Table 2 Parameter values of simulated models in FSC with the best composite likelihood for each of the three studied species and 95% confidence interval (in parentheses) obtained with parametric bootstraps.

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.

TaxonModelParameters
M. lugubrismig_siz_
All_G-PhoCS
Ne SolimoesNe NegroNe MadeiraNe AmazonasNe n-mNe n-m-aNe ancMs→nMn→sMs→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→sMs→aMa→sMn→mMm→nMn→aMa→nMm→aMa→mEpsilon 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 nEpsilon mEpsilon aTau sTau nTau mTau 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. nigrocinereusmig_siz_
All_G-PhoCS
Ne
Solimoes
Ne NegroNe
Madeira
Ne
Amazonas
Ne
Tapajos
Ne s-mNe a-tNe a-t-nNe ancMs→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→sMs→aMa→sMs→mMm→sMn→aMa→nMn→mMm→nMa→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→aMa→tMt→aEpsilon sEpsilon nEpsilon mEpsilon aEpsilon tTau sTau 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 mTau aTau t
19,378
(3,871–
18,503)
11,112
(1,429–
12,285)
13,927
(9,354–
46,256)
M. assimilismig_0sizNe
Solimoes
Ne
Amazonas/
Negro
Ne
Madeira
Ne m-a/nNe ancMm→sMs→mMm→a/nMa/n → mMs→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→sTdiva/n-m
3.07
(3.93–5.74)
166,612
(24,182–
173,088)