allocTM: Site allocation criterion that uses two initial matrices

In SURDES: Functions for a stratified SURvey DESign

Description

A stratified survey design that selects a set of sampling localities from a universe of available sites using an allocation procedure in which environmental and geographical distances are assumed to be surrogates for diversity variations. Environmental and geographical distances are considered separately.

The procedure selects the sampling points with a set of iterative rules. First step: maximizises the amount of environmental coverage using a p-median allocation procedure (for further explanations see Faith 1996, Hortal and Lobo 2005, Hortal et al. 2009). Second step: Takes the sampling localities selected in the previous step and uses a p-median allocation procedure to maximize the amount of geographical distance covered. Next steps: Takes the sampling localities selected after second step and uses a set of rules or conditions defined by the user to select final localities. Conditions should be related to the prioritisation in the selection procedure, for example: conservation status or distance to roads. For each rule a vector of values and the type of criteria should be defined (see definition of criteria and conditions).

Usage

  allocTM(dist, m, vini=rep(0, dim(dist)[2]), vtarget=rep(1, dim(dist)[2]), 
  	criteria, sdint=rep(1, length(criteria)), conditions, iter)

Arguments

dist	Geographical distance matrix, a dissimilarity matrix containing all pairwise distances between the available sites in the region usually calculated with daisy() from package cluster or similar function.
m	Environmental distance matrix, a dissimilarity matrix containing all pairwise distances between the available sites in the region, usually calculated with daisy() from package cluster or similar function.
vini	See definition in alloc().
vtarget	See definition in alloc().
criteria	See definition in alloc().
sdint	See definition in alloc().
conditions	See definition in alloc().
iter	See definition in alloc().

Details

In each iteration, the procedure first selects a set of sample sites minimizing the environmental distance between the non selected sites (p-median procedure), then from the sites selected in the first step selects a second set of sites minimizing the geographical distance between the non selected sites (p-median procedure), and in the following steps, criteria defined by the user in conditions are used iteratively to restrict the number of selected sites. If more than one point remain selected after applying all the conditions, the function selects one at random. Therefore, in each step just one sample site is selected. The next iteration will start with all the points minus the selected point in the previous iteration.

Value

See definition in alloc().

Author(s)

Nagore Garcia Medina & Bernardo Garcia Carreras

References

Church, R.L. & Sorensen, P. (1994) Integrating Normative location models into GIS: problems and prospects with the p-median model. Technical Report, NGCIA.

Church, R.L. (2002) Geographical information systems and location science. Computers and Operation Research 29: 541-562.

Faith, D.P. & Walker, P.A. (1996) Environmental diversity: on the best possible use of surrogate data for assessing the relative biodiversity of sets of areas. Biodiversity and Conservation 5: 399-415.

Hortal, J., Araujo, M.B. & Lobo, J.M. (2009) Testing the effectiveness of discrete and continuous environmental diversity as a surrogate for species diversity. Ecological Indicators 9: 139-149.

Hortal, J. & Lobo, J.M. (2005) An ED-based protocol for the optimal sampling of diversity. Biodiversity and Conservation 14: 2913-2947.

Examples

  # load the environmental and spatial matrices
  data(env)
  data(geogr)

  # load a matrix containing the conditions, the initial vector and the target
  # points
  data(conditions)
  
  # define vector of initial points  
  data(vini)

  # define the criteria to apply to the conditions: maximise conservation
  # (qualitative variable), maximise area of the site (qualitative variable)
  # and minimize distance to roads (quantitative variable)
  data(criteria)

  result <- allocTM(m=env, dist=geogr, vini=vini, criteria=criteria, 
  	conditions=conditions, iter=20)

  uncov <- rowSums(result$pmmatrix)
  plot(1:length(uncov),uncov)

SURDES documentation built on May 2, 2019, 6:22 p.m.