"Supporting Information Table S1 Results of model fitting for the 39 alternative models of divergence for pool-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 and heterogeneity in both migration rate and population size (2N2M2P)."																									
Model	k	LogL	AIC	Model description	Model comparison within	Model comparison between																			
SI	4	-2421.226	4850.451	Strict isolation																					
IM	6	-2383.521	4779.041	Isolation-with-migration	SI***																				
AM	7	-2362.277	4738.554	Ancient migration	"SI***, IM***, SC+++, PSC+++"																				
SC	7	-2382.615	4779.230	Secondary contact	"SI***, IMNS, PSC-1.81"																				
PAM	7	-2360.540	4735.080	Ancient migration with two phases of contact	"SI***, IM***, SC+++, PSC+++, AM-3.47"																				
PSC	7	-2383.520	4781.040	Secondary contact with two phases of contact	"SI***, IMNS"																				
SIex	7	-2234.797	4483.594	 Expansion		SI***																			
IMex	9	-2226.699	4471.397		SIex***	"IM***, IM2M2P+++"																			
AMex	10	-2145.733	4311.465		"SIex***, IMex***, SCex+++, PSCex+++"	"AM***, AM2M2P+++, AM2N+++, AM2N2M2P+++"																			
SCex	10	-2226.699	4473.398		"SIex**, IMex NS, SCex-0.002"	"SC***, SC2M2P+++"																			
PAMex	10	-2114.967	4249.933		"SIex***, IMex***, SCex+++, PSCex+++, AMex +++"	"PAM***, PAM2M2P+++, PAM2N+++, PAM2N2M2P+++"																			
PSCex	10	-2226.700	4473.400		"SIex**,  IMex NS"	"PSC***, PSC2M2P+++"																			
IM2M2P	8	-2244.500	4505.001	Heterogeneity in gene flow across the genome		IM***																			
AM2M2P	9	-2229.833	4477.666		"IM2M2P***, SC2M2P+++, PSC2M2P+++"	AM***																			
SC2M2P	9	-2236.918	4491.835		"IM2M2P***, PSC2M2P+"	SC***																			
PAM2M2P	9	-2229.342	4476.684		"IM2M2P***, SC2M2P+++, PSC2M2P+++, AM2M2P-0.98"	PAM***																			
PSC2M2P	9	-2241.334	4500.668		IM2M2P*	PSC***																			
IM2M2Pex	11	-2142.048	4306.095	Heterogeneity in gene flow across the genome  + Expansion		"IM***, IMex***, IM2M2P***, IM2N+++, IM2Nex+++"																			
AM2M2Pex	12	-2118.034	4260.068		"IM2M2Pex***, SC2M2Pex+++, PSC2M2Pex+++"	"AM***, AMex***, AM2M2P***, AM2N+++"																			
SC2M2Pex	12	-2136.592	4297.184		"IM2M2Pex***, PSC2M2Pex-0.54"	"SC***, SCex***, SC2M2P***, SC2N+++, SC2Nex+++"																			
PAM2M2Pex	12	-2112.475	4248.950		"IM2M2Pex***, AM2M2Pex++, SC2M2Pex+++, PSC2M2Pex+++"	"PAM***, PAMexNS, PAM2M2P***, PAM2N+++"																			
PSC2M2Pex	12	-2136.864	4297.728		IM2M2Pex**	"PSC***, PSCex***, PSC2M2P***, PSC2N+++, PSC2Nex+++"																			
SI2N	6	-2196.623	4405.246	heterogeneity in Ne		"SI***, SIex+++"																			
IM2N	8	-2182.470	4380.940		SI2N***	"IM***, IMex+++, IM2M2P+++, IM2N2M2P-4.00"																			
AM2N	9	-2182.417	4382.834		"SI2N***, IM2NNS"	"AM***, AM2M2P+++, AM2N2M2P-4.02"																			
SC2N	9	-2179.895	4377.791		"SI2N***, IM2N*, AM2N-5.04, PSC2N-2.50"	"SC***, SCex+++, SCM2M2P+++, SC2N2M2P-4.00"																			
PAM2N	9	-2176.357	4370.715		"SI2N***, IM2N***, AM2N++, SC2N+, PSC2N+"	"PAM***, PAM2M2P+++, PAM2N2M2P-5.13"																			
PSC2N	9	-2181.144	4380.288		"SI2N***, IM2NNS, AM2N-2.55"	"PSC***, PSCex+++, PSC2M2P+++, PSC2N2M2P-4.01"																			
SI2Nex	9	-2180.330	4378.660	Heterogeneity in Ne + expansion		"SI***, SIex***, SI2N***"																			
IM2Nex	11	-2172.316	4366.632		SI2Nex***	"IM+++, IMex***, IM2M2P+++, IM2N***, IM2N2M2P+++"																			
AM2Nex	12	-2117.316	4258.633		"SI2Nex***, IM2Nex***, SC2Nex+++, PSC2Nex+++"	"AM+++, AMex***, AM2M2P+++, AM2M2Pex-1.45, AM2N***,  AM2N2M2P+++"																			
SC2Nex	12	-2171.326	4366.653		"SI2Nex***, IM2NexNS"	"SC+++, SCex***, SC2N***, SC2M2P+++, SC2N2M2P+++"																			
PAM2Nex	12	-2086.311	4196.623		"SI2Nex***, IM2Nex***, AM2Nex+++, SC2Nex+++, PSC2Nex+++, "	"PAM+++, PAMex***, PAM2N***, PAM2M2P+++, PAM2M2Pex+++, PAM2N2M2P+++"																			
PSC2Nex	12	-2172.088	4368.176		"SI2Nex***, IM2NexNS"	"PSC+++, PSCex***, PSC2M2P+++, PSC2N***, PSC2N2M2P+++"																			
IM2N2M2P	10	-2182.472	4384.944	Heterogeneity in Ne + Heterogeneity in gene flow across the genome		"IM+++, IMex+++, IM2M2P***"																			
AM2N2M2P	11	-2182.426	4386.851		IM2N2M2PNS	"AM+++, AM2M2P***"																			
SC2N2M2P	11	-2179.896	4381.792		"IM2N2M2P*, AM2N2M2P-5.06, PSC2N2M2P-2.51"	"SC+++, SCex+++, SC2M2P***"																			
PAM2N2M2P	11	-2176.924	4375.848		"IM2N2M2P***, AM2N2M2P++, SC2N2M2P+, PSC2N2M2P+"	"PAM+++, PAM2M2P***"																			
PSC2N2M2P	11	-2181.150	4384.300		"IM2N2M2PNS, AM2N2M2P-2.55"	"PSC+++, PSCex+++, PSC2M2P***"																			
"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)"