Models are described in Fig. 4. mig_0siz, demographic model assuming migration between populations but no population size changes; mig_siz_ALL_G-PhoCS, demographic model assuming migration between populations and population size changes with all divergence times fixed on G-PhoCS mean estimations (tables S3 to S5); Ne, effective population size (number of diploid individuals). Ancestral population sizes follow the phylogenetic relationship between populations; n-m, ancestral population of Negro and Madeira; n-m-a, ancestral population of Amazonas, Negro, and Madeira; s-m, ancestral population of Solimões and Madeira; a-t, ancestral population of Amazonas and Tapajos; a-t-n, ancestral population of Amazonas, Tapajos, and Negro; m-a/n, ancestral population of Madeira and Amazonas/Negro; anc, ancestral population of the species complex; Mx → y, estimated migration band from x to y forward in time (number of individuals per generation); Tdiv, divergence time in years; s, Solimões population; m, Madeira population; n, Negro population; a, Amazonas population; t, Tapajos population; Epsilon, the ratio between the ancestral population size in relation to the current one when size change was allowed; tau, time of population size change.
| Taxon | Model | Parameters | |||||||||
| M. lugubris | mig_siz_ All_G-PhoCS | Ne Solimoes | Ne Negro | Ne Madeira | Ne Amazonas | Ne n-m | Ne n-m-a | Ne anc | Ms→n | Mn→s | Ms→m |
| 577,831 (139,204– 297,980) | 187,753 (88,058– 211,804) | 41,753 (20,230– 41,237) | 64,241 (20,490– 41,960) | 592,914 (303,123– 541,514) | 402,991 (247,756– 635,255) | 88,469 (86,784– 552,158) | 0.04 (0.00– 0.24) | 0.50 (0.64– 2.56) | 0.02 (0.00– 1.49) | ||
| Mm→s | Ms→a | Ma→s | Mn→m | Mm→n | Mn→a | Ma→n | Mm→a | Ma→m | Epsilon s | ||
| 0.02 (0.01–0.23) | 1.55 (0.00–3.70) | 0.07 (0.01–0.10) | 1.67 (0.03–4.68) | 0.003 (0.00–0.04) | 1.88 (0.00–4.35) | 0.001 (0.002– 0.08) | 0.10 (0.09– 6.39) | 5.77 (0.00– 10.49) | 0.22 (0.22– 1.38) | ||
| Epsilon n | Epsilon m | Epsilon a | Tau s | Tau n | Tau m | Tau a | |||||
| 3.96 (0.65–8.74) | 5.50 (3.65–8.49) | 0.3 (0.28–5.18) | 20,203 (18,539– 105,746) | 21,632 (2,545– 59,913) | 20,255 (11,054– 31,161) | 20,025 (2,489– 23,263) | |||||
| T. nigrocinereus | mig_siz_ All_G-PhoCS | Ne Solimoes | Ne Negro | Ne Madeira | Ne Amazonas | Ne Tapajos | Ne s-m | Ne a-t | Ne a-t-n | Ne anc | Ms→n |
| 231,432 (88,960– 238,231) | 196,767 (50,976– 178,292) | 127,012 (40,956– 134,760) | 100,777 (30,694– 77,297) | 116,840 (20,538– 141,563) | 311,298 (63,291– 407,013) | 447,604 (312,473– 707,007) | 211,583 (85,335– 550,942) | 356,013 (93,022– 534,331) | 1.36 (1.02– 2.48) | ||
| Mn→s | Ms→a | Ma→s | Ms→m | Mm→s | Mn→a | Ma→n | Mn→m | Mm→n | Ma→m | ||
| 0.52 (0.25–2.33) | 0.064 (0.00–1.88) | 1.15 (0.24–4.18) | 0.30 (0.00–0.14) | 1.04 (0.68–3.08) | 0.03 (0.00–1.55) | 0.57 (0.17– 1.13) | 0.22 (0.00– 0.69) | 0.08 (0.00–0.62) | 0.01 (0.00– 0.43) | ||
| Mm→a | Ma→t | Mt→a | Epsilon s | Epsilon n | Epsilon m | Epsilon a | Epsilon t | Tau s | Tau n | ||
| 0.00 (0.00–5.46) | 0.26 (0.06–0.51) | 0.01 (0.00–1.52) | 0.27 (0.38–5.88) | 1.09 (2.01–7.15) | 6.27 (3.62– 15.70) | 4.43 (1.43– 18.93) | 0.34 (0.22– 5.06) | 79,733 (34,392– 138,714) | 60,520 (7,006– 113,621) | ||
| Tau m | Tau a | Tau t | |||||||||
| 19,378 (3,871– 18,503) | 11,112 (1,429– 12,285) | 13,927 (9,354– 46,256) | |||||||||
| M. assimilis | mig_0siz | Ne Solimoes | Ne Amazonas/ Negro | Ne Madeira | Ne m-a/n | Ne anc | Mm→s | Ms→m | Mm→a/n | Ma/n → m | Ms→a/n |
| 358,432 (193,676– 396,955) | 525,318 (505,290– 570,850) | 765,488 (778,199– 1,322,214) | 195,303 (841,052– 960,669) | 249,877 (635,438– 960,239) | 0.34 (0.00–0.14) | 0.20 (0.00– 0.81) | 3.05 (5.53– 8.63) | 3.94 (0.00–0.58) | 2.37 (3.02– 6.79) | ||
| Ma/n→s | Tdiva/n-m | ||||||||||
| 3.07 (3.93–5.74) | 166,612 (24,182– 173,088) |