Appendix II
To investigate effects of the pesticide on the population’s distribution we assessed the degree of spatial clustering and segregation by distance by using a generalized version of the inhomogeneous K-function for non-stationary point patterns, proposed by Baddeley et al (2000). This was implemented by the spatial statistic package ‘spatstat’ in R, version 2.8.1 (Baddeley and Turner, 2005), with edge corrections (Ripley, 1988). The function, denoted Kinhom, was developed from Ripley’s K-function (Baddeley et al., 2000).
Co-ordinates of all voles were sampled on 31 December of years 30, 60, 90 and 120 from 15 replicates of each experimental design, in total 135 samples (15 replicates x 9 landscapes). Kinhom was evaluated inside radii from 200 up to 1500 meters in intervals of 100 meters around each animal’s location. The resulting statistics was divided by the expected value assuming voles distributed at random according to the heterogeneous Poisson distribution with the observed mean density. This process was repeated 20 times for each replicate and the mean was used in all subsequent analyses. 20 were chosen as the point at which adding further replicate analyses did not change the relative Kinhom value. The statistics were evaluated for all four sampling periods using the 15 replicates for the 9 landscapes. To chart the pesticide’s impact in the measured phases we used the Kinhom value measured at year 30 as a reference point and calculated the relative Kinhom values (rki) for the other temporal samples by subtracting them from this.
(1)
where is the estimate Kinhom value at phase m (year 60, 90 or 120) and is the estimated Kinhom value at year 30 before pesticide treatment. Figure 1 shows the measured rki values for the years 60; 90 and 120 at all the evaluated radii for the default landscape. To obtain a method for comparing between treatments we used the rki value at radius 200 m denoted RKi, was chosen.
Figure 1: rki values as a function of the examined radii for the default landscapes. The rki values were obtained by evaluating the inhomogeneous k function around each animal’s location and the resulting statistic divided by the expected value assuming an inhomogeneous Poisson point pattern. This was performed at simulation year 30; 60; 90 and 120 and provided us with Kinhom values for each period and examined radius. We used the measured Kinhom values at year 30 as a reference point and calculated rki from the other temporal samples by subtracting them from the reference value for all radii. Positive values signify segregation relative to simulation year 30.
References
Baddeley, A. J., Moller, J. & Waagepetersen, R. (2000) Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica, 54, 329-350. Times Cited: 56
Baddeley, A. J. & Turner, R. (2005) Spatstat: An R package for analysing spatial point patterns. Journal of statistical Software, 12, 1-42.
Ripley, B. (1988) Statistical inference for spatial processes. Cambridge university press, Cambridge.
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