dbmss (version 1.2.4)

DEnvelope: Estimation of the confidence envelope of the D function under its null hypothesis

Description

Simulates point patterns according to the null hypothesis and returns the envelope of D according to the confidence level.

Usage

DEnvelope(NumberOfSimulations, Alpha, X, r, Cases, Controls, Intertype = FALSE)

Arguments

NumberOfSimulations

The number of simulations to run.

Alpha

The risk level.

X

A point pattern (ppp.object), marks must be a dataframe with two columns: PointType: labels, as factors. PointWeight: weights.

r

A vector of distances.

Cases

One of the point types

Controls

One of the point types.

Intertype

Logical; if TRUE, D is computed as Di in Marcon and Puech (2012).

Value

• A list:
• Simulations
  A matrix containing the simulated values (each line is a simulation, each column a value of D(R)
• Min
  A vector: the lower bound of the envelope
• Max
  A vector: the upper bound of the envelope

Details

This envelope is local, that is to say it is computed separately at each distance. See Loosmore and Ford (2006) for a discussion.

References

Kenkel, N. C. (1988). Pattern of Self-Thinning in Jack Pine: Testing the Random Mortality Hypothesis. Ecology 69(4): 1017-1024. Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87(8): 1925-1931. Marcon, E. and F. Puech (2012). A typology of distance-based measures of spatial concentration. HAL SHS. 00679993.

See Also

Kd.r

Examples

data(paracou16)
# Keep only 20% of points to run this example
X <- rthin(paracou16, 0.2)
plot(X)

# Calculate K
r <- 0:30
ActualValues.X <- D.r(X, r, "V. Americana", "Q. Rosea", Intertype = TRUE)

# Calculate confidence envelope (should be 1000 simulations, reduced to 20 to save time)
NumberOfSimulations <- 20
Alpha <- .05
LocalEnvelope.X <- DEnvelope(NumberOfSimulations, Alpha, X, r, 
    "V. Americana", "Q. Rosea", Intertype = TRUE)

# Plot
PlotResults(r, DivideByPiR2(ActualValues.X, r), lapply(LocalEnvelope.X, DivideByPiR2, r), 
    ylab="D / (pi R^2)", ReferenceValue=0)