AHMbook (version 0.2.5)

simPPe: Simulate a spatial point pattern in a heterogeneous landscape

Description

The function simulates a spatial point pattern in a heterogeneous landscape simulated on a square landscape. The study area ('core') is simulated inside the larger landscape that includes a buffer. The size of the core is defined by the lscape.size minus twice the buffer.

There is one habitat covariate X that affects the intensity of the points. X is spatially structured with negative-exponential spatial autocorrelation; the parameters of the field can be chosen to create large 'islands' of similar values or no 'islands' at all, in which case the field is spatially unstructured.

The intensity of STATIC points (e.g. animal activity centers) may be inhomogeneous and affected by the coefficient beta, which is the log-linear effect of X.

To recreate the data sets used in the book with R 3.6.0 or later, include sample.kind="Rounding" in the call to set.seed. This should only be used for reproduction of old results.

Usage

simPPe(lscape.size = 150, buffer.width = 25, variance.X = 1, theta.X = 10,
  M = 250, beta = 1, quads.along.side = 6, show.plots = TRUE)

Arguments

lscape.size

size (width = height) of the square landscape, including core and buffer.

buffer.width

width of buffer around core study area.

variance.X

variance of Gaussian random field (covariate X).

theta.X

scale parameter of correlation in field (must be >0).

M

expected number of activity centers in core area.

beta

coefficient of the habitat covariate.

quads.along.side

number of quadrats along the side of the core area; the total number of quadrats will be quads.along.side^2, thus indirectly defining the quadrat area.

show.plots

if TRUE, summary plots are displayed.

Value

A list with the values of the input arguments and the following additional elements:

core

range of x and y coordinates in the 'core'

M2

number of ACs in the total landscape, including the buffer

grid

coordinates of the center of each pixel

pixel.size

length of side of each pixel

size.core

the width=height of the core area

prop.core

the proportion of the landscape inside the core

X

matrix of covariate values for each pixel

probs

matrix of probabilities of an AC being inside each pixel (sums to 1)

pixel.id

the ID of the pixel for each AC

u

2-column matrix, coordinate of each AC

nsite

number of quadrats

quad.size

width = height of each quadrat

breaks

boundaries of the quadrats

mid.pt

mid-points of the quadrats

lambda_pp

intensity of point pattern (ACs per unit area)

Nac

site-specific abundance of ACs

zac

site-specific occurrence (0/1) of ACs

E_N

average realized abundance per quadrat

E_z

average realized occupancy per quadrat

References

K<U+00E9>ry, M. & Royle, J.A. (2021) Applied Hierarchical Modeling in Ecology AHM2 - 10.

Examples

# NOT RUN {
# Nice plot (produces the really nice Fig. 10-2 in the book)
# RNGkind(sample.kind = "Rounding") # run this for R >= 3.6.0
set.seed(117, kind="Mersenne-Twister")
str(dat <- simPPe(lscape.size = 200, buffer.width = 25, variance.X = 1,
  theta.X = 70, M = 200, beta = 1, quads.along.side = 6))

# }
# NOT RUN {
# Smaller study area, fewer individuals (M)
str(dat <- simPPe(lscape.size = 24, buffer.width = 2, variance.X = 1,
  theta.X = 10, M = 50, beta = 1, quads.along.side = 6))

# Stronger habitat heterogeneity (variance.X): more aggregation
str(dat <- simPPe(lscape.size = 24, buffer.width = 2, variance.X = 10,
  theta.X = 10, M = 50, beta = 1, quads.along.side = 6))

# Longer habitat gradient (theta.X)
str(dat <- simPPe(lscape.size = 24, buffer.width = 2, variance.X = 1,
  theta.X = 100, M = 250, beta = 1, quads.along.side = 6))

# No habitat variability (variance.X): homogeneous point process
str(dat <- simPPe(lscape.size = 24, buffer.width = 2, variance.X = 0,
  theta.X = 10, M = 100, beta = 1, quads.along.side = 6))
# No habitat preference (beta): homogeneous point process
str(dat <- simPPe(lscape.size = 24, buffer.width = 2, variance.X = 1,
  theta.X = 10, M = 100, beta = 0, quads.along.side = 6))
# Habitat heterogeneity at very small scale (theta.X)
str(dat <- simPPe(lscape.size = 1000, buffer.width = 20, variance.X = 1,
  theta.X = 0.001, M = 250, beta = 1, quads.along.side = 6))

str(simPPe(M = 1))      # Often produces no point at all
str(simPPe(M = 10))
str(simPPe(M = 100))
str(simPPe(M = 1000))

str(simPPe(M = 20, quads.along.side = 100)) # Lots of small sites
str(simPPe(M = 20, quads.along.side = 10))
str(simPPe(M = 20, quads.along.side = 5))
str(simPPe(M = 20, quads.along.side = 1))   # whole study area is 1 site
# }