"Supporting Information Table S4 Results of model fitting for the 39 alternative models of divergence for RAD-seq data. Models are ranked by model category. SI, strict isolation; IM, isolation-with-migration; AM, ancient migration with one contact period; PAM, ancient migration with two periods of contact; SC, secondary contact with one period of contact; PSC, the same model with two periods of contact. Models involving strict isolation were implemented with no recent expansion, recent expansion (ex), heterogeneity of effective population size across the genome (2N) and both heterogeneity of  effective population size across the genome and recent expansion (2Nex). All models of divergence-with-gene-flow were implemented with recent expansion (ex), heterogeneity of migration rate across the genome (2M2P), heterogeneity of migration rate across the genome and recent expansion (2M2Pex) and heterogeneity in both migration rate and population size (2N2M2P)."							
Model	k	LogL	AIC	Model description	Model comparison within	Model comparison between	
SI	4	-2568.120	5144.240	Strict isolation			
IM	6	-2565.527	5143.054	Isolation-with-migration	SINS		
AM	7	-2539.555	5093.111	Ancient migration	"SI***, IM***, SC+++, PSC+++"		
SC	7	-2565.527	5145.054	Secondary contact	"SINS, IMNS"		
PAM	7	-2538.780	5091.561	Ancient migration with two phases of contact	"SI***, IM***, SC+++, PSC+++, AM1.55"		
PSC	7	-2565.527	5145.054	Secondary contact with two phases of contact	"SINS, IMNS, SC-0.01"		
SIex	7	-2536.229	5086.458	 Expansion		SI***	
IMex	9	-2536.229	5090.459		SIexNS	"IM***, IM2M2P+++"	
AMex	10	-2524.505	5069.009		"SIex***, IMex***, SCex+++, PSCex+++"	"AM***, AM2N2M2P-4.17"	
SCex	10	-2536.229	5092.458		"SIexNS, IMexNS, PSCex0.00"	"SC***, SC2M2P+++"	
PAMex	10	-2524.505	5069.009		"SIex***, IMex***, SCex+++, PSCex+++, Amex-0.00"	"PAM***, PAM2N-0.17"	
PSCex	10	-2536.229	5092.459		"SIexNS, IMexNS"	"PSC***, PSC2M2P+++"	
IM2M2P	8	-2544.450	5104.900	Heterogeneity in gene flow across the genome		IM***	
AM2M2P	9	-2519.986	5057.971		"IM2M2P***, SC2M2P+++, PSC2M2P+++, PAM2M2P-0.80"	"AM***, AMex++"	
SC2M2P	9	-2544.447	5106.894		"IM2M2PNS, PSC2M2P-0.02"	SC***	
PAM2M2P	9	-2520.384	5058.769		"IM2M2P***, SC2M2P+++, PSC2M2P+++"	"PAM***, PAMex++, PAM2N++"	
PSC2M2P	9	-2544.455	5106.911		IM2M2PNS	"PSC***,"	
IM2M2Pex	11	-2523.537	5069.074	Heterogeneity in gene flow across the genome   + Expansion		"IM***, IMex***, IM2M2P***"	
AM2M2Pex	12	-2510.315	5044.629		"IM2M2Pex***, SC2M2Pex+++, PSC2M2Pex+++, AM2M2Pex-0.03"	"AM***, AMex***, AM2M2P***, AM2N+"	
SC2M2Pex	12	-2523.538	5071.075		"IM2M2PexNS, PSC2M2Pex-0.00"	"SC***, SCex***, SC2M2P***, SC2N+++"	
PAM2M2Pex	12	-2510.328	5044.657		"IM2M2Pex***, SC2M2Pex+++, PSC2M2Pex+++, "	"PSC***, PSCex***, PSC2M2P***"	
PSC2M2Pex	12	-2523.538	5071.075		IM2M2PexNS	"PAM***, PAMex***, PAM2M2P***"	
SI2N	6	-2525.592	5063.183	heterogeneity in Ne		"SI***, SIex+++"	
IM2N	8	-2525.592	5067.184		"SI2NNS, SC2NNS, PAM2NNS"	"IM***, IMex+++, IM2M2P+++, IM2N2M2P-4.00"	
AM2N	9	-2516.533	5051.065		"SI2N***, IM2N***, SC2N+++, PSC2N+++, PAM2N+++"	"AM***, AMex+++, AM2M2P-6.91, AM2N2M2P+++"	
SC2N	9	-2525.592	5069.184		"SI2NNS, IM2NNS"	"SC***, SCex+++, SC2M2P+++, SC2N2M2P-4.00"	
PAM2N	9	-2525.592	5069.184		"SI2NNS, IM2NNS, SC2N-0.00"	PAM***	
PSC2N	9	-2525.591	5069.182		"SI2NNS, IM2NNS, SC2N-0.00, PAM2N0.00"	"PSC***, PSCex+++, PSC2M2P+++, PSC2N2M2P-4.00"	
SI2Nex	11	-2511.182	5040.364	Heterogeneity in Ne + expansion		"SI***, SIex***, SI2N***"	
IM2Nex	11	-2510.959	5043.917		SI2NexNS	"IM***, IMex***, IM2M2P+++, IM2M2Pex+++, IM2N2M2P+++"	
AM2Nex	12	-2509.976	5043.952		"SI2NexNS, IM2NexNS, SC2Nex-1.95, PAM2N-1.99"	"AM***, AMex***, AM2M2P+++, AM2M2Pex-0.68, AM2N2M2P+++"	
SC2Nex	12	-2510.952	5045.904		"SI2NexNS, IM2NexNS, AM2Nex-1.95"	"SC***, SCex***, SC2M2P+++, SC2M2Pex+++, SC2N2M2P+++"	
PAM2Nex	12	-2508.429	5040.859		"SI2NexNS, IM2Nex*, PSC2Nex-5.08, SC2Nex-5.04, AM2Nex-3.09"	"PAM***, PAMex***, PAM2M2P+++, PAM2M2Pex-3.80, PAM2N2M2P+++"	
PSC2Nex	12	-2510.973	5045.946		"SI2NexNS, IM2NexNS"	"PSC***, PSCex***, PSC2M2P+++, PSC2M2Pex+++, PSC2N2M2P+++"	
IM2N2M2P	10	-2525.594	5071.188	Heterogeneity in Ne + Heterogeneity in gene flow across the genome		"IM***, IMex+++"	
AM2N2M2P	11	-2525.592	5073.184		"IM2N2M2PNS, PAM2N2M2P+++"	AM***	
SC2N2M2P	11	-2525.592	5069.184		"IM2N2M2PNS, AM2N2M2P-0.00, PSC2N2M2P-0.00"	"SC***, SCex+++"	
PAM2N2M2P	11	-2518.686	5059.373		"IM2N2M2P***, AM2N2M2P++, SC2N2M2P++, PSC2N2M2P++"	"PAM***, PAMex++, PAM2N+++"	
PSC2N2M2P	11	-2525.592	5073.183		"IM2N2M2PNS, AM2N2M2P-0.00"	"PSC***, PSCex+++"	
"k is the number of parameters and AIC the Akaike Information Criterion. Model comparisons within and between classes of models are shown. Nested models were compared using likelihood ratio tests, with subscripts indicating significance levels (abbreviated ***P<0.001; **P <0.01; *P<0.05, NS non-significant). Non-nested models were compared using AIC with relative likelihood of each model compared to the best model L(Mi|Mbest)=exp((AICmin-AICi)/2) (abbreviated +++L(Mi|Mbest)<0.001; ++L(Mi|Mbest) <0.01; +L(Mi|Mbest)<0.05, L(Mi|Mbest)> 0.05 : AIC difference shown)"