In NINAnor/oneimpact: Tools for the assessment of the cumulative impacts of anthropogenic features in ecological studies
knitr::opts_chunk$set(
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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 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 habitat amount and fragmentation
and the scale of effect of spatial variables on species-habitat relationships,
widely explored in the landscape ecology literature (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:
library(devtools)
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 parameter where. On the one hand, 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. On the other hand, in GRASS GIS,
it is possible to compute the ZOI for very large maps using the
software's compiled tools, and given that 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 might 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 zone of influence functions implemented in oneimpact are
shown in Table 1 and might be explored with the command help(zoi_functions).
They might 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 might be used in both calc_zoi_nearest()
and 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 might be created through 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 might be determined by the user (parameter 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 might 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 (parameter radius) controls how far this effect reaches. 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. |
| 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 neareast 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 (parameter 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 (parameter type). The calc_zoi_nearest() function might 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 might follow different shapes (parameter type) and cover an area according to the ZOI radius (parameter 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
threshold_decay(10, radius = 10) # at or beyond the radius
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
linear_decay(10, radius = 10) # at or beyond the radius
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 might be calculated using the exp_decay() function:
# exponential decay ZOI with radius = 10
exp_decay(5, radius = 10) # within the radius
exp_decay(10, radius = 10) # at the radius
exp_decay(15, radius = 10) # beyond the radius
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 might be changed by
the user (e.g. to 0.01 or other small value). Changing zoi_limit changes the
interpretation of the ZOI radius parameter, though:
# changing zoi_limit changes the interpretation of radius
exp_decay(5, radius = 10, zoi_limit = 0.01) # within the radius
exp_decay(10, radius = 10, zoi_limit = 0.01) # at the radius
exp_decay(15, radius = 10, zoi_limit = 0.01) # beyond the radius
We 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")
We add to the plot a horizontal dashed line at zoi_limit = 0.05 and vertical dashed
lines at x = 10 and x = -10 (since radius = 10), to show that the ZOI radius
represents 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 might 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
gaussian_decay(10, radius = 10) # at or beyond the radius
gaussian_decay(15, radius = 10) # at or beyond the radius
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 for all the
functions, the change in their shape strongly modifies the interpretation of how
the ZOI changes with distance. These functions set here might 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
accomodate 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
might be calculated for the zone of influence: the ZOI of the nearest feature alone and the cumulative ZOI of multiple features.
To exemplify their difference, we illustrate them using a 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 1.
Now we do the same but considering that the ZOI of each feature accumulates. We do it 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 might be higher
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(). To give 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 might 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
# 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. In our case, since it is in vector format, it must be rasterized first.
For many types of anthropogenic infrastructure or disturbance which are represented
by lines or polygons (e.g. roads, power lines, areas of deforestation), it is enough 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 large enough pixels size, though,
it might be more interesting to
count the number of features per pixel, since there might 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 parameter 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
# 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
This map might be used as it is as input for calc_zoi_nearest(). For this function,
is it important for the background values of the input raster map (pixels with no cabins)
to be NA (no-data). 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 (parameter
where = "R").
# calculate ZOI
cabins_nearest <- calc_zoi_nearest(cabins_rast, radius = 1000, type = "Gauss")
# plot
plot(cabins_nearest)
The shape of the ZOI might be changed through the parameter type, using the
functions presented above. This parameter might be also set to
type = "euclidean"
for only the computation of the Euclidean distance to the nearest feature or to
"log" or "sqrt" for the log- or sqrt-transformed distance from the nearest
feature.
Compute the cumulative ZOI of multiple features
Differently from calc_zoi_nearest(), the input raster map for the calc_zoi_cumulative()
should present zeros as the background (pixels with no cabins). In R, background NA
values might be checked and reclassified to zero using the zeroAsNA = TRUE parameter,
but in GRASS GIS this is not implemented. 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 might also be changed through the
parameter type, using the functions presented above. Alternatively, a customized
weight matrix might be defined by the user and used as the radius parameter,
in case which the user must set type = "mfilter". Other functions to define
weight matrices might 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 might 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
might assumes values much higher 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 1.
As a consequence, the density of features generally presents values lower 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.
knitr::include_graphics("figure_workflow.png")
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 feaure 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.
Here 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 parameter 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 - nearest
zoi_exp_nearest <- calc_zoi_nearest(cabins_rast, radius = radii,
type = "exp_decay")
# exp decay ZOI - cumulative
zoi_exp_cumul <- calc_zoi_cumulative(cabins_rast, radius = radii,
type = "exp_decay", zeroAsNA = TRUE)
plot(zoi_all)
# 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.
# 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)
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).
Such statistical modeling procedures are beyond the scope of oneimpact.
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statistical learning: With applications in R (Second edition). Springer.
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using threshold regression. Working Papers in Transport, Tourism, Information
Technology and Microdata Analysis, 2020:01, 1–16.
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1717–1724. https://doi.org/10.1111/2041-210X.12830
Niebuhr, B. B., van Moorter, B., Stien, A., Tveraa, T., Strand, O., Langeland, K.,
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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 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 habitat amount and fragmentation and the scale of effect of spatial variables on species-habitat relationships, widely explored in the landscape ecology literature (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:
library(devtools) 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 parameter where. On the one hand, 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. On the other hand, in GRASS GIS,
it is possible to compute the ZOI for very large maps using the
software's compiled tools, and given that 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 might 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 zone of influence functions implemented in oneimpact are
shown in Table 1 and might be explored with the command help(zoi_functions).
They might 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 might be used in both calc_zoi_nearest()
and 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 might be created through 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 might be determined by the user (parameter 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 might 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 (parameter radius) controls how far this effect reaches. 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. |
| 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 neareast 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 (parameter 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 (parameter type). The calc_zoi_nearest() function might 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 might follow different shapes (parameter type) and cover an area according to the ZOI radius (parameter 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 threshold_decay(10, radius = 10) # at or beyond the radius
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 linear_decay(10, radius = 10) # at or beyond the radius
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 might be calculated using the exp_decay() function:
# exponential decay ZOI with radius = 10 exp_decay(5, radius = 10) # within the radius exp_decay(10, radius = 10) # at the radius exp_decay(15, radius = 10) # beyond the radius
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 might be changed by
the user (e.g. to 0.01 or other small value). Changing zoi_limit changes the
interpretation of the ZOI radius parameter, though:
# changing zoi_limit changes the interpretation of radius exp_decay(5, radius = 10, zoi_limit = 0.01) # within the radius exp_decay(10, radius = 10, zoi_limit = 0.01) # at the radius exp_decay(15, radius = 10, zoi_limit = 0.01) # beyond the radius
We 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")
We add to the plot a horizontal dashed line at zoi_limit = 0.05 and vertical dashed
lines at x = 10 and x = -10 (since radius = 10), to show that the ZOI radius
represents 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 might 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 gaussian_decay(10, radius = 10) # at or beyond the radius gaussian_decay(15, radius = 10) # at or beyond the radius
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 for all the
functions, the change in their shape strongly modifies the interpretation of how
the ZOI changes with distance. These functions set here might 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
accomodate 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 might be calculated for the zone of influence: the ZOI of the nearest feature alone and the cumulative ZOI of multiple features.
To exemplify their difference, we illustrate them using a 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 1.
Now we do the same but considering that the ZOI of each feature accumulates. We do it 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 might be higher 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(). To give 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 might 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 # 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. In our case, since it is in vector format, it must be rasterized first.
For many types of anthropogenic infrastructure or disturbance which are represented
by lines or polygons (e.g. roads, power lines, areas of deforestation), it is enough 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 large enough pixels size, though,
it might be more interesting to
count the number of features per pixel, since there might 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 parameter 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 # 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
This map might be used as it is as input for calc_zoi_nearest(). For this function,
is it important for the background values of the input raster map (pixels with no cabins)
to be NA (no-data). 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 (parameter
where = "R").
# calculate ZOI cabins_nearest <- calc_zoi_nearest(cabins_rast, radius = 1000, type = "Gauss") # plot plot(cabins_nearest)
The shape of the ZOI might be changed through the parameter type, using the
functions presented above. This parameter might be also set to
type = "euclidean"
for only the computation of the Euclidean distance to the nearest feature or to
"log" or "sqrt" for the log- or sqrt-transformed distance from the nearest
feature.
Compute the cumulative ZOI of multiple features
Differently from calc_zoi_nearest(), the input raster map for the calc_zoi_cumulative()
should present zeros as the background (pixels with no cabins). In R, background NA
values might be checked and reclassified to zero using the zeroAsNA = TRUE parameter,
but in GRASS GIS this is not implemented. 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 might also be changed through the
parameter type, using the functions presented above. Alternatively, a customized
weight matrix might be defined by the user and used as the radius parameter,
in case which the user must set type = "mfilter". Other functions to define
weight matrices might 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 might 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
might assumes values much higher 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 1.
As a consequence, the density of features generally presents values lower 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.
knitr::include_graphics("figure_workflow.png")
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 feaure 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.
Here 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 parameter 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 - nearest zoi_exp_nearest <- calc_zoi_nearest(cabins_rast, radius = radii, type = "exp_decay") # exp decay ZOI - cumulative zoi_exp_cumul <- calc_zoi_cumulative(cabins_rast, radius = radii, type = "exp_decay", zeroAsNA = TRUE) plot(zoi_all)
# 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.
# 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)
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).
Such statistical modeling procedures are beyond the scope 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.
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