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Table 1 Model checking for introduction scenarios 1, 2 and 3.

From: Inference on population history and model checking using DNA sequence and microsatellite data with the software DIYABC (v1.0)

   

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

  1. 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 (tsimulated <tobserved) 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(tsimulated <tobserved) and 1.0 - Prob (tsimulated <tobserved) for Prob (tsimulated <tobserved) ≤ 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 = FST 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.