the cumulative ZOI of multiple features using different ZOI decay shapes and radii, it is possible to use these different metrics as covariates in ecological models and evaluate how strongly different infrastructure types affect ecological processes, how their impact spreads in space, how far they reach, and if the impact of multiple features accumulate. The approach is described in details in Niebuhr et al. (submitted) and exemplified in this document.

The discussion around the impacts of anthropogenic disturbance and their zone of influence is closely linked to the studies on quantity, quality, and fragmentation of suitable habitat and the scale of effect of spatial variables on species-habitat relationships (e.g. Miguet et al., 2016; Huais, 2018). For all practical purposes, estimating the ZOI of anthropogenic disturbances is similar to estimating their scale of effect while also taking into account the shape of their influence (i.e. how they are spatially weighted; Miguet et al., 2017).

Here, we give an overview of the functions in oneimpact, define and illustrate the zone of influence functions, show how to use the main package functions, and provide an example of how to use this approach to annotate data for statistical analysis.

To install the oneimpact package, it is possible to use the devtools::install_github() function:

devtools::install_github(repo = "NINAnor/oneimpact", ref = "HEAD")

Once installed, we now load the oneimpact package and other packages used in this vignette.

library(oneimpact)

library(ggplot2) # for plots
library(terra) # for spatial processing
library(sf) # for spatial operations with vectors
library(dplyr) # for data wrangling

Overview of the package

The oneimpact package has two main functions to calculate zones of influence, the functions calc_zoi_nearest() and calc_zoi_cumulative(). Alternatively, the function calc_zoi() can calculate both ZOI metrics in the same run. These functions’ main arguments are the type, which defines the shape of the spatial decay of the ZOI, and radius, which defines how far the influence expands in space (or how fast it decreases with distance).

Both functions can be run in R environment (R Core Team, 2021) and in GRASS GIS environment (GRASS Development Team, 2017). This is defined by the argument where. Computations in R are generally fast and easy-to-use, since they make use of the optimized functions from the terra package (Hijmans, 2022). However, computations might become slow for large maps. Alternatively, in GRASS GIS, it is possible to compute the ZOI for very large maps using the software’s compiled tools as GRASS GIS does not store maps in the computer’s memory. In GRASS GIS, the calculation of the ZOI requires an active connection between the R session and a GRASS GIS location and mapset (through the package rgrass7; Bivand, 2022) and that the input maps are already loaded within this GRASS GIS mapset. Furthermore, in GRASS GIS, the function returns only the name of the output map. This map is stored in the GRASS GIS location/mapset, and may be retrieved to R through the rgrass7::read_RAST() function or exported outside GRASS using the r.out.gdal module, for instance. See this other vignette for more details on how to compute ZOI metrics in GRASS.

The ZOI of the nearest feature (the output of calc_zoi_nearest()) is based on transformations of the map of distance to the nearest feature. First, this map is computed through the terra::distance() function in R or the r.grow.distance module in GRASS. Then, ZOI functions are applied to transform these maps into zones of influence. The ZOI functions implemented in oneimpact are shown in Table 1 and can be explored with the command help(zoi_functions). The ZOI functions can also be plotted in 1 dimensional space with the plot_zoi1d() function, for illustration of their behavior.

The cumulative ZOI of multiple features (the output of calc_zoi_cumulative()) is based on a neighborhood analysis using spatial filters that determine the ZOI functions. The same ZOI functions can be used in either calc_zoi_nearest() or calc_zoi_cumulative(), accounting for different ZOI shapes and radii, but in the latter they are used to create weight matrices as input for the neighborhood analysis. The function already has built-in choices for the ZOI functions that determine the weight matrix. These and other weight matrices can be created using the function filter_create(). The function calc_zoi_cumulative() computes the neighborhood analysis through the terra::focal() function in R or through one of the tools in GRASS GIS: r.mfilter, r.resamp.filter, or r.neighbors. The tool to be used can be determined by the user (argument module).

Table 1: Main functions in oneimpact used to compute zones of influence. They are divided in three types: zone of influence functions (“ZOI functions”), functions to compute the ZOI for raster maps (“Compute ZOI”), and functions to create filters or weight matrices for use in the computation of the cumulative ZOI (“Create filters”).

Type of function	Function	Description	Input	Output
ZOI functions	`dist_decay()` `threshold_decay()` `step_decay()` `linear_decay()` `bartlett_decay()` `tent_decay()` `exp_decay()` `gaussian_decay()` `half_norm_decay()`	These functions compute Zone of Influence (ZOI) decay values. The shape of the zone of influence can be changed through the argument `type` in the generic function `dist_decay()`, or through calling the other specific functions. The functions with different shapes represent multiple ways the ZOI of an infrastructure or disturbance might affect a given process in space, and the ZOI radius (argument `radius`) controls how far this effect extends. The rate of decay of the different ZOI functions is parameterized based on the ZOI radius – e.g. the slope of `linear_decay()` is defined so that the function decreases to zero at the ZOI radius. These functions can be used to transform arrays of (Euclidean) distance values (in one dimension) or rasters of (Euclidean) distance (in two dimensions) into values of a zone of influence. The distance might represent the distance to anthropogenic infrastructure, sources of disturbance, or more broadly any type of land use class or spatial variable.	Vector of distance values or raster of (Euclidean) distance from sources of disturbance; ZOI shape and radius	Vector or raster of ZOI values
ZOI functions	`plot_zoi1d()`	This function plots the zone of influence functions in 1 dimensional space, for illustration purposes. When there is more than one value for `points` (the location of infrastructure or sources of disturbance), either the ZOI of the nearest feature or the cumulative ZOI can be plotted. The ZOI of the nearest feature corresponds to the maximum ZOI value from all infrastructure at each position. The cumulative ZOI corresponds to the sum of the ZOI of all infrastructure at each position.	Vector of x-axis location(s) of infrastructure	Plot of computed nearest or cumulative ZOI
Compute ZOI	`calc_zoi_nearest()`	This function takes in a raster with locations or counts of infrastructure features and calculates a raster representing the zone of influence from the nearest feature of that type of infrastructure. Zones of influence are defined by functions that decay with the distance from each infrastructure and their rate of decay is controlled by the ZOI radius (argument `radius`), which defines how far the influence of an infrastructure feature goes. By default, the Gaussian decay ZOI is calculated, but other decay functions might be used (argument `type`). The `calc_zoi_nearest()` function can also return the Euclidean distance to the nearest feature or a transformation from it (e.g. log- and sqrt-distance from the nearest feature).	Raster(s) with location of disturbance sources; ZOI shape and radius	Raster(s) of ZOI of the nearest feature
Compute ZOI	`calc_zoi_cumulative()`	This function takes in a raster with locations or counts of infrastructure features and calculates a raster representing the cumulative zone of influence or the density of features in space. The process is done through a moving window/neighborhood analysis. The ZOI or weight matrix is defined from zone of influence functions, which may follow different shapes (argument `type`) and cover an area according to the ZOI radius (argument `radius`).	Raster(s) with location of disturbance sources; ZOI shape and radius	Raster(s) of the cumulative ZOI of multiple features
Compute ZOI	`calc_zoi()`	This function takes in a raster with locations or counts of infrastructure and calculates a raster with either or both zone of influence metrics: the ZOI of the nearest feature and the cumulative ZOI. I.e., `calc_zoi()` can compute both `calc_zoi_nearest` and `calc_zoi_cumulative` in a single run.	Raster(s) with location of disturbance sources; ZOI shape and radius	Raster(s) with either the ZOI of the nearest feature or the cumulative ZOI, or both
Create filters	`filter_create()`	This function creates matrices of weights following different functions to be used in neighborhood analyses for rasters. In the context of cumulative impact analysis, they represent the Zone of Influence (ZOI) of each infrastructure point/pixel, to be used to calculate the cumulative ZOI or density of features.	Reference raster; ZOI shape and radius	Weight matrix (or matrices when there is more than one value for the ZOI shape or radius). It can also write the matrices to files using `filter_save`
Create filters	`filter_save()`	This function saves a matrix with weights (filter or kernel matrix) in an external text file. It can save either the raw matrix or save a file using the standards for running the `r.mfilter` algorithm within GRASS GIS.	Matrix of weights	Text file (no output within R)

The concept of zone of influence

The zone of influence (ZOI) is the function $\phi$ that informs how the impact of a given infrastructure feature, source of disturbance, or landscape element decreases with distance. Formally, the ZOI $\phi = f(d, r)$ is any decay function that has a maximum value 1 where disturbance is located, decreases towards zero as the distance $d$ increases, and possibly vanishes at a given point, the ZOI radius $r$ . Broadly speaking, the ZOI is characterized by its shape and radius. Four sets of functions are implemented in oneimpact: threshold decay, linear decay, exponential decay, and Gaussian decay. Some of these functions present the same definition with multiple function names, to accommodate how different algorithms call the same functions (e.g. linear_decay() and bartlett_decay() represent the same function).

ZOI functions

Functions with a well-defined ZOI radius

Some functions vanish for a certain non-infinite distance and therefore present well-defined ZOI radii. Here the ZOI radius $r$ represents the distance at which $\phi = 0$ . Two functions of this type are implemented in oneimpact: the threshold and the linear decay functions.

Threshold decay function

The threshold function is constant if the distance $d$ to infrastructure or source of disturbance is smaller than the ZOI radius $r$ , and zero beyond that. It can be computed using the threshold_decay() or the step_decay() functions:

# threshold ZOI with radius = 10
threshold_decay(5, radius = 10) # within the radius
#> [1] 1
threshold_decay(10, radius = 10) # at or beyond the radius
#> [1] 0

To visualize the function shape in 1 dimension space, we make use of the function plot_zoi1d(). This plot assumes the source of disturbance is located at x = 0 and the distance to it increases for both sides in the x axis:

# threshold ZOI with radius = 10
plot_zoi1d(points = 0, radius = 10, fun = threshold_decay, range_plot = c(-20, 20))

Linear decay function

The linear decay (also Bartlett or tent decay) function decreases linearly with the distance $d$ to infrastructure or source of disturbance and becomes zero at and beyond the ZOI radius $r$ . It can be computed using the following functions: linear_decay(), bartlett_decay(), and tent_decay(). Here we show the use of the function:

# linear decay ZOI with radius = 10
linear_decay(5, radius = 10) # within the radius
#> [1] 0.5
linear_decay(10, radius = 10) # at or beyond the radius
#> [1] 0

We again visualize the function shape in 1 dimension space using the function plot_zoi1d():

# threshold ZOI with radius = 10
plot_zoi1d(points = 0, radius = 10, fun = linear_decay, range_plot = c(-20, 20))

Functions that do not vanish with distance

Some functions decrease but do not vanish as the distance from infrastructure increases. In these cases we define the ZOI radius $r$ as the distance at which the ZOI decreases to $\phi = \phi_{limit}$ , an arbitrary small ZOI value beyond which the influence of the infrastructure is considered to be negligible. In these cases, the ZOI definition needs an extra parameter and is defined as $\phi = f(d, r, \phi_{limit})$ . Two functions of this type are implemented in oneimpact: the exponential decay and the Gaussian decay functions.

Exponential decay function

The exponential decay function decays exponentially with the distance $d$ to infrastructure, and the rate of decay is set so that $\phi = \phi_{limit}$ at the ZOI radius ( $d = r$ ). The exponential decay can be calculated using the exp_decay() function:

# exponential decay ZOI with radius = 10
exp_decay(5, radius = 10) # within the radius
#> [1] 0.2236068
exp_decay(10, radius = 10) # at the radius
#> [1] 0.05
exp_decay(15, radius = 10) # beyond the radius
#> [1] 0.01118034

As it is possible to see, an exponential decay ZOI with radius = 10 does not imply the function is null beyond the ZOI radius, but that it goes below the zoi_limit. By default, zoi_limit = 0.05, but this value can be changed by the user (e.g. to 0.01 or another small value). Changing zoi_limit changes the interpretation of the ZOI radius argument, though:

# changing zoi_limit changes the interpretation of radius
exp_decay(5, radius = 10, zoi_limit = 0.01) # within the radius
#> [1] 0.1
exp_decay(10, radius = 10, zoi_limit = 0.01) # at the radius
#> [1] 0.01
exp_decay(15, radius = 10, zoi_limit = 0.01) # beyond the radius
#> [1] 0.001

We can visualize the function shape in 1 dimension space:

# threshold ZOI with radius = 10
plot_zoi1d(points = 0, radius = 10, fun = exp_decay, range_plot = c(-20, 20)) +
  geom_hline(yintercept = 0.05, linetype = 2, color = "grey") +
  geom_vline(xintercept = c(-10, 10), linetype = 2, color = "grey")

The additional horizontal dashed line at zoi_limit = 0.05 and vertical dashed lines at x = 10 and x = -10 (since radius = 10) illustrate how the ZOI radius corresponds to the distance where the ZOI reaches zoi_limit.

Gaussian decay function

The Gaussian (or half-normal) decay function decays following a half normal shape, and the rate of decay is set so that $\phi = \phi_{limit}$ at the ZOI radius ( $d = r$ ). The Gaussian decay can be calculated using the gaussian_decay() and half_norm_decay() functions:

# Gaussian decay ZOI with radius = 10
gaussian_decay(5, radius = 10) # within the radius
#> [1] 0.4728708
gaussian_decay(10, radius = 10) # at or beyond the radius
#> [1] 0.05
gaussian_decay(15, radius = 10) # at or beyond the radius
#> [1] 0.001182177

We visualize the function shape in 1 dimension space:

# threshold ZOI with radius = 10
plot_zoi1d(points = 0, radius = 10, fun = gaussian_decay, range_plot = c(-20, 20)) +
  geom_hline(yintercept = 0.05, linetype = 2, color = "grey") +
  geom_vline(xintercept = c(-10, 10), linetype = 2, color = "grey")

Notice that, even though the ZOI radius $r$ is defined as 10 for all the decay functions, the change in their shape strongly modifies the interpretation of how the ZOI changes with distance. These functions set here can be used to calculate the ZOI of nearest feature or to define weight matrices and calculate the cumulative ZOI of multiple features. Alternatively, the generic function dist_decay() can accommodate all these shapes by using the argument type. For instance, to compute the ZOI of a disturbance source following a linear decay shape with radius of 6, one can use linear_decay(x = 0, radius = 6) or dist_decay(x = 0, radius = 6, type = "linear").

ZOI metrics

Given a ZOI function was set with a specific shape and ZOI radius and there is more than one infrastructure feature or source of disturbance in space, two metrics can be calculated for the zone of influence: the ZOI of the nearest feature alone and the cumulative ZOI of multiple features.

To illustrate the difference between ‘nearest’ and ‘cumulative’ ZOI, we will plot the Gaussian decay ZOI in 1 dimension space using the plot_zoi1d() function. We set four sources of disturbance (e.g. houses) located at x = 0, x = 2, x = 8, and x = 12, and set the ZOI radius of each feature as radius = 3. We start by plotting the ZOI of the nearest feature alone by setting zoi_metric = "nearest":

disturbance_locations <- c(0, 2, 8, 12)
plot_zoi1d(points = disturbance_locations, radius = 3, fun = gaussian_decay,
           zoi_metric = "nearest", range_plot = c(-10, 20)) +
  labs(x = "Space") +
  ylim(0, 1.5) +
  geom_vline(xintercept = disturbance_locations, linetype = 2, color = "grey")

The location of the disturbance sources is shown by the vertical dashed lines. Notice that the the maximum value for the ZOI of the nearest feature is always 1.

Now, we do the same but considering that the ZOI of each feature is additive by setting zoi_metric = "cumulative" in plot_zoi1d():

plot_zoi1d(points = disturbance_locations, radius = 3, fun = gaussian_decay,
           zoi_metric = "cumulative", range_plot = c(-10, 20)) +
  labs(x = "Space") +
  ylim(0, 1.5) +
  geom_vline(xintercept = disturbance_locations, linetype = 2, color = "grey")

Notice that the the maximum value for the cumulative ZOI of multiple features may be greater than 1 where the ZOI of different features overlap.

Calculating the ZOI metrics for rasters

Define the input raster map

To calculate the ZOI metrics for 2 dimensional, raster objects, we use the functions calc_zoi_nearest() and calc_zoi_cumulative(). As an example, we present a data set with the location of private cabins in Norway, subset for a small sample region in Southern Norway. The data is mapped as points in vector format; more information about it can be found using the command help(sample_area_cabins.gpkg). We read the vector file using the package terra and plot it:

# file path
s <- system.file("vector/sample_area_cabins.gpkg", package = "oneimpact")
# read file
cabins_vect <- terra::vect(s)
# check
cabins_vect
#> class       : SpatVector
#> geometry    : points
#> dimensions  : 6875, 4  (geometries, attributes)
#> extent      : 146900.1, 194694.6, 6622822, 6658891  (xmin, xmax, ymin, ymax)
#> source      : sample_area_cabins.gpkg
#> coord. ref. : ETRS89 / UTM zone 33N (EPSG:25833)
#> names       :   cat buildtype  city value
#> type        : <int>     <chr> <int> <int>
#> values      :     1       161   604     1
#>                   2       161   604     1
#>                   3       161   604     1
#>               ...
# plot
plot(cabins_vect, cex = 0.5)

If the input map is already in raster format, it can be used directly in the calc_zoi_*() functions. However, in our case, the data must be rasterized first since it is in vector format. For many types of anthropogenic infrastructure or disturbance that are represented by lines or polygons (e.g. roads, power lines, areas of deforestation), it is sufficient to create a binary raster as a dummy variable with value 1 where the disturbance is located and 0 (or NA) elsewhere (see an example at this other oneimpact vignette). For point representation of infrastructure and when the raster resolution is coarse relative to vector data, it might be more interesting to count the number of features per pixel, as there may be more than one feature within each pixel. To create a raster with the number of cabins per pixel, we use the function terra::rasterize() with argument fun = length. We load another raster with 100 m resolution for the area to use it as a grid for the rasterization process.

# load grid
s2 <- system.file("raster/sample_area_cabins.tif", package = "oneimpact")
grid <- terra::rast(s2)
# rasterize
cabins_rast <- terra::rasterize(cabins_vect, grid, fun = length)
cabins_rast
#> class       : SpatRaster
#> size        : 361, 478, 1  (nrow, ncol, nlyr)
#> resolution  : 100, 100  (x, y)
#> extent      : 146900, 194700, 6622800, 6658900  (xmin, xmax, ymin, ymax)
#> coord. ref. : +proj=utm +zone=33 +ellps=GRS80 +units=m +no_defs
#> source(s)   : memory
#> varname     : sample_area_cabins
#> name        : V1
#> min value   :  1
#> max value   :  8
# plot
plot(cabins_rast)

This map presents the number of cabins in each pixel and NA where there are no cabins. As a similar procedure in GRASS GIS, it is possible to use the ancillary oneimpact function grass_v2rast_count() to count the number of features of a vector in each pixel and get the output as a raster object.

Compute the ZOI of the nearest feature only

A raster map of ZOI of the nearest feature can be computed using calc_zoi_nearest() using a raster of infrastructure locations as input. For this function, is it important for the background values of the input raster map (pixels with no cabins) to be NA (no-data). For illustration, we compute the ZOI of the nearest feature using a Gaussian shaped ZOI with radius = 1000 m. By default, the computation is done in R (argument where = "R").

# calculate ZOI
cabins_nearest <- calc_zoi_nearest(cabins_rast, radius = 1000, type = "Gauss")
# plot
plot(cabins_nearest)

The shape of the ZOI can be changed through the argument type, using the functions presented above. The type argument can be set to type = "euclidean" for calculation of the Euclidean distance to the nearest feature, "log" for the log-transformed distance, or "sqrt" for the square root-transformed distance from the nearest feature.

Compute the cumulative ZOI of multiple features

In contrast to calc_zoi_nearest(), the input raster map for the calc_zoi_cumulative() must use zeros as the background without infrastructure (e.g. pixels with no cabins). In R, background NA values can be checked and reclassified to zero using the zeroAsNA = TRUE argument, however, this is not implemented in GRASS GIS. In this case, the easiest procedure is to prepare the input raster map outside GRASS or make use of the module [r.null](https://grass.osgeo.org/grass82/manuals/r.null.html) for managing no-data values is rasters within GRASS. We calculate the cumulative ZOI of multiple features using the same setup – a Gaussian shaped ZOI with radius = 1000 m.

# calculate ZOI
cabins_cumul <- calc_zoi_cumulative(cabins_rast, 
                                    radius = 1000, 
                                    type = "gaussian_decay",
                                    zeroAsNA = TRUE)
# plot
plot(cabins_cumul)

Notice that the output map differs considerably from the ZOI of the nearest feature only. Here, the shape of the ZOI can also be changed through the argument type, using the functions presented above. Alternatively, a customized weight matrix can be defined by the user and used as the radius argument, in case which the user must set type = "mfilter". Other functions to define weight matrices can be set e.g. through terra::focalMat() (Hijmans, 2022) or smoothie::kernel2dmeitsjer() (Gilleland, 2013) functions. Notice, however, that these functions are parameterized differently, with no reference to the ZOI radius as the ones defined in oneimpact.

For calc_zoi_cumulative(), the user can choose between computing the cumulative ZOI metric when output_type = "cumulative_zoi" (default) or the density of features if output_type = "density". The cumulative ZOI is the (distance weighted) number of features per unit of space, and can produce values much greater than one when there are features located closer than the ZOI (see the illustrations above). The calculation of the density of features, on the other hand, occurs after a normalization of the weight matrix, so that its values sum to 1. As a consequence, the density of features generally presents values smaller than or close to 1. Both measures represent the same spatial variation, but the interpretation of their values is different.

Using the ZOI approach to annotate and analyze data

In the cumulative impact assessment proposed in oneimpact, the calculation of the ZOI ( $\phi$ ) is done before statistical analysis. In this formulation, $\phi$ defined based on different shapes and radii are considered as different candidates of predictor variables in statistical models (see figure below). Therefore, the evaluation of how the impact of multiple infrastructure features accumulate and the identification of the ZOI shape and radius are recasted as a model selection rather than a parameterization problem.

The figure above shows a workflow for calculating the ZOI metrics and using them to annotate biological data for the estimation of cumulative impacts. Infrastructure raster data are input to the calc_zoi_*() functions, which allow the computation of the ZOI of the nearest feature and the cumulative ZOI based on arguments for the ZOI shape and radius. The output influence rasters and other environmental data are then annotated to biological data, and for each infrastructure type each ZOI metric defined by a shape and radius is considered as a different candidate for a predictor variable. The annotated data is then analyzed through the statistical modeling procedures selected by the user to estimate the effect size and the ZOI radius for each infrastructure type and calculate the impact.

Next, we simulate a data set of sampling points and a theoretical random biological response variable to show the process of calculation of ZOI variables and the annotation of the biological data.

First we create in the study area n = 40 random locations representing sampling points for a given response variable z (e.g. species richness or abundance). We sample the locations using the set_points() function from the package oneimpact and simulate the response variable z as a Poisson distributed random variable with mean $\lambda = 10$ . The simulated sampled data is plotted below.

# seed
set.seed(111)
# get extent of the study area
extent <- terra::ext(cabins_rast)
# sample n = 40 random locations and simulate biological data
# get only coordinates with $pts at the end
bio_data <- set_points(40, method = "random", res = 100, 
                       extent_x = extent[c(1,2)], extent_y = extent[c(3,4)])$pts |> 
  sf::st_as_sf(coords = c(1,2), crs = crs(cabins_rast)) |> # change to sf object
  dplyr::mutate(id = 1:40, z = rpois(40, lambda = 10)) |> # add id and simulate response z 
  terra::vect() # transform to vect to use with SpatRaster object
# plot
plot(cabins_vect, cex = 0.5)
plot(bio_data, col = "red", add = T)

Now, we use the same procedure presented above to calculate the ZOI of the nearest feature and the cumulative ZOI for different radii. We use an exponential decay ZOI and vary the ZOI radius from 500 m to 1500 m. However, we use the calc_zoi() function which can compute both ZOI metrics at once. To do so, we set the argument zeroAsNA to FALSE, since our input raster map has NA as background values. We plot the ZOI layers below.

# radii
radii <- c(500, 1000, 1500)
# exp decay ZOI - both nearest and cumulative
# use zeroAsNA = FALSE since the input has NULL as background
zoi_all <- oneimpact:::calc_zoi(cabins_rast, 
                                radius = radii, type = "exp_decay",
                                zoi_metric = "all", 
                                zeroAsNA = FALSE)
# plot
plot(zoi_all)

Finally, the ZOI variables can be used to annotate the biological data for statistical analysis using terra::extract().

# extract values
zoi_sampling_pts <- terra::extract(zoi_all, bio_data, )
# combine response variable with extracted data
bio_data_annotated <- dplyr::left_join(as.data.frame(bio_data, geom = "XY"), 
                                       zoi_sampling_pts, by = c("id" = "ID"))
# show annotated data
head(bio_data_annotated)
#>   id  z        x       y zoi_nearest_exp_decay500 zoi_nearest_exp_decay1000
#> 1  1  6 175244.5 6645947             1.334868e-07              0.0003653584
#> 2  2  9 181625.8 6634659             4.711992e-02              0.2170712325
#> 3  3  8 164606.2 6645748             8.455576e-02              0.2907847396
#> 4  4 11 171513.4 6656320             1.152959e-01              0.3395525377
#> 5  5 10 164952.3 6643566             1.445658e-02              0.1202355317
#> 6  6 13 166896.5 6636037             1.088078e-04              0.0104310997
#>   zoi_nearest_exp_decay1500 _zoi_cumulative_exp_decay500
#> 1               0.005110688                   0.00000000
#> 2               0.361189277                   0.08906389
#> 3               0.438915658                   0.12350292
#> 4               0.486711178                   0.18623277
#> 5               0.243606320                   0.03573248
#> 6               0.047740474                   0.00000000
#>   _zoi_cumulative_exp_decay1000 _zoi_cumulative_exp_decay1500
#> 1                    0.00000000                    0.02269499
#> 2                    1.16104432                    4.87939875
#> 3                    0.88921937                    2.34383617
#> 4                    0.88243528                    1.75187108
#> 5                    0.38080083                    1.07029764
#> 6                    0.04619249                    0.45860291

From this point, biological data can also be annotated with the ZOI of other disturbance variables and with other environmental covariates and used as input for the estimation of the effect sizes $\beta$ and evaluation of the cumulative effects for different types of infrastructure through statistical models. Statistical analyses can make use of model selection (Burnham & Anderson, 2002; Jackson & Fahrig, 2015; Huais, 2018), penalized regression (Lee et al., 2020), or machine learning approaches, for example (James et al., 2021). These statistical modeling procedures are represented in the other vignettes of oneimpact.

References

Bivand, R. (2022). rgrass7: Interface Between GRASS Geographical Information System and R. R package version 0.2-10. https://CRAN.R-project.org/package=rgrass7

Burnham, K. P., & Anderson, D. R. (2002). Model selection and multimodel inference: A practical information-theoretic approach (2nd ed). Springer.

Gilleland, E. (2013). Two-dimensional kernel smoothing: Using the R package smoothie. NCAR Technical Note, TN-502+STR, 17pp., doi:10.5065/D61834G2.

GRASS Development Team (2017) Geographic Resources Analysis Support System (GRASS GIS) Software, Version 7.8. Open Source Geospatial Foundation.

Hijmans, R. J. (2022). terra: Spatial Data Analysis. R package version 1.5-21. https://CRAN.R-project.org/package=terra

Huais, P. Y. (2018). multifit: An R function for multi-scale analysis in landscape ecology. Landscape Ecology, 33(7), 1023–1028. https://doi.org/10.1007/s10980-018-0657-5

Jackson, H. B., & Fahrig, L. (2015). Are ecologists conducting research at the optimal scale? Global Ecology and Biogeography, 24(1), 52–63. https://doi.org/10.1111/geb.12233

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2021). An introduction to statistical learning: With applications in R (Second edition). Springer.

Lee, Y., Alam, M., Sandström, P., & Skarin, A. (2020). Estimating zones of influence using threshold regression. Working Papers in Transport, Tourism, Information Technology and Microdata Analysis, 2020:01, 1–16.

Miguet, P., Jackson, H. B., Jackson, N. D., Martin, A. E., & Fahrig, L. (2016). What determines the spatial extent of landscape effects on species? Landscape Ecology, 31(6), 1177–1194. https://doi.org/10.1007/s10980-015-0314-1

Miguet, P., Fahrig, L., & Lavigne, C. (2017). How to quantify a distance‐dependent landscape effect on a biological response. Methods in Ecology and Evolution, 8(12), 1717–1724. https://doi.org/10.1111/2041-210X.12830

Niebuhr, B. B., van Moorter, B., Stien, A., Tveraa, T., Strand, O., Langeland, K., Alam, M., Skarin, A., & Panzacchi, M. Estimating the cumulative impact and zone of influence of anthropogenic infrastructure on biodiversity. Methods in Ecology and Evolution, 14, 2362–2375. https://doi.org/10.1111/2041-210X.14133

R Core Team (2021). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.