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Ecography ECOG-00205Naimi, B., Hamm, N. A. S., Groen, T. A., Skidmore, A. K. and Toxopeus, A. G. 2013. Where is positional uncertainty a problem for species distribution modelling? – Ecography 36: xxx–xxx.
Supplementary material
Appendix 1 This appendix represents the equations that have been used in the main text. S1‐1‐ Variance Inflation Factor (VIF) VIF is based on the square of the multiple correlation coefficient ( 2
pR ) resulting from regressing the
predictor variable xp against all other predictor variables. Then the VIFp associated with the pth predictor, is:
where n is the number of predictor variables. If xp has a strong linear relationship with at least one other variable, 2
pR would be close to 1, and VIFp would be large.
S1‐2‐ K statistic Equation 2 gives the K statistic in standardized form for each environmental variable at each grid cell. where Ki is the unstandardized K statistic at grid cell i:
𝑲𝒊 = 𝝎𝒊𝒋 𝒙𝒊 − 𝒙𝒋𝒋
𝝎𝒊𝒋 is a binary weight which specifies if the cell j is within a specified distance from cell i; and are the attribute values at cell i and j, respectively. The mean and variance of the K statistic for all grid cells were calculated using equations 4 and 5: 𝐸 𝐾! = 𝑊!𝐷! (4) where:
𝑊! = 𝝎𝒊𝒋!
𝐷! =𝑧! − 𝑧!!
𝑛 − 1
xxz ii −= ; xxz jj −= and n is the number of cells.
(3)
(5)
(2) { })(Var)(E)(
i
iii K
KKKz −=
npRp
p ,...,1,11VIF 2 =−
= (1)
𝑉𝑎𝑟 𝐾! =𝑊!× 𝑛 − 1 −𝑊! × 𝑡!! − 𝐷!!
𝑛 − 2
where:
)1()( 22 −−=∑ nzztj jii
is the mean square error for iz .
Appendix 2 This appendix demonstrates the use of the usdm package to explore whether and where positional uncertainty in species occurrence data is a problem for species distribution modelling. usdm (uncertainty analysis for species distribution models) is an R package, developed by Naimi (2012), aims to provide functions to assess the impact of different sources of error and uncertainty on species distribution models. The approach presented in this study has been implemented as a function, speciesLisa, which calculates the K statistic (and, optionally, other local indicators of spatial associations) in predictors at each sample location. Given species sample locations, an estimate of the positional uncertainty, as well as a set of predictors and their importance, this function returns an object of a class of “speciesLISA” including K statistic (or other LISAs) for each predictor at each sample location and an aggregated K statistic. plot function maps the results which allows us to target the locations that are likely to affect the predictions from the SDMs. usdm also includes some other functions related to the purpose of the package. To install the packge: install.packages('usdm') The following commands demonstrate the calculation of the K statistics for a sample dataset in the Netherlands (case study of nl1): library(usdm) # reading predictor variables: file <- system.file("external/predictors.grd", package="usdm") predictors<-brick(file) plot(predictors) # reading species data dsn <- system.file("external", package="usdm") sp <- readOGR(dsn=dsn,layer="species_nl") # quantifying the level of local spatial association given positional uncertainty: spl<-speciesLisa(predictors,sp,uncertainty=15000,weights=c(0.14,0.2,0.38,0.2,0.08)) spl # visualizing the level of lisa at species occurrence locations plot(spl) # reading boundary map dsn <- system.file("external", package="usdm") bnd <- readOGR(dsn=dsn,layer="boundary") # including boundary in the map: plot(spl,bnd)
Appendix 3 Figure A1 Interaction plots for the case study nl1 based on the Friedman test – difference of AUC mean
between three scenarios (S.all, S.low, S.rand, and S.high) and different sample size (x‐axis) for different
SDMs
Figure A2 Interaction plots for the case study es1 based on the Friedman test– difference of AUC mean between three scenarios (S.all, S.low, S.rand, and S.high) and different sample size (x‐axis) for different SDMs
Figure A3 The interaction of the local spatial association and positional uncertainty for the case study of es2. (a) The level of local spatial association at the location of species occurrences, lower K indicates higher local spatial association. (b) Histogram of the K statistics. (c) Interaction plots based on the Friedman test – difference of AUC mean between three scenarios (S.all, S.low, S.rand, and S.high) and different sample size (x‐axis) for different SDMs; S.all represents the scenario for which the positional error was introduced in all species sample locations; in the S.low and S.high scenarios, the positional error was introduced to half of all occurrences where the value of K statistics were lower and higher
than median of the K statistics, respectively. In the S.rand, the positional error was introduced to the half of randomly selected occurrences (d) Variation of the model accuracy (AUC) over the Monte Carlo simulation for different scenarios of the impact of positional uncertainty on SDMs prediction based on the local spatial association (S.all, S.low, S.rand and S.high on x‐axis) and six SDMs with increasing sample size; each box represents the results for 1000 Monte Carlo runs. (e) The level of significance for AUC mean comparison between different scenarios.
Figure A4 The interaction of the local spatial association and positional uncertainty for the case study of es3. The different sub‐figures are described in Fig. S1.
Figure A5 The interaction of the local spatial association and positional uncertainty for the case study of nl2. The different sub‐figures are described in Fig. S1.