dbmss (version 1.2.4)

KdEnvelope: Estimation of the confidence envelope of the Kd function under its null hypothesis

Description

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

Usage

KdEnvelope(NumberOfSimulations, Alpha, X, r, ReferenceType, NeighborType, 
    Weighted = FALSE, SimulationType = "RandomLocation")

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.

ReferenceType

One of the point types.

NeighborType

One of the point types.

Weighted

Logical; if TRUE, estimates the Kemp function.

SimulationType

A string describing the null hypothesis to simulate. The null hypothesis may be "RandomLocation": points are redistributed on the actual locations; "RandomLabeling": randomizes point types, keeping locations and weights unchanged; "P

Value

• A list:
• Simulations
  A matrix containing the simulated values (each line is a simulation, each column a value of Kd(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.

See Also

Kd.r

Examples

data(paracou16)
# Keep only 50% of points to run this example
X <- rthin(paracou16, 0.5)
plot(X)

# Calculate Kd
r <- 0:100
ActualValues.X <- Kd.r(X, r, "Q. Rosea", "Q. Rosea")

# Calculate confidence envelope (should be 1000 simulations, reduced to 20 to save time)
NumberOfSimulations <- 20
Alpha <- .20
LocalEnvelope.X <- KdEnvelope(NumberOfSimulations, Alpha, X, r, "Q. Rosea", "Q. Rosea")
GlobalEnvelope.X <- GlobalEnvelope(LocalEnvelope.X$Simulations, Alpha)

# Plot
PlotResults(r, ActualValues.X, LocalEnvelope.X, GlobalEnvelope.X, ylab="Kd", Legend=TRUE, 
    LegendItems=c("M", "Local CI", "Global CI"), LegendPosition="bottomright")