Table 1.

Model checking for introduction scenarios 1, 2 and 3.

			Probability (tsimulated<tobserved)
	Test quantity (t)	Observed value	Scenario 1	Scenario 2	Scenario 3
Test quantities	NAL_S	13.6000	0.7275	0.2871	0.6235
corresponding	NAL_1	3.4000	0.7542	0.9865 (*)	0.4252
to thesummary	NAL_2	3.6500	0.6455	0.4102	0.4761
statistics used	HET_S	0.8429	0.5621	0.2471	0.4488
to discriminate	HET_1	0.5151	0.4938	0.9890 (*)	0.4339
among	HET_2	0.5725	0.9125	0.9188	0.8221
scenarios and	MGW_S	0.8242	0.3593	0.7656	0.5230
compute	MGW_1	0.4072	0.3782	0.6713	0.4524
parameter	MGW_2	0.4834	0.6117	0.8499	0.7297
posterior	FST_S_1	0.2170	0.7882	0.0371 (*)	0.8105
distributions	FST_S_2	0.2050	0.6180	0.4606	0.6052
	FST_2_3	0.1761	0.0001 (***)	0.9580 (*)	0.6289
Test quantities	VAR_S	21.7561	0.7476	0.2538	0.6209
corresponding	VAR_1	9.3385	0.4861	0.3561	0.3598
to summary	VAR_2	9.5277	0.5232	0.1792	0.3748
statistics NOT	LIK_1_S	38.5648	0.7867	0.4503	0.7240
used to	LIK_1_2	31.7504	0.0001 (***)	1.0000 (***)	0.7162
discriminate	LIK_2_1	32.1075	0.0001 (***)	0.9850 (*)	0.7836
among	H2P_S_1	0.7734	0.6563	0.8411	0.6115
scenarios and	H2P_S_2	0.7993	0.9231	0.8239	0.8664
compute	H2P_1_2	0.6020	0.0315 (*)	0.9975 (**)	0.7193
parameter	DAS_S_1	0.1329	0.2298	0.4582	0.2639
posterior	DAS_S_2	0.1099	0.0559	0.1681	0.0816
distributions	DAS_1_2	0.3402	1.0000 (***)	0.0001 (***)	0.2529

Evolutionary scenarios 1, 2 and 3 are detailed in Figure 3. The single "pseudo-observed" test data set analyzed here was simulated under scenario 3. The probability (t_simulated <t_observed) given for each test quantities (t) was computed from 10,000 data sets simulated from the posterior distributions of parameters obtained under a given scenario. Corresponding tail-area probabilities, or p-values, of the test quantities (t) can be easily obtained as Prob(t_simulated <t_observed) and 1.0 - Prob (t_simulated <t_observed) for Prob (t_simulated <t_observed) ≤ 0.5 and > 0.5, respectively [22]. The test quantities correspond to the summary statistics used to discriminate among scenarios and compute the posterior distributions of parameters or to other statistics. NAL_i = mean number of alleles in population i, HET_i = mean expected heterozygosity in population i [38], MGW_i = mean ratio of the number of alleles over the range of allele sizes [54], FST_i_j = F_ST value between populations i and j [39], VAR_i = mean allelic size variance in population i, LIK_i_j = mean individual assignment likelihoods of population i assigned to population j [22], H2P_i_j = mean expected heterozygosity pooling samples from populations i and j, DAS_i_j = shared allele distance between populations i and j [55]. Populations i and j correspond to populations S, 1 or 2 in Figure 3. *, **, *** = tail-area probability < 0.05, < 0.01 and < 0.001, respectively. Significant tail-area probabilities after applying the false discovery rate correction method of Benjamini and Hochberg [43] are given in bold italic characters.