Function to calculate the optimal distance threshold for nearest neighborhood sampling.

The method is based on the assumption that the underlying dataset has a connected structure. By looking at the distance between points in areas with a low density, ie large distances between points, we can determine the distance that a realistic points could have if it originated from the observed environment to the realized data point. If we set the maximal distance to half the distance between points in the low density region, excluding outlayers, we exclude points that originate from "empty cells" in the classical case. We still over-sample the border regions, as the possible directions in which a possible real point can lay are limited compared to points on the inside.

Usage

optimalDistanceThresholdNn(
  env.data = NULL,
  index.for.cutof = 5,
  dimensions = c("PC1", "PC2"),
  num.neighbors = 3
)

Arguments

env.data

Dataframe containing the environmental observation

index.for.cutof

Index that is supposed to describe a low density point but not an outlayer

dimensions

Vector containing the dimensions included in the analysis

num.neighbors

Number of Neighbors

Value

maximal distance a point should be remapped from to have originated from a region inside of the environmental space.

Details

A possible way to eliminate this issue could be to find n neighbors in the real dataset, look at the direction in which we can find them and reject a point with a probability of one minus the ration of the covered directions to the full hyper-sphere. In the high dimensional case this seems difficult, therefore it was not implemented.

The issue is analogue to cells that only partially overlap with the environmental space. For the points in these cells the probability to be sampled is higher than it should be.