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1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 r y = -0.0009x + 0.0727 R² = 0.080 0 50 100 150 200 250 300 Geographic distance (km) Fig. 1 Isolation by distance relationship between pairwise relatedness and geographical distance of rock wren (Xenicus gilviventris) across the lower South Island. The trend, represented as a solid line, was significant (p < 0.001) as determined through Mantel tests with 9,999 permutations. a) K b) 0 1000000 Number of MCMC 1 2 3 4 5 6 7 K Fig. 2 Number of rock wren (Xenicus gilviventris) genetic populations simulated from the posterior distribution generated in GENELAND visualised as a) trace of number of populations (K) along one million MCMC iterations showing good mixing around K=2 and b) histogram showing simulated number of populations with a clear mode at K=2. ∆K 250 -3000 150 -3100 100 -3150 50 -3200 ∆K -3050 0 Ln P(X|K) Ln P(X|K) 200 -3250 1 2 3 4 5 6 7 K Fig. 3 Determination of K, the number of genetic populations of rock wren (Xenicus gilviventris) in the lower South Island from STRUCTURE analysis. The mean loglikelihood of the data was lowest for the model K = 1 and then increased sharply for K = 2, after which there was an overall plateau through to K = 7. When ln P(X|K) plateaus or increases only slightly, then the model with the lowest value of K that captures the major structure of the data is usually the best choice (Pritchard et al. 2010). Delta-K (∆K) cannot be calculated for K = 1; however given that ln P(X|K) was lowest at K = 1 this indicates that this was not the best model for our data. The highest estimate for ∆K was at K = 2, confirming this model was a better choice than any of the models with larger values of K (Evanno et al. 2005).