Estimating and accounting for genotyping errors in RAD-seq experiments

Estimating and accounting for genotyping errors in RAD-seq

experiments

Luisa Bresadola

1

Պ| Vivian Link

1,2

Պ| C. Alex Buerkle

3

Պ| Christian Lexer

4†

Պ|

Daniel Wegmann

1,2 1 _{;r-u|l;m|o=boѴo]‹ķ&mbˆ;uvb|‹o=} ub0o†u]ķ ub0o†u]ķ"‰b|Œ;uѴ-m7 2_{"‰bvvmv|b|†|;o=bobm=oul-|b1vķ ub0o†u]ķ} "‰b|Œ;uѴ-m7 3 _{;r-u|l;m|o=o|-m‹ķ&mbˆ;uvb|‹o=} )‹olbm]ķ-u-lb;ķ)+ķ&" 4 _{;r-u|l;m|o=o|-m‹-m7bo7bˆ;uvb|‹} !;v;-u1_ķ&mbˆ;uvb|‹o=(b;mm-ķ(b;mm-ķ †v|ub-Correspondence -mb;Ѵ);]l-mmķ ;r-u|l;m|o= boѴo]‹ķ&mbˆ;uvb|‹o= ub0o†u]ķ ub0o†u]ķ "‰b|Œ;uѴ-m7ĺ l-bѴĹ7-mb;Ѵĺ‰;]l-mmŠ†mb=uĺ1_ Funding information "1_‰;bŒ;ubv1_;u-|bom-Ѵ=om7vŒ†u क़u7;u†m]7;u)bvv;mv1_-=|Ѵb1_;m ouv1_†m]ķu-m|ņ‰-u7†l0;uĹ ƒƐƏƏƒōƐƓƖƒƏѵ-m7ƒƐƏƏƒōƐƕƒƏѵƑ

Abstract

mmomŊlo7;Ѵou]-mbvlvķ;ˆoѴ†|bom-u‹t†;v|bomv-u;=u;t†;m|Ѵ‹-77u;vv;7†vbm]u;-7†1;7u;ru;v;m|-|bomv;t†;m1bm]|;1_mbt†;v7†;|o|_;buѴo‰1ov|ķ;-v;o=†v;ķ-m7 0;1-†v;|_;‹7omo|u;t†bu;];molb1u;vo†u1;vv†1_-v-u;=;u;m1;];mol;ĺo‰;ˆ;uķ ;ˆb7;m1; bv -11†l†Ѵ-|bm] |_-| v†1_ |;1_mbt†;v l-‹ 0; -==;1|;7 0‹ vr;1b=b1 0b-v;vķ t†;v|bombm]|_;-11†u-1‹o=o0|-bm;7];mo|‹r;vķ-m7-v-1omv;t†;m1;ķ|_;bu†v;=†Ѵ- m;vvbm;ˆoѴ†|bom-u‹v|†7b;vĺ;u;ķ‰;bm|uo7†1;|_u;;v|u-|;]b;v|o;v|bl-|;];mo-|‹rbm];uuouu-|;v=uolv†1_7-|-Ĺ|_uo†]_|_;1olr-ubvom|o_b]_t†-Ѵb|‹];mo|‹r;v o0|-bm;7‰b|_-7b==;u;m||;1_mbt†;ķ=uolbm7bˆb7†-Ѵu;rѴb1-|;vķou=uol-ror†Ѵ-|bom v-lrѴ; ‰_;m -vv†lbm] -u7‹Ŋ);bm0;u] ;t†bѴb0ub†lĺ rrѴ‹bm] |_;v; v|u-|;]b;v |o 7-|-o0|-bm;7‰b|_!;v|ub1|bomvb|;vvo1b-|;7 v;t†;m1bm]Ő! Ŋv;tőķ-u]†-0Ѵ‹ |_; lov| ror†Ѵ-u u;7†1;7 u;ru;v;m|-|bom v;t†;m1bm] |;1_mbt†;ķ u;ˆ;-Ѵ;7 r;uŊ-ѴѴ;Ѵ; ];mo|‹rbm];uuouu-|;v|_-|‰;u;l†1__b]_;u|_-mv;t†;m1bm];uuouu-|;vķr-u|b1†Ѵ-uѴ‹ -| _;|;uoŒ‹]o†v vb|;v |_-| ‰;u; ‰uom]Ѵ‹ bm=;uu;7 -v _oloŒ‹]o†vĺ v ‰; ;Š;lrѴb=‹ |_uo†]_|_;bm=;u;m1;o=];mol;Ŋ‰b7;-m7Ѵo1-Ѵ-m1;v|u‹o=‰;ѴѴ1_-u-1|;ubŒ;7_‹-0ub7vo=|‰o†u-vb-mrorѴ-uŐPopulusővr;1b;vķv†1__b]_;uuouu-|;vl-‹Ѵ;-7|o‰uom] 0boѴo]b1-Ѵ 1om1Ѵ†vbomvĺ ‹ ruor;uѴ‹ -11o†m|bm] =ou |_;v; ;uuou u-|;v bm 7o‰mv|u;-l -m-Ѵ‹v;vķ;b|_;u0‹bm1ourou-|bm]];mo|‹rbm];uuouv7bu;1|Ѵ‹ou0‹u;1-Ѵb0u-|bm]];mo- |‹r;Ѵbh;Ѵb_oo7vķ‰;‰;u;m;ˆ;u|_;Ѵ;vv-0Ѵ;|o†v;|_;! Ŋv;t7-|-|ov†rrou|0bo-Ѵo]b1-ѴѴ‹l;-mbm]=†Ѵ-m7uo0†v|bm=;u;m1;vo=-m1;v|u‹-lom]Populus_‹0ub7vĺ-v;7 om|_;v;=bm7bm]vķ‰;v|uom]Ѵ‹u;1oll;m71-u;=†ѴѴ‹-vv;vvbm]];mo|‹rbm];uuouu-|;v bmu;7†1;7u;ru;v;m|-|bomv;t†;m1bm];Šr;ubl;m|vķ-m7|oruor;uѴ‹-11o†m|=ou|_;v; bm7o‰mv|u;-l-m-Ѵ‹v;vķ=oubmv|-m1;†vbm]|_;|ooѴvru;v;m|;7_;u;ĺ K E Y W O R D S ];mo|‹r;Ѵbh;Ѵb_oo7vķ];mo|‹rbm]ķ];mo|‹rbm];uuouvķor†Ѵ†vķ! Ŋv;t

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;vrb|; |_; blru;vvbˆ; -7ˆ-m1;l;m|v bm v;t†;m1bm] |;1_mbt†;v -m7|_;7;1u;-v;o=u;Ѵ-|;71ov|vķ‰_oѴ;];mol;v;t†;m1bm]Ő)"ő u;l-bmvruo_b0b|bˆ;Ѵ‹;Šr;mvbˆ;‰_;m‰ouhbm]‰b|_-Ѵ-u];m†l0;u o=v-lrѴ;vouvr;1b;v‰b|_Ѵ-u];];mol;vĺ"bm1;l-m‹-rrѴb1-|bomv 7omo|u;t†bu;bm=oul-|bomom|_;‰_oѴ;];mol;ķu;7†1;7u;ru;v;m- |-|bomv;t†;m1bm]|;1_mbt†;v-u;ˆ-Ѵ†-0Ѵ;-Ѵ|;um-|bˆ;v-m7_-ˆ;0;-1ol;‰b7;Ѵ‹†v;7=ou];mol;Ŋ‰b7;"7bv1oˆ;u‹-m7];mo|‹rbm]ķ ;vr;1b-ѴѴ‹bmvr;1b;v‰b|_roou];molb1u;vo†u1;vŐm7u;‰vķoo7ķ † _;1;-v;7 u;v-7oѴ--m7bmh;t†-ѴѴ‹1om|ub0†|;7|o|_bvv|†7‹ĺ

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Published in "Molecular Ecology Resources 20(4): 856–870, 2020"

which should be cited to refer to this work.

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1ollomѴ‹†v;7u;7†1;7u;ru;v;m|-|bomv;t†;m1bm]|;1_mbt†; bv !;v|ub1|bom vb|; vvo1b-|;7  v;t†;m1bm] Ő-bu7 ;| -Ѵĺķ ƑƏƏѶĸ bѴѴ;uķ †m_-lķlou;vķu;vhoķşo_mvomķƑƏƏƕőķ‰_b1_-ѴѴo‰v|_; v;t†;m1bm]o=l-vvbˆ;Ѵ‹l†Ѵ|brѴ;Š;7v-lrѴ;v-|lbmbl-Ѵ1ov|v0‹=o- 1†vbm]om|_;v;t†;m1;v-7f-1;m||ou;v|ub1|bomvb|;vĺ"bm1;u;v|ub1-|bomvb|;v-u;o=|;mv_-u;70;|‰;;mbm7bˆb7†-Ѵv‰b|_bm-vr;1b;v-m7 o=|;m-Ѵvo0;|‰;;m1Ѵov;Ѵ‹u;Ѵ-|;7vr;1b;vŐ-ubo†ķ †u;|ķş_-uѴ-|ķ ƑƏƐƒőķ=o1†vbm]om-7f-1;m|v;t†;m1;v]†-u-m|;;v|_-|v;t†;m1;7 Ѵo1b-u;lov|Ѵ‹oˆ;uѴ-rrbm]-1uovvv-lrѴ;vĺ ub;=Ѵ‹ķ|_;=buv|v|;rbm|_;oub]bm-Ѵ! Ŋv;truo|o1oѴbv|_;7b-];v|bom o= ];molb1  ‰b|_ - u;v|ub1|bom ;mŒ‹l;ĺ $_; u;v†Ѵ|bm] =u-]l;m|v-u;Ѵb]-|;7|o-m-7-r|ou-m7-†mbt†;0-u1o7;=ou;-1_ v-lrѴ;ķ-m7l†Ѵ|brѴ;bm7bˆb7†-Ѵv-u;rooѴ;7ĺ$_;=u-]l;m|v-u;|_;m v_;-u;7†vbm]-vomb1-|ou-m7|_ov;v_o‰bm]|_;ruor;uvbŒ;-u;v;-Ѵ;1|;7 -m7 -lrѴb=b;7 |_uo†]_ roѴ‹l;u-v; 1_-bm u;-1|bom Ő!őĺ | |_bvrobm||_;Ѵb0u-u‹bvv†b|-0Ѵ;=ouv;t†;m1bm]ĺ‹=o1†vbm]|_;v;-t†;m1bm] ;==ou| om |-]];7 u;v|ub1|bom vb|;vķ u-|_;u |_-m om -ѴѴ u-m-7olѴ‹v_;-u;7];molb1=u-]l;m|vŐumoѴ7ķou0;||Ŋ ;|b]ķ-u|Ѵķş ol0Ѵb;vķ ƑƏƐƒĸ !o‰;ķ !;m-†|ķ ş †]]bv0;u]ķ ƑƏƐƐőķ |_; m†l0;u o=l-uh;uv1-m0;1†v|olbŒ;7|_uo†]_|_;1_ob1;o=u;v|ub1|bom;m-Œ‹l;vĺ$_bv1_ob1;‰bѴѴ-Ѵvobm=Ѵ†;m1;‰_b1_=;-|†u;vo=|_;];mol; -u;v-lrѴ;7ķvbm1;1;u|-bm;mŒ‹l;vru;=;u;m|b-ѴѴ‹1†|bm;Šomb1u;-]bomvķ ‰_bѴ; o|_;uv |-u];| bm|;u];mb1 -m7 bm|uomb1 u;]bomv ŐumoѴ7 ;|-ѴĺķƑƏƐƒĸoo|-h_-l;|-ѴĺķƑƏƐѵőĺ

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"ol;1omv;t†;m1;vo=|_;v;0b-v;vbm7o‰mv|u;-l-m-Ѵ‹v;v-u; ‰;ѴѴ7o1†l;m|;7ĺ-†|b;u;|-ѴĺŐƑƏƐƒőķ=ou;Š-lrѴ;ķ=o†m7|_-|†m7;u 1;u|-bm1bu1†lv|-m1;v-ѴѴ;Ѵ;7uoro†|Ѵ;-7v|obm1ouu;1|;v|bl-|;vo= ];m;|b1 7bˆ;uvb|‹ĺ umoѴ7 ;| -Ѵĺ ŐƑƏƐƒő 7;lomv|u-|;7 |_uo†]_ 0o|_ vbl†Ѵ-|bomv-m7u;-Ѵ7-|-|_-|;v|bl-|;vo=v†ll-u‹v|-|bv|b1v1ol-lomѴ‹†v;7|obm=;u7bˆ;uvb|‹-m7r-v|7;lo]u-r_‹=uol! 7-|- -u; v;ˆ;u;Ѵ‹ -==;1|;7 0‹ lbvvbm] _-rѴo|‹r;v -m7 l-‹ v_o‰ v|uom] 7;ˆb-|bomv =uol |u†; ˆ-Ѵ†;vĺ bm-ѴѴ‹ķ -ubo†ķ †u;|ķ -m7 _-uѴ-| ŐƑƏƐѵőbѴѴ†v|u-|;7|_-|-ѴѴ;Ѵ;7uoro†|1-mѴ;-7|o†m7;u;v|bl-|bomo= 7bˆ;uvb|‹ķ;vr;1b-ѴѴ‹bm_b]_Ѵ‹roѴ‹lour_b1vr;1b;vĺ mѴb]_|o=|_;v;ro|;m|b-ѴѴ‹1ollombvv†;vķo†u-blv_;u;‰;u;|o 7;ˆ;Ѵorv|u-|;]b;vŐ-ő|o;v|bl-|;];mo|‹rbm];uuouu-|;vbm! 7-|-ĸ -m7Ő0ő|oruor;uѴ‹bm1ourou-|;|_;u;v†Ѵ|bm]];mo|‹rbm]†m1;u|-bm|‹ bm7o‰mv|u;-l-m-Ѵ‹v;v|olb|b]-|;|_;1omv;t†;m1;vo=;uuouvĺ ou |_bv‰;ru;v;m|l;|_o7v|o;v|bl-|;];mo|‹rbm];uuouvbm|_u;;7b=-=;u;m|‰-‹vĺ buv|ķ0‹|-hbm]-7ˆ-m|-];o=-ˆ-bѴ-0Ѵ;];mo|‹rbm]7-|- 0-v;7om-7b==;u;m|ķlou;u;Ѵb-0Ѵ;l;|_o7Ő;ĺ]ĺķ†vbm]-1_brou_b]_Ŋ 7;r|_ v;t†;m1bm]őĺ ";1om7ķ 0‹ †vbm] bm7;r;m7;m| ! Ŋv;t u;rѴb-1-|;vo=bm7bˆb7†-Ѵvĺ$_bu7ķ0‹-vv†lbm]-u7‹Ŋ);bm0;u]ruorou|bomv -lom]ror†Ѵ-|bomv-lrѴ;vĺ&vbm]vbl†Ѵ-|bomv‰;v_o‰|_-|-ѴѴ|_;v; l;|_o7v-u;ro‰;u=†Ѵbmbm=;uubm];uuouu-|;v;ˆ;mb=Ѵblb|;7v-lrѴ;v -u;-ˆ-bѴ-0Ѵ;ĺv-1-v;v|†7‹ķ‰;|_;m-rrѴb;7|_;v;l;|_o7v|o! Ŋ v;t 7-|- o= |_; |‰o ‰b7;vru;-7ķ ];m;|b1-ѴѴ‹ -m7 ;1oѴo]b1-ѴѴ‹ 7bˆ;u-];m||u;;vr;1b;vPopulus albaŐ)_b|;rorѴ-uő-m7P. tremulaŐ†uor;-m -vr;mő-m7bm=;uu;7_b]_];mo|‹rbm];uuouu-|;vo=l†Ѵ|brѴ;r;u1;m|ĺ‹ ruor;uѴ‹-11o†m|bm]=ou];mo|‹rbm]†m1;u|-bm|‹ķ_o‰;ˆ;uķ‰;o0|-bm 0boѴo]b1-ѴѴ‹l;-mbm]=†Ѵ;v|bl-|;vo=];mol;Ŋ‰b7;-m7Ѵo1-Ѵ-m1;v|u‹ĺ

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;|†v7;mo|;0‹g_il|_;o0v;uˆ;7];mo|‹r;o=bm7bˆb7†-ѴiƷƐķĻķI -|Ѵo1†vlƷƐķĻķLķ‰_;u;g_ilƷƏķƐķƑu;=Ѵ;1|v|_;m†l0;uo=1orb;v

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o=|_;-Ѵ|;um-|bˆ;-ѴѴ;Ѵ;-|-0b-ѴѴ;Ѵb1Ѵo1†vĺbˆ;mr;uŊ-ѴѴ;Ѵ;];mo|‹r-bm];uuouu-|;vε₀ and ε₁

-|_oloŒ‹]o†v-m7_;|;uoŒ‹]o†vvb|;vķu;-vr;1|bˆ;Ѵ‹ķ |_; ruo0-0bѴb|b;v PŐg_il|γķ ε₀ķε1ő o= o0v;uˆbm] ];mo|‹r; gil

-|-Ѵo1†v‰b|_|u†;];mo|‹r;γƷƏķƐķƑ-u;]bˆ;mbm$-0Ѵ;Ɛĺ);m;Š| 7;v1ub0;|_u;;v|u-|;]b;v|o;v|bl-|;|_;];mo|‹rbm];uuouu-|;vε0ķ and ε₁=uol1-ѴѴ;7];mo|‹rb17-|-ĺ)_bѴ;‰;ru;v;m||_;v;l;|_o7v bm|_;1om|;Š|o=!;v|ub1|bomvb|;-vvo1b-|;7 v;t†;m1bm]Ő! Ŋ v;tőķ‰;v|u;vv|_-||_;‹-u;-rrѴb1-0Ѵ;|o];mo|‹rb17-|-o0|-bm;7 =uol-m‹7-|-vo†u1;ĺ

ƑĺƐĺƐՊ|Պ uol-|u†|_v;|

omvb7;u -11†u-|; ];mo|‹r;vγ_il o0|-bm;7 bm7;r;m7;m|Ѵ‹ =ou vol;

bm7bˆb7†-Ѵv-m7Ѵo1bĺvv†lbm]-ѴѴγil

|o0;1ouu;1|-m7];mo|‹rbm];u-uouv|o0;bm7;r;m7;m|0;|‰;;mvb|;v-m7bm7bˆb7†-Ѵvķ|_;Ѵbh;Ѵb_oo7

o=|_;o0v;uˆ;7];mo|‹r;vg = {g₁₁ķĻķg_I1ķĻg_ŕbv|_;m]bˆ;m0‹

‰_;u;γ = {γ₁₁ķĻķγ_I1ķĻķγ_} and PŐg_il | γ_ilķε₀ķε₁őbv]bˆ;mbm$-0Ѵ;Ɛĺ);

o0|-bml-Šbl†lѴbh;Ѵb_oo7;v|bl-|;v𝜀̂0 and 𝜀̂1

|_uo†]_m†l;ub1-Ѵl-Š-blbŒ-|bomŐv;;"†rrou|bm]m=oul-|bomőĺ

ƑĺƐĺƑՊ|Պ uolbm7bˆb7†-Ѵu;rѴb1-|;v

omvb7;ubm7bˆb7†-Ѵv=ou‰_b1_l†Ѵ|brѴ;bm7;r;m7;m|v;t†;m1bm];Š-r;ubl;m|v‰;u;1om7†1|;7ĺ;|†v7;mo|;0‹g(j)_il |_;bm=;uu;7];mo-|‹r;o=bm7bˆb7†-Ѵi-|Ѵo1†vlbmu;rѴb1-|;jƷƐķĻķr₁ĺ$_;Ѵbh;Ѵb_oo7o= |_;=†ѴѴ7-|-bv|_;m]bˆ;m0‹

‰_;u; g 7;mo|;v |_; ˆ;1|ou o= -ѴѴ o0v;uˆ;7 ];mo|‹r;vķγ |_;

†mo0-v;uˆ;7|u†;];mo|‹r;ķPŐγЬf_iγőƷf_iγ|_;=u;t†;m1‹o=];mo|‹r;γ-lom]

-ѴѴѴo1bo=bm7bˆb7†-ѴiķfƷŔ=₁₀ķĻķf_I0ķĻķf_I2} and P(g(j)_il|𝛾,𝜀0,𝜀1)bv]bˆ;mbm $-0Ѵ;Ɛĺ);o0|-bml-Šbl†lѴbh;Ѵb_oo7;v|bl-|;v𝜀̂₀ķ𝜀̂₁-m7‰b|_-m Šr;1|-|bomŊ-ŠblbŒ-|bomŐő-Ѵ]oub|_l-v7;|-bѴ;7bm|_;"†rrou|bm] m=oul-|bomĺ

ƑĺƐĺƒՊ|Պ uolror†Ѵ-|bomv-lrѴ;v

omvb7;ubm7bˆb7†-Ѵvv-lrѴ;7=uol-u-m7oll-|bm]ror†Ѵ-|bomv†1_ |_-||_;7bv|ub0†|bomo=|_;|u†;];mo|‹r;vbv‰;ѴѴ7;v1ub0;70‹-u7‹Ŋ );bm0;u]ruorou|bomvĺ)_bѴ;|_;Ѵo1†vŊvr;1b=b1-ѴѴ;Ѵ;=u;t†;m1b;vf_l -u;†mhmo‰mķѴ;|†v-vv†l;|_-||_;‹=oѴѴo‰-;|-7bv|ub0†|bom‰b|_ r-u-l;|;uvαķβv†1_|_-|flŜ;|-Ő αķβő-vbv;Šr;1|;7†m7;um;†|u-Ѵ-b|‹Ő)ub]_|ķƐƖƒƐőĺ$_;Ѵbh;Ѵb_oo7o=|_;=†ѴѴ7-|-bv|_;m]bˆ;m0‹

‰_;u;|_;v†lu†mvoˆ;u|_;†mhmo‰m|u†;];mo|‹r;γķPŐγ|f_iγő-u;|_;

-u7‹Ŋ);bm0;u]ruorou|bomv]bˆ;m-ѴѴ;Ѵ;=u;t†;m1b;vf_iγ and PŐg_ilЬγķε0ķ

ε₁

őbv]bˆ;mbm$-0Ѵ;Ɛĺm1om|u-v||o|_;o|_;u|‰olo7;Ѵvķ|_;1ol-r†|-|bom-ѴѴ‹ ;==b1b;m| l-Šbl†l Ѵbh;Ѵb_oo7 v1_;l; u;v†Ѵ|;7 bm 0b-v;7 ;v|bl-|;v ‰_;m ‰ouhbm] ‰b|_ ror†Ѵ-|bom v-lrѴ;vĺ ); |_;u;=ou; u;-vou||o-m-rruo-1_†m7;u--‹;vb-mv1_;l;Őv;;"†rrou|bm]

m=oul-|bomő‰b|_;Šrom;m|b-Ѵrubouvε₀ķε₁ŜŠrŐλő|u†m1-|;7-|ƏĺƔ

-m7moul-ѴrubouvѴo]ŐαőķѴo]ŐβőŜŐμķσ2_{őĺ);†v;7λƷƔķμƷѴo]ŐƏĺƔő-m7}

σ2_{ƷƏĺƑƔ|_uo†]_o†|ĺ);-Ѵvo;Š|;m7|_;lo7;Ѵ|o1omvb7;u7-|-=uol} l†Ѵ|brѴ;ror†Ѵ-|bomvfobm|Ѵ‹ķ]bˆ;m|_-|l†Ѵ|brѴ;v-lrѴ;v-u;-ˆ-bѴ-0Ѵ; =ou;-1_ror†Ѵ-|bomŐv;;"†rrou|bm]m=oul-|bomőĺ

ƑĺƐĺƓՊ|Պ";|vr;1b=b1;uuouu-|;v

ѴѴl;|_o7vbm|uo7†1;7-0oˆ;-u;u;-7bѴ‹;Š|;m7;7|ofobm|Ѵ‹bm=;u ;uuouu-|;v=oul†Ѵ|brѴ;v;|vo=];mo|‹r;1-ѴѴv|_-|7b==;ubm|_;bu;uuou u-|;vķv†1_-v];mo|‹r;vo0|-bm;7‰b|_7b==;u;m|v;t†;m1bm]7;r|_ ou=uol7b==;u;m|0-|1_;vķ=ou;Š-lrѴ;7b==;u;m|v;t†;m1bm]Ѵb0u-u-b;vŐv;;"†rrou|bm]m=oul-|bomőĺm=;uubm]|_;;uuouu-|;vo=-ѴѴv;|v fobm|Ѵ‹bv0;m;=b1b-Ѵbm|_;1-v;o=bm7bˆb7†-Ѵu;rѴb1-|;vouror†Ѵ-|bom

v-lrѴ;vķ-vbm=oul-|bom-0o†|_b;u-u1_b1-Ѵr-u-l;|;uvv†1_-vbm7b-ˆb7†-Ѵ];mo|‹r;=u;t†;m1b;vf_i = {f_i0ķf_i1ķf_i2ŕou|_;r-u-l;|;uvαķβo=

|_;;|-7bv|ub0†|bom-u;v_-u;7-1uovv|_;lĺ

ƑĺƐĺƔՊ|Պ!;1-Ѵb0u-|bm]];mo|‹r;Ѵbh;Ѵb_oo7v

); u;1-Ѵb0u-|; ];mo|‹r; Ѵbh;Ѵb_oo7v 0‹ 7;|;ulbmbm] |_;

Ѵbh;Ѵb-_oo7v PŐg_il|γķ ε₀ķε1ő o= |_; 1-ѴѴ;7 ];mo|‹r; gil =ou -ѴѴγ Ʒ Əķ Ɛķ Ƒ

-11ou7bm]|o$-0Ѵ;Ɛ-m7†vbm]r-u-l;|;u;v|bl-|;vε₀ and ε₁

ob-

|-bm;7=ou|_;u;Ѵ;ˆ-m|v;|ĺ=-|u†|_v;|bv-ˆ-bѴ-0Ѵ;ķ‰;-Ѵvo1-Ѵ1†-Ѵ-|;|_;;lrbub1-ѴѴbh;Ѵb_oo7vPŐg_il|γ_il = gő-1uovv-ѴѴ];mo|‹r;vγ_il = g

o=-r-u|b1†Ѵ-uv;|ĺ

ƑĺƐĺѵՊ|ՊlrѴ;l;m|-|bom

);blrѴ;l;m|;7-ѴѴ-Ѵ]oub|_lv7;ˆ;Ѵor;7_;u;bm|_;or;mŊvo†u1; ƳƳ ruo]u-l $b];u Ő$ooѴv |o m1ourou-|; ;mo|‹rbm] !uouvőķ

P(g|𝛾,𝜀₀,𝜀₁)= L ∏ l=1 I ∏ i=1 P(gil|𝛾il,𝜀0,𝜀1), P(g|𝜀0,𝜀1,f)= L ∏ l=1 I ∏ i=1 2 ∑ 𝛾=0 [ P(𝛾|fi𝛾) ri ∏ j=1 P(g(j)_il|𝛾,𝜀0,𝜀1) ] , P(g|𝜀₀,𝜀₁,𝛼,𝛽)= L ∏ l=1 1 ∫ 0 P(fl|𝛼,𝛽) I ∏ i=1 2 ∑ 𝛾=0 [ P(gil|𝛾,𝜀0,𝜀1)P(𝛾|fl) ] dfl, $     Ɛ Պ ;uŊ-ѴѴ;Ѵ;];mo|‹rbm];uuoulo7;Ѵ True genotype Observed genotype 0 1 2 0 ŐƐŊε0ő2 2ε0ŖŐƐŊε0ő ε02 1 ε1ŖŐƐŊε1ő ŐƐŊε1ő2Ƴε12 ε1ŖŐƐŊε1ő 2 ε02 2ε0ŖŐƐŊε0ő ŐƐŊε0ő2 $_;ruo0-0bѴb|b;vo=o0v;uˆbm]-! Ŋv;t];mo|‹r;]bˆ;m|_;|u†; ];mo|‹r;-m7|_;r;uŊ-ѴѴ;Ѵ;];mo|‹rbm];uuouu-|;ε-u;v_o‰mĺ

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-ˆ-bѴ-0Ѵ; |_uo†]_ |_; ]b| u;rovb|ou‹ -| _||rvĹņņ0b|0†1h;|ĺou]ņ ‰;]l-mmѴ-0ņ|b];uĺ$b];u‰ouhv7bu;1|Ѵ‹o==( =bѴ;vbm=oul-|ƓĺƑķ ‰_b1_1om|-bmv];mo|‹r;1-ѴѴv;m1o7;70‹|_;l-m7-|ou‹$=b;Ѵ7ĺ r|bom-ѴѴ‹ķ|_;7;r|_;m1o7;70‹|_;=b;Ѵ7 bv†v;7|o0bm];mo-|‹r;1-ѴѴvbm|o7b==;u;m|v;|vķ‰_b1_l-‹=†u|_;u0;v|u-|b=b;7om-r;u v-lrѴ;0-vbvĺѴѴl;|_o7vu;-7bѴ‹_-m7Ѵ;lbvvbm]7-|-ĺ

ƑĺƐĺƕՊ|Պ"bl†Ѵ-|bomv

);†v;7vbl†Ѵ-|bomv|o-vv;vv|_;ro‰;uo=|_;l;|_o7vbm|uo7†1;7 -0oˆ;|obm=;u];mo|‹rbm];uuouu-|;vĺѴѴvbl†Ѵ-|bomv‰;u;];m;u-|;7 7bu;1|Ѵ‹†m7;u|_;-vv†l;7lo7;Ѵv†vbm]uo†|bm;v‰;blrѴ;l;m|;7 bm$b];uĺ&m7;u|_;|u†|_v;|ouu;rѴb1-|;lo7;Ѵķ;-1_vbl†Ѵ-|;77-|- v;|1omvbv|;7o=ƔƏѷ_;|;uoŒ‹]o†v];mo|‹r;vĺ&m7;u|_;ror†Ѵ-|bom v-lrѴ;vlo7;Ѵ‰;7u;‰|u†;-ѴѴ;Ѵ;=u;t†;m1b;v=uol-;|-7bv|ub0†-|bom‰b|_r-u-l;|;uvα = βƷƏĺƕķblrѴ‹bm]-0o†|ƑƖѷo=_;|;uoŒ‹-]o†v];mo|‹r;vĺ

$o -vv;vv |_; 0b-v bm bm=;uubm] ;uuou u-|;v =uol - |u†|_ v;| o0-|-bm;7‰b|_v_o|]†mv;t†;m1bm]7-|-ķ‰;vbl†Ѵ-|;7v;t†;m1bm]7-|-

=ouƐƏ4_{|u†Ѵ‹_;|;uoŒ‹]o†vķƔƵƐƏ}3_{|u†Ѵ‹_oloŒ‹]o†vu;=;u;m1;-m7}

ƔƵƐƏ3|u†Ѵ‹_oloŒ‹]o†v-Ѵ|;um-|bˆ;Ѵo1b-|7b==;u;m|l;-m7;r|_੿ĺ

"r;1b=b1-ѴѴ‹ķ‰;7u;‰Ѵo1†vvr;1b=b17;r|_vd_lŜobvŐμő=uol-obvvom

7bv|ub0†|bom‰b|_l;-m੿-m7|_;mvbl†Ѵ-|;7|_;m†l0;uo=o0v;uˆ;7

u;=;u;m1;-ѴѴ;Ѵ;vr_lŜbmŐd_lķp_l

ő=uol-0bmolb-Ѵ7bv|ub0†|bom‰b|_ruo0--0bѴb|‹p_l = 1-eķƏĺƔķe=ou_oloŒ‹]o†vu;=;u;m1;ķ_;|;uoŒ‹]o†v-m7

_oloŒ‹]o†v -Ѵ|;um-|bˆ; Ѵo1bķ u;vr;1|bˆ;Ѵ‹ķ -vv†lbm] - v;t†;m1bm] ;uuou u-|; e Ʒ ƏĺƏƐĺ ); m;Š| 7;|;ulbm;7 |_; l-Šbl†l Ѵbh;Ѵb_oo7

];mo|‹r;v̂𝛾l †m7;u |_; v-l; lo7;Ѵ -m7 †v;7 |_ov; |o bm=;u ;uuou

u-|;v𝜀̂₀ and 𝜀̂1=uol];mo|‹r;vgl‰;vbl†Ѵ-|;7-11ou7bm]|o$-0Ѵ;Ɛ

‰b|_ε0 = ε1ƷƏĺƏƐouƏĺƐĺ);|_;m];m;u-|;7ƐƏ6u;rѴb1-|;v=ou;-1_

l;-m7;r|_μƷƐķƑķĻķƒƏ-m7t†-m|b=b;7|_;0b-v;vb0=(𝜀̂0−𝜀0)∕𝜀0

and b1=(𝜀̂1−𝜀1)∕𝜀1.

ƑĺƑՊ|ՊrrѴb1-|bom|oPopulus species

ƑĺƑĺƐՊ|Պ"|†7‹v‹v|;l-m7rѴ-m|l-|;ub-Ѵ

); ];m;u-|;7 ! Ŋv;t 7-|- o= ƐƒƖ bm7bˆb7†-Ѵv o= |_; |‰o ‰b7;-vru;-7|u;;vr;1b;vPopulus alba and P. tremulaķ-m7|_;bu_‹0ub7vŐP.

x canescensőbm|‰ov;|vb7;-ѴѴ‹v†b|;7|o|;v||_;bm=;u;m1;o=;uuou

u-|;v=uol-|u†|_v;|-m7bm7bˆb7†-Ѵu;rѴb1-|;vķu;vr;1|bˆ;Ѵ‹ĺ$_;=buv| v;|1omvbv|;7o=Ɛƒѵbm7bˆb7†-ѴvŐ$-0Ѵ;"Ɛő]uo‰m‰b|_lbmbl-Ѵbm|;u-=;u;m1;bm-1ollom]-u7;m;v|-0Ѵbv_;7-||_;&mbˆ;uvb|‹o= ub0o†u] Ő"‰b|Œ;uѴ-m7ő -m7 ru;ˆbo†vѴ‹ ];mo|‹r;7 ‰b|_ - ];mo|‹rbm]Ŋ0‹Ŋv;-t†;m1bm]Ő"őruo|o1oѴŐbm7|h;ķolr;u|ķ;Š;uķş†;uhѴ;ķƑƏƐƓőĺ ѴѴ|_;v;bm7bˆb7†-Ѵv]u;‰=uolv;;7v1oѴѴ;1|;7=uolƐƔlo|_;u|u;;v bm-m-|†u-Ѵ_‹0ub7Œom;bm|_;-u1ool0-u7o7;ѴѴ-(-ѴѴ;7;Ѵ$b1bmo bmou|_;um|-Ѵ‹‰_;u;bm7bˆb7†-Ѵvo=|_;|‰ovr;1b;v-m7|_;bu_‹-0ub7v]uo‰vb7;0‹vb7;Ő_ubv|;;|-ѴĺķƑƏƐѵĸbm7|h;;|-ѴĺķƑƏƐƑőĺ $_;v;1om7v;|1omvbv|;7o==o†ubm7bˆb7†-Ѵv=ou‰_b1_‰;];m;u--|;7l†Ѵ|brѴ;u;rѴb1-|;vĹ-_‹0ub7bm7bˆb7†-ѴŐ ƏƒƖōƏƔő-Ѵvobm1Ѵ†7;7

-lom] |_; v-lrѴ;v o= |_; =buv| v;|ķ - v;1om7 _‹0ub7 bm7bˆb7†-Ѵ Őƒƕƒōő-Ѵvo=uol|_;$b1bmo_‹0ub7Œom;0†|]uo‰mbm-1ollom ]-u7;mbm"-Ѵ;umoķ|-Ѵ‹ķ-r†u;P. albabm7bˆb7†-ѴŐƐő=uol|_;-Ѵॕm ubˆ;ubm|_;0uo‰-|;uv_;7Őou|_;-v|o=|_;0;ub-m;mbmv†Ѵ-őķ-m -vv†l;7 ƐŊ_‹0ub7 |u;; Ő$ő =uol - ror†Ѵ-|bom bm |_; $-fo ubˆ;u _;-7‰-|;uvŐ;m|u-Ѵ0;ub-m;mbmv†Ѵ-őĺ$_;|‰o0;ub-mbm7bˆb7†-Ѵv ‰;u;ru;ˆbo†vѴ‹];mo|‹r;7†vbm]lb1uov-|;ѴѴb|;vŐ-1-‹-Ŋ"-mŒ;|-Ѵĺķ ƑƏƐƐőĺ

ƑĺƑĺƑՊ|Պ ;Š|u-1|bom-m7! v;t†;m1bm]

ou-ѴѴv-lrѴ;vķ ‰-v;Š|u-1|;7=uolƐƔŋƑƏl]o=vbѴb1-Ŋ7ub;7Ѵ;-= l-|;ub-Ѵ‰b|_|_; b-];m ;-v‹Ѵ-m|bmbb|ĺ$_;1om1;m|u-|bom o= ‰-vl;-v†u;7‰b|_- †0b|ƑĺƏ=Ѵ†ouol;|;u†vbm]|_;7v  "-vv-‹hb|Őmˆb|uo];mőķ-m7b|vbm|;]ub|‹ˆ;ub=b;7‰b|_;Ѵ;1|uor_ou;-vbvomƐĺƔѷ-]-uov;];ѴvŐƐ*$őĺom1;m|u-|bomv‰;u;v|-m7-u7bŒ;7 |oƑƏm]ņμѴ-m7bm7bˆb7†-Ѵv-lrѴ;v‰;u;v†0lb||;7=ou! Ѵb0u-u‹ ru;r-u-|bom-m7v;t†;m1bm]|o Ѵou-];m;Šĺ$_;u;ķ-ѴѴ;Š|u-1|bomvo= |_; bm7bˆb7†-Ѵv o= |_; =buv| v;|ķ -v ‰;ѴѴ -v |_; u;rѴb1-|; ;Š|u-1|bomv o= ƏƒƖōƏƔ -m7 ƒƕƒōķ ‰;u; ruo1;vv;7 Ő|o];|_;u ‰b|_ -77b|bom-Ѵ v-lrѴ;vru;r-u;7bm|_;v-l;‰-‹őķbm=bˆ;Ѵb0u-ub;vo=ƖƔbm7bˆb7†--Ѵv ;-1_ĺ $_;v; Ѵb0u-ub;v ‰;u; ru;r-u;7 -11ou7bm] |o Ѵou-];m;ŠĽ v|-m7-u71oll;u1b-Ѵruo|o1oѴĹ];molb1 ‰-v7b];v|;7‰b|_|_; u;v|ub1|bom;m7om†1Ѵ;-v;PstŐ_ubv|;;|-ѴĺķƑƏƐѵĸ1_ov;m-11ou7bm] |oru;ˆbo†vv|†7b;vom|_;v;vr;1b;vŊ"|क़Ѵ|bm];|-ѴĺķƑƏƐƒő-m7!  Ѵb0u-ub;v‰;u;ru;r-u;7‰b|_-l;|_o7vblbѴ-u|o|_;om;7;v1ub0;7 bm -bu7 ;| -Ѵĺ ŐƑƏƏѶőĺ $_bv ruo|o1oѴ bm1Ѵ†7;7 ƐѶ ! 1‹1Ѵ;vķ -=|;u ‰_b1_  =u-]l;m|v u-m]bm] =uol ƒƏƏ |o ƔƏƏ 0r ‰;u; u;|-bm;7ĺ ѴѴ=bˆ;Ѵb0u-ub;v‰;u;v;t†;m1;7bm-vbm]Ѵ;u†mom-mѴѴ†lbm-b";t ƑķƔƏƏbmv|u†l;m|ķ0†|ombm7bˆb7†-ѴѴ-m;vĺ$_bv7-|-bv-ˆ-bѴ-0Ѵ;bm|_; ";t†;m1;!;-7u1_bˆ;|_uo†]_0boruof;1|!ƔƑѶѵƖƖĺ oѴѴo‰bm]|_;v-l;ruo|o1oѴķ-m-77b|bom-ѴѴb0u-u‹‰-v];m;u-|;7 -m7v;t†;m1;70‹ Ѵou-];m;Šbm-v;r-u-|;;Šr;ubl;m|ķ1omvbv|bm] o=|‰o-m7|_u;;u;rѴb1-|;;Š|u-1|bomvo=Ɛ-m7$ķu;vr;1|bˆ;Ѵ‹ķ -v‰;ѴѴ-v;Š|u-1|bomv=uolo==vrubm]o=-1om|uoѴѴ;71uovv0;|‰;;m |_;lĺ$_bv7-|-bv-ˆ-bѴ-0Ѵ;bm|_;";t†;m1;!;-7u1_bˆ;|_uo†]_ 0boruof;1|!ƔƑѶƕƏѵĺ

ƑĺƑĺƒՊ|Պbobm=oul-|b17-|-ruo1;vvbm]

);-vvb]m;7u;-7v|obm7bˆb7†-Ѵvouu;rѴb1-|;v‰b|_=-v|tŊl†Ѵ|ŠŐ;-Ŋ †|bѴvĸuom;v|‹ķƑƏƐƐőķ-ѴѴo‰bm]om;lbvl-|1_bm|_;ƐƔ0rbm1Ѵ†7bm] 0-u1o7;-m7u;v|ub1|bomvb|;ĺ!;-7t†-Ѵb|‹‰-v1_;1h;7‰b|_ -v|  ƏĺƐƏĺƐ Őm7u;‰vķ ƑƏƐƏő -m7 Ѵo‰ t†-Ѵb|‹ 0-v;v -m7 7v ‰;u; u;-loˆ;7‰b|_1om7;|ubˆĺƑĺƒŐ"l;7vşুmv|m;uķƑƏƐƐő†vbm]7;=-†Ѵ| r-u-l;|;uvķ;Š1;r|=ou|_;or|bomvŊ_tŐ_b]_t†-Ѵb|‹|_u;v_oѴ7ő-m7 ŊѴ=u-1Ől-Šbl†l-11;r|-0Ѵ;=u-1|bomo=0-v;v-=|;ut†-Ѵb|‹|ubllbm] ‰b|_t†-Ѵb|‹v1ou;vѴo‰;u|_-m|_;|_u;v_oѴ7ŊѴtőķ=ou‰_b1_-ˆ-Ѵ†;o= ƐƔ-m7ƏĺƐ‰;u;1_ov;mķu;vr;1|bˆ;Ѵ‹ĺ

b]_Ŋt†-Ѵb|‹ u;-7v ‰;u; -Ѵb]m;7 -]-bmv| |_; P. tremula lb|o-1_om7ub-Ѵu;=;u;m1;v;t†;m1;Ő;uv|;m;|-ѴĺķƑƏƐѵő-m7-]-bmv||_;

m†1Ѵ;-uu;=;u;m1;];mol;o=P. trichocarpaŐ|ub1_o1-ur-ōƑƐƏōˆƒĺƏĸ $†vh-m ;| -Ѵĺķ ƑƏƏѵő †vbm] o‰|b;Ƒ ƑĺƒĺƏ Ő-m]l;-7 ş "-ѴŒ0;u]ķ ƑƏƐƑő ‰b|_ ľ;m7Ŋ|oŊ;m7Ŀ -m7 ľˆ;u‹ v;mvb|bˆ;Ŀ v;||bm]vĺ !;-7v ‰b|_ l-rrbm] t†-Ѵb|‹ Ѵo‰;u |_-m ƑƏ ‰;u; 7bv1-u7;7 †vbm] v-l|ooѴv Ɛĺƒ Őb;|-ѴĺķƑƏƏƖő-m7u;-7]uo†rbm=oul-|bom‰-v-77;7‰b|_rb1-u7 |ooѴv ƐĺƐƒƖ Ő_||rĹņņ0uo-7bmv|b|†|;ĺ]b|_†0ĺboņrb1-u7őĺ ); |_;m †v;7 |_; |ooѴv $-u];|u;-|ou -m7 m7;Ѵ!;-Ѵb]m;u o= $ ƒĺѶ Ő ;ubv|o ;|-ѴĺķƑƏƐƐő|ou;-Ѵb]m-uo†m7bm7;Ѵvķ-m7u;1-Ѵb0u-|;70-v;t†-Ѵb|‹ v1ou;v =ou ;-1_ bm7bˆb7†-Ѵ †vbm] |_; l;|_o7 0‹ o†v-|_-m-v ;| -Ѵĺ ŐƑƏƐƕőblrѴ;l;m|;7bm$"Őbmh;|-ѴĺķƑƏƐƕőomlb|o1_om7ub-Ѵv;- t†;m1;vĺ$_bvl;|_o77o;vmo|u;t†bu;-ruboubbm=oul-|bomom];m-o|‹r;v-m7bmv|;-7Ѵ;-umv0-v;t†-Ѵb|b;v=uol_-rѴob7u;]bomv‰_bѴ; bm|;]u-|bm]oˆ;u];mo|‹r;†m1;u|-bm|‹ĺ bm-ѴѴ‹ķ‰;1-ѴѴ;7];mo|‹r;v ‰b|_&mb=b;7;mo|‹r;ubm$ƒĺѶŐ ;ubv|o;|-ѴĺķƑƏƐƐőĺ $o|_;momѴ‹u;|-bmu;Ѵb-0Ѵ;vb|;v=ou1olr-ubvomķ‰;=bѴ|;u;7u;-v†Ѵ|bm]ˆ-ub-m|v†vbm]ˆ1=|ooѴvŐ -m;1;h;|-ѴĺķƑƏƐƐő-m71†v|ol! v1ubr|vĹ=buv|ķ‰;u;loˆ;7vb|;v‰b|_-m-ˆ;u-];7;r|_-1uovvbm7bˆb7-†-ѴvƾƑƓŐ|_;ƖѶĺƕѷt†-m|bѴ;ő|o;Š1Ѵ†7;ro|;m|b-ѴѴ‹r-u-Ѵo]o†vѴo1bĺ ";1om7ķ‰;omѴ‹h;r|vbm]Ѵ;m†1Ѵ;o|b7;ˆ-ub-m|vŐ"(vő‰b|_-|lov| |‰o v;]u;]-|bm] -ѴѴ;Ѵ;vĺ $_bu7ķ ‰; u;loˆ;7 -ѴѴ ˆ-ub-m| vb|;v ‰b|_bm Ɣ0ro=-mbm7;Ѵ|o-ˆob7"(v7†;|olbv-Ѵb]ml;m|vĺ

ƑĺƑĺƓՊ|Պ$u†|_v;|

;mo|‹r;v o= |_; Ɛƒѵ bm7bˆb7†-Ѵv ]uo‰m bm |_; 1ollom ]-u7;mv ‰;u; ru;ˆbo†vѴ‹ o0|-bm;7 Őbm7|h; ;| -Ѵĺķ ƑƏƐƓő ‰b|_ - ];mo|‹rbm]Ŋ 0‹Ŋv;t†;m1bm] Ő"ő ruo|o1oѴ ˆ;u‹ vblbѴ-u |o |_; 77!  ruo|o1oѴ Ő;|;uvom;|-ѴĺķƑƏƐƑő-m7†vbm]|_;u;v|ub1|bom;mŒ‹l;vEcoRI and

Mseĺ lrou|-m|Ѵ‹ķ bm7|h; ;| -Ѵĺ ŐƑƏƐƓő ];m;u-|;7 v;t†;m1bm] 7-|-

-Ѵvo =ou |_; ƐƔ lo|_;u |u;;v -m7 †v;7 vb0v_brv bm - -‹;vb-m -r-ruo-1_|obm=;u];mo|‹r;v‰_bѴ;-11o†m|bm]=ou=-lbѴb-Ѵu;Ѵ-|bomv_brvĺ $o1olr-u;|_;v;_b]_t†-Ѵb|‹];mo|‹r;v|o|_ov;o0|-bm;7=uol o†u o‰m ! Ŋv;t ;Šr;ubl;m|ķ Ѵo1b 1oˆ;u;7 bm 0o|_ v|†7b;v _-7 |o 0;b7;m|b=b;7=buv|ĺ"bm1;bm7|h;;|-ѴĺŐƑƏƐƓő†v;7-moѴ7;uP.

trem-ulau;=;u;m1;ķ‰;;Š|u-1|;7=uol|_bvu;=;u;m1;‰bm7o‰vo=ƑƏƐ0r

-uo†m7;-1_Ѵo1†vbm|_;"7-|-v;|ŐƐƏƏ0rom;b|_;uvb7;őĺ); |_;m l-rr;7 |_;v; ;Š|u-1|;7 v;t†;m1;v -]-bmv| |_; P. trichocarpa u;=;u;m1; ‰b|_ o‰|b;Ƒ ƑĺƒĺƏ Ő-m]l;-7 ş "-ѴŒ0;u]ķ ƑƏƐƑő ‰b|_ ľ;m7Ŋ|oŊ;m7Ŀ -m7 ľˆ;u‹ v;mvb|bˆ;Ŀ v;||bm]v -m7 u;|-bm;7 omѴ‹ |_ov; v;t†;m1;v |_-| l-rr;7 †mbt†;Ѵ‹ ‰b|_ t†-Ѵb|‹ o= ƑƏ ou lou;ĺ ); |_;m h;r| -ѴѴ Ѵo1b oˆ;uѴ-rrbm] 0;|‰;;m |_; |‰o 7-|- v;|vķ 0†| u;-loˆ;7=o†uѴo1b=ou‰_b1_7b==;u;m|-Ѵ|;um-|bˆ;-ѴѴ;Ѵ;v‰;u;1-ѴѴ;7ĺ$o ;mv†u;_b]_-11†u-1‹o=|_;"7-|-ķ‰;u;v|ub1|;7-ѴѴ1olr-ubvomv |o ];mo|‹r;v 1-ѴѴ;7 ‰b|_ - rov|;ubou ruo0-0bѴb|‹ ƾƖƖѷ 0‹ bm7|h; ;|-ѴĺŐƑƏƐƓőĺ

ƑĺƑĺƔՊ|Պv|bl-|bm]];mo|‹rbm];uuouu-|;v

);;v|bl-|;7];mo|‹rbm];uuouu-|;v=uolo†u! Ŋv;t7-|-=uol 0o|_bm7bˆb7†-Ѵu;rѴb1-|;v-v‰;ѴѴ-v|_uo†]_|_;1olr-ubvom|o|_; |u†|_7-|-7;v1ub0;7-0oˆ;ĺ"bm1;o†u7-|-7o;vmo|u;=Ѵ;1|u-m7ol v-lrѴ;vo=-ror†Ѵ-|bomķ‰;1o†Ѵ7mo|0;m;=b|=uol|_;ror†Ѵ-|bom v-lrѴ;l;|_o7bm|uo7†1;7-0oˆ;ĺ

ƑĺƑĺѵՊ|Պ †-m|b=‹bm]-ѴѴ;Ѵ;7uoro†|

);o0|-bm;7-m-rruoŠbl-|;;v|bl-|;o=-ѴѴ;Ѵ;7uoro†|0‹u;l-rrbm] |_;u-‰"7-|--]-bmv||_;P. trichocarpau;=;u;m1;‰b|_0‰-Ŋl;l Őbķ ƑƏƐƒőķ b7;m|b=‹bm] |_; lov| Ѵbh;Ѵ‹ -Ѵ|;um-|bˆ; -ѴѴ;Ѵ; -m7 1-ѴѴbm] ];mo|‹r;v†vbm]|_;|-vhl-foubmouo=$"Őbmh;|-ѴĺķƑƏƐƕő=ou -ѴѴvb|;v‰b|_bmPst1†|vb|;vķ‰_b1_‰;b7;m|b=b;7bm|_;P. trichocarpa u;=;u;m1; †vbm] ! v;t Ő_;mķ ,_†ķ -bm;uķ 1-mm;ѴѴķ ş -ŒŒboķ ƑƏƐƓőĺ);|_;mt†-m|b=b;7|_;=u-1|bomo=1†|vb|;v-1uovvbm7bˆb7†--Ѵv‰b|_-|Ѵ;-v|om;_;|;uoŒ‹]o†v];mo|‹r;ķo†|o=-ѴѴ1†|vb|;v|_-| ‰;u;1oˆ;u;7-|7;r|_ƾƒƵ-|-ѴѴvb|;vĺ

ƑĺƑĺƕՊ|Պv|bl-|bm]o=];mol;Ŋ‰b7;-m7

interspecific ancestry

ou;-1_o=|_;Ɛƒѵ1ollom]-u7;mv-lrѴ;v‰;;v|bl-|;7|_;];-mol;Ŋ‰b7;ruorou|bomo=P. alba-m1;v|u‹Ő];mol;Ŋ‰b7;-m1;v|u‹qő -m7|_;ruorou|bomo=|_;];mol;_;|;uoŒ‹]o†v=ou|_;|‰o-m1;v-|ub;vŐbm|;uvr;1b=b1-m1;v|u‹Q₁₂ő†vbm];m|uor‹Őolr;u|;|-ѴĺķƑƏƐƓőķ -ruo]u-l|_-|blrѴ;l;m|v-lo7;ѴvblbѴ-u|o|_;-7lbŠ|†u;lo7;Ѵ bm v|u†1|†u; Őub|1_-u7ķ "|;r_;mvķ ş omm;ѴѴ‹ķ ƑƏƏƏőĺ m 1om|u-v| |o v|u†1|†u;ķ _o‰;ˆ;uķ ;m|uor‹ 1-m -Ѵvo l-h; †v; o= †m1;u|-bm ];mo- |‹r;v=uolѴo‰7;r|_v;t†;m1;7-|-0‹‰ouhbm]7bu;1|Ѵ‹‰b|_];mo-|‹r;Ѵbh;Ѵb_oo7vķu-|_;u|_-m];mo|‹r;1-ѴѴvĺ;u;‰;u-m;m|uor‹om |_;u-‰];mo|‹r;Ѵbh;Ѵb_oo7vruoˆb7;70‹&mb=b;7;mo|‹r;uķ-v‰;ѴѴ -vom];mo|‹r;Ѵbh;Ѵb_oo7vu;1-Ѵb0u-|;7†vbm];lrbub1-ѴѴbh;Ѵb_oo7v;v-|bl-|;7=uol|_;1olr-ubvom|o-|u†|_v;|ķ;Š1Ѵ†7bm]vb|;v‰b|_ƻƔƏѷ lbvvbm] 7-|- bm 0o|_ 1-v;vĺ $o v|u-|b=‹ |_; ;v|bl-|;v -m7 _-ˆ; v†=- =b1b;m|o0v;uˆ-|bomv|o;v|bl-|;|_;v;ruo0-0bѴb|b;vu;Ѵb-0Ѵ‹ķ‰;1om-vb7;u;7=bˆ;! Ŋv;t7;r|_1Ѵ-vv;vĹƐŋƒķƓŋƕķѶŋƐƔķƐѵŋƒƐ-m7ƾƒƑĺ

ƑĺƑĺѶՊ|Պm=;u;m1;o=Ѵo1†vŊvr;1b=b1-m1;v|u‹

$obm=;uѴo1†vŊvr;1b=b1-m1;v|u‹ķ‰;u-m!"0;uu‹Ő);]l-mm;|-Ѵĺķ ƑƏƐƐőķ‰_b1_blrѴ;l;m|v-b77;m-uhoˆo7;ѴŐő|o;ŠrѴ-bm _-rѴo|‹r;v o= -7lbŠ;7 bm7bˆb7†-Ѵv -v - lov-b1 o= ruoˆb7;7 u;=;u-;m1; _-rѴo|‹r;v =ou ;-1_ vr;1b;vĺ ); o0|-bm;7 v†b|-0Ѵ; u;=;uu;=;u-;m1; _-rѴo|‹r;v 0‹ r_-vbm] ru;ˆbo†vѴ‹ 1_-u-1|;ubŒ;7 r†u; P. alba and r†u; P. tremula bm7bˆb7†-Ѵv ŐƔƐ ;-1_ő =uol |_; |-Ѵb-mķ †v|ub-m -m7 †m]-ub-m_‹0ub7Œom;vŐ_ubv|;;|-ѴĺķƑƏƐѵő†vbm] -v|_-v;Ő"1_;;| ş "|;r_;mvķ ƑƏƏѵőķ 0†bѴ7bm] bmr†| =bѴ;v ‰b|_ =1 Ő!ov_‹-u- ş "1_oѴŒķ ƑƏƐƓőĺ ou †v; bm !"0;uu‹ķ bm7bˆb7†-Ѵv bm |_; u;=;u;m1; r-m;Ѵv ‰;u; mo| -ѴѴo‰;7 |o _-ˆ; lbvvbm] 7-|-ĺ ); |_†v u;v|ub1|;7 |_;1olr-ubvom|oomѴ‹|_;"(v1oˆ;u;7bm-ѴѴr-u;m|-Ѵbm7bˆb7†-Ѵvĺ

$o1olr†|;|u-mvb|bomruo0-0bѴb|b;vbm!"0;uu‹ķ‰;†v;7 -7;=-†Ѵ|u;1ol0bm-|bomu-|;o=Ɣ1ņ0-v;v|bl-|;70‹$†vh-m;|-Ѵĺ ŐƑƏƏѵőbmP. trichocarpa-m7|_;;v|bl-|;vo=|_;];mol;Ŋ‰b7;-m1;v|u‹

q=ou;-1_v-lrѴ;o0|-bm;7‰b|_;m|uor‹=uol|_;;uuou1ouu;1|;77-|-ĺ oulov|o|_;ur-u-l;|;uv‰;†v;7ru;ˆbo†v;v|bl-|;v=ouP. alba and

P. tremula _‹0ub7Œom;vŐ_ubv|;;|-ѴĺķƑƏƐѵőķ0†|v1-Ѵ;7|_;v;-vruo-rov;7 0‹ );]l-mm ;| -Ѵĺ ŐƑƏƐƐő |o u;=Ѵ;1| |_; vbŒ; o= |_; u;=;u;m1; r-m;Ѵĺ $_;v; bm1Ѵ†7; |_; -m1;v|u-Ѵ ror†Ѵ-|bom u;1ol0bm-|bom u-|;v ŐƒƐƔ -m7 ƖƏƏ =ou P. alba and P. tremulaķu;vr;1|bˆ;Ѵ‹őķl†|-|bomu-|;v ŐƏĺƏƏƐѶƔ-m7ƏĺƏƏƒƓƖķu;vr;1|bˆ;Ѵ‹őķ|_;lbv1or‹bm]u-|;ŐƏĺƏƐő-m7|_; lbv1or‹l†|-|bomu-|;ŐƏĺƏƐőĺo‰;ˆ;uķ‰;v;||_;|bl;vbm1;-7lbŠ-|†u;|o=bˆ;Őu-|_;u|_-mom;ő|ou;=Ѵ;1||_;7b==;u;m|v-lrѴbm]v|u-|;]‹ĺ $o-11o†m|=ou];mo|‹rbm];uuouvķ‰;7;|;ulbm;7-r;uŊ-ѴѴ;Ѵ;];-mo|‹rbm];uuouε-v|_;‰;b]_|;7-ˆ;u-];-1uovv7;r|_Ŋvr;1b=b1;uuou u-|;vo0|-bm;7†m7;u|_;|u†|_v;|lo7;Ѵķ‰b|_|_;1omv|u-bm|ε₀ = ε₁ -m7‰;b]_|vu;=Ѵ;1|bm]|_;7bv|ub0†|bomo=7;r|_bm|_;vb|;vbm1Ѵ†7;7 bm|_;-m-Ѵ‹vbvĺ);|_;m-77;7|_bv;uuouu-|;;v|bl-|;|o|_;ror-†Ѵ-|bomvr;1b=b1-m7lbv1or‹l†|-|bomu-|;vĺ&m7;u|_;!"0;uu‹ 1or‹bm]lo7;Ѵķ|_;v;r-u-l;|;uv1om|uoѴ|_;u-|;-|‰_b1_|_;v-l-rѴ;];mo|‹r;v7b==;u=uol|_;u;=;u;m1;_-rѴo|‹r;=uol‰_b1_|_; v-lrѴ; bv 1or‹bm]ĺ $_-| u-|; |_†v 7;r;m7v om |_; u;=;u;m1; r-m;Ѵ vbŒ;ķ0†|-Ѵvoom];mo|‹rbm];uuouvĺ

); 1-ѴѴ;7 -m1;v|u‹ v;]l;m|v -v -m‹ v|u;|1_ om - 1_uolovol; ‰b|_bm‰_b1_|_;rov|;ubouruo0-0bѴb|b;v=ou-r-u|b1†Ѵ-u-m1;v|u‹Ő_o-loŒ‹]o†vP. albaķ_;|;uoŒ‹]o†v-m1;v|u‹ou_o‰b|_bm‰_b1_|_;rov|;ubouruo0-0bѴb|b;v=ou-r-u|b1†Ѵ-u-m1;v|u‹Ő_o-loŒ‹]o†vP. tremulaő ‰-vƻƏĺƔ-|-ѴѴ"(vķ-m7l;-v†u;7b|vѴ;m]|_=uol|_;=buv||o|_; Ѵ-v|"(ĺ

ƒՊ|Պ! "&$"

ƒĺƐՊ|Պo‰;u|obm=;u];mo|‹rbm];uuouu-|;v

"bl†Ѵ-|bomv v†]];v| |_-| - =;‰ |_o†v-m7 Ѵo1b -u; v†==b1b;m| |o -1- 1†u-|;Ѵ‹;v|bl-|;];mo|‹rbm];uuouu-|;v;ˆ;m=uolf†v|-=;‰v-l-rѴ;vŐ b]†u;Ɛőĺ †;|o|_;;Š|u-bm=oul-|bomruoˆb7;7ķ|_;vl-ѴѴ;v| ;v|bl-|bom;uuouv‰;u;o0|-bm;7‰_;m†vbm]-|u†|_v;|ĹƻƖƏѷo=-ѴѴ ;v|bl-|;v=;ѴѴ‰b|_bm-u-m];=uol_-Ѵ=|o|‰oŊ=oѴ7|_;|u†;ˆ-Ѵ†;Ő Ƒķ ;ĺ]ĺķ ‰b|_bm ŒƏĺƏƏƔķ ƏĺƏƑœ =ou - |u†; ;uuou u-|; o= ƏĺƏƐő b= ;v|bl-|;7

];mo|‹r;v‰;u;1olr-u;7-|ƑƏƏ-m7ƓƏƏvb|;v=ouε0 and ε1

ķu;vr;1-|bˆ;Ѵ‹ĺ"blbѴ-u-11†u-1‹‰-v-1_b;ˆ;7†m7;u|_;ror†Ѵ-|bomv-lrѴ;v lo7;Ѵ-vvoom-vƔķƏƏƏvb|;v‰;u;†v;7ĺ

$_;Ѵo‰;v|-11†u-1‹‰-vo0v;uˆ;7†m7;u|_;u;rѴb1-|;vlo7;Ѵķ ;vr;1b-ѴѴ‹b=;uuouu-|;v‰;u;Ѵo‰ĺ&vbm]ƔķƏƏƏvb|;vķ=oubmv|-m1;ķ-ѴѴ

;v|bl-|;v‰;u;‰b|_bm Ƒ=ou-|u†;ˆ-Ѵ†;o=ε₀ = ε₁ƷƏĺƐķ0†|omѴ‹

vѴb]_|Ѵ‹-0oˆ;ѶƏѷo=-ѴѴ;v|bl-|;v=ou-|u†;ˆ-Ѵ†;o=ε0 = ε1 = 0.01. $_bvbvu;-7bѴ‹;ŠrѴ-bm;70‹|_;=-1||_-|omѴ‹ˆ;u‹Ѵblb|;7bm=oul--|bom-0o†||_;|u†;];mo|‹r;bv-ˆ-bѴ-0Ѵ;Ĺb=|_;|‰ou;rѴb1-|;v7b==;u bm|_;bu];mo|‹r;ķb|bvmo|1Ѵ;-u‰_b1_om;bv1ouu;1|ĺomv;t†;m|Ѵ‹ķ |_;-11†u-1‹o=bm=;u;m1;bvl†1_bm1u;-v;7b=lou;|_-m|‰ou;rѴb-1-|;v-u;-ˆ-bѴ-0Ѵ;r;ubm7bˆb7†-ѴŐ b]†u;"Ɛőĺom;|_;Ѵ;vvķ;ˆ;mvl-ѴѴ ;uuouu-|;v1-m0;;v|bl-|;7u;Ѵ-|bˆ;Ѵ‹-11†u-|;Ѵ‹ķ-vƻƖƏѷo=-ѴѴ;v-|bl-|;v=ou|u†;ˆ-Ѵ†;o=ε₀ = ε₁ƷƏĺƏƐ=;ѴѴ‰b|_bm Ƒ-vvoom-vƐƏ4 oulou;1olr-ubvomv‰;u;†v;7ĺ

lrou|-m|Ѵ‹ķ |_; -11†u-1‹ bv - =†m1|bom o= |_; =u-1|bom o= |u†Ѵ‹

_;|;uoŒ‹]o†v ];mo|‹r;v bm |_; 7-|- v;|ķ ‰b|_ |_; -11†u-1‹ o=ε1

bm1u;-vbm] ‰b|_ lou; _;|;uoŒ‹]o†v 1-ѴѴvķ -m7 |_-| o=ε0 and ε0

de-1u;-vbm]ĺ;u;ķ‰;vbl†Ѵ-|;7ƔƏѷ_;|;uoŒ‹]o†v];mo|‹r;v=ou|_; |u†|_ v;| -m7 u;rѴb1-|; lo7;Ѵv -m7 -0o†| ƑƖѷ _;|;uoŒ‹]o†v ];m-o|‹r;v =ou |_; ror†Ѵ-|bom v-lrѴ; lo7;Ѵĺ = |_; m†l0;u o= _;|;uo-Œ‹]o†v ];mo|‹r;v ‰;u; Ѵo‰;uķ ruorou|bom-ѴѴ‹ lou; vb|;v ‰o†Ѵ7 0; m;;7;7|o-1_b;ˆ;|_;-11†u-1‹ru;v;m|;7_;u;ĺ=ƑƏѷo=-ѴѴ];mo-|‹r;v‰;u;_;|;uoŒ‹]o†vķ=oubmv|-m1;ķ-uo†m7ƐƏ5_{vb|;v-u;u;t†bu;7} †m7;u|_;u;rѴb1-|;lo7;Ѵ‰b|_|‰ou;rѴb1-|;vr;uv-lrѴ;ĺ

ƒĺƑՊ|Պ&vbm]‰_oѴ;Ŋ];mol;v;t†;m1bm]|o;v|-0Ѵbv_

a truth set

vv_o‰m-0oˆ;ķ];mo|‹rbm];uuouu-|;v-u;bm=;uu;7r-u|b1†Ѵ-uѴ‹ -11†u-|;Ѵ‹‰_;m1olr-ubm]1-ѴѴv|o-|u†|_v;|ĺm;rovvb0bѴb|‹|o ;v|-0Ѵbv_v†1_-|u†|_v;|bv|ov_o|Ŋ]†mv;t†;m1;-v†0v;|o=bm7b-ˆb7†-Ѵv-m7|obm=;u];mo|‹r;v=uol|_bv7-|-ĺ$_bvbv-Ѵvo=;-vb0Ѵ; bm1-v;mou;=;u;m1;];mol;bv-ˆ-bѴ-0Ѵ;-v|_;v_o|Ŋ]†mu;-7v1-m 0; l-rr;7 7bu;1|Ѵ‹ -]-bmv| |_; ! ŊѴo1bĺ o‰;ˆ;uķ vbm1; ];mo- |‹rbm];uuouvbm|_;|u†|_v;|Ѵ;-7|o-moˆ;u;v|bl-|bomo=];mo-|‹rbm];uuouu-|;vķv†==b1b;m|Ѵ‹_b]_7;r|_l†v|0;†v;7ĺ;u;ķ‰; †v;7 vbl†Ѵ-|bomv |o -vv;vv |_bv 0b-v =ou |_; 1-v; o= v_o|Ŋ]†m

v;-t†;m1bm]om;bm7bˆb7†-Ѵ-|ƐƏ4_{_oloŒ‹]o†v-m7ƐƏ}4_{_;|;uoŒ‹]o†v}

! Ѵo1bĺ

vv_o‰mbm b]†u;Ƒ=ouε0 = ε1ƷƏĺƏƐķ];mo|‹rbm];uuouu-|;v

l-‹0;oˆ;u;v|bl-|;71omvb7;u-0Ѵ‹†mѴ;vv|_;7;r|_†v;7|o;v|-0-Ѵbv_ |_; |u†|_ v;| ‰-v u;Ѵ-|bˆ;Ѵ‹ _b]_ĺ | - l;-m 7;r|_ o= ƐƏƵķ =ou

bmv|-m1;ķ|_;l;7b-mu;Ѵ-|bˆ;0b-v‰-vƐĺƖƑ-m7ƏĺƔƏ=ouε₀ and ε₁ķ

u;vr;1|bˆ;Ѵ‹ķ-m7_;m1;om|_;v-l;ou7;u-v|_;bm=;uu;7;uuouu-|;ĺ |-l;-m7;r|_o=ƒƏƵķ|_;l;7b-moˆ;u;v|bl-|bom7uorr;70;Ѵo‰ ƏĺƏƐbm0o|_1-v;vĺlrou|-m|Ѵ‹ķѴ-u];ut†-m|bѴ;v7uorl†1_vѴo‰;uķ v†]];v|bm]|_-|-lbmbl-Ѵ0b-vbv_-u7|ooˆ;u1ol;;ˆ;m‰b|_ˆ;u‹

_b]_ 7;r|_vĺ o|;‰ou|_‹ķ ‰; o0v;uˆ;7 - v|uom];u 0b-v =ouε0 |_-m

ε₁ -| -ѴѴ 7;r|_vķ - u;v†Ѵ| o= lou; o=|;m 1-ѴѴbm] |u†Ѵ‹ _;|;uoŒ‹]o†v

vb|;v_oloŒ‹]o†v|_-mˆb1;ˆ;uv-=uolm;Š|Ŋ];m;u-|bomv;t†;m1bm] 7-|-ĺ!;v†Ѵ|v‰;u;ˆbu|†-ѴѴ‹b7;m|b1-Ѵ=ou|_;1-v;o=ε₀ = ε₁ƷƏĺƐķ0†| v1-Ѵ;77†;|o|_;Ѵ-u];u|u†;;uuouŐ b]†u;"Ƒőĺ

ƒĺƒՊ|Պb]_];mo|‹rbm];uuouu-|;vbm! Ŋv;t

);m;Š|†v;7o†ubm=;u;m1;l;|_o7v|ot†-m|b=‹];mo|‹rbm];uuouv =uolo†u! Ŋv;t;Šr;ubl;m|o=Ɛƒƕbm7bˆb7†-Ѵvo=|_;|‰o‰b7;-vru;-7|u;;vr;1b;vPopulus alba and P. tremulaķ-m7|_;bu_‹0ub7vŐP.

x canescens). m -ˆ;u-];ķ o†u ;Šr;ubl;m| u;v†Ѵ|;7 bm ѶƒƐķƐѵƐ ŐSD ƐƔƒķƓƒƓőu;-7vr;uv-lrѴ;|_-|r-vv;7t†-Ѵb|‹|ubllbm]-m7l-rr;7 -]-bmv||_;u;=;u;m1;];mol;o=P. trichocarpa‰b|_l-rrbm]t†-Ѵb|‹ ƾƑƏĺ uol|_ov;ķ‰;1-ѴѴ;7ƔƑƖķƒƏƔ"(vķ-=|;uu;loˆbm]l†Ѵ|b-Ѵ-Ѵ;Ѵb1vb|;vķ|_ov;‰b|_;Š1;vvbˆ;7;r|_ķbm7;Ѵv-m7ˆ-ub-m|vb|;v-uo†m7 bm7;Ѵvĺ ); ;v|bl-|;7 r;uŊ-ѴѴ;Ѵ; ];mo|‹rbm] ;uuou u-|;v =uol |_;v; "(v|_uo†]_-1olr-ubvom‰b|_ru;ˆbo†vѴ‹r†0Ѵbv_;7ķ_b]_Ŋt†-Ѵb|‹ ];mo|‹r;vŐ|u†|_v;|őķ-m7=uoll†Ѵ|brѴ;u;rѴb1-|;Ѵb0u-ub;vv;t†;m1;7 =ou-v†0v;|o=o†uv-lrѴ;vŐu;rѴb1-|;vőĺ

ƒĺƒĺƐՊ|Պ$u†|_v;|

); ;v|bl-|;7 r;uŊ-ѴѴ;Ѵ; ];mo|‹rbm] ;uuouv 0‹ 1olr-ubm] ];mo-|‹r; 1-ѴѴv =uol o†u ! Ŋv;t ;Šr;ubl;m| |o |_ov; o= - ru;ˆbo†vѴ‹

r†0Ѵbv_;7 " 7-|- v;| Őbm7|h; ;| -Ѵĺķ ƑƏƐƓő =ou Ɛƒѵ bm7bˆb7†-Ѵv ru;v;m| bm 0o|_ v|†7b;vĺ m |o|-Ѵķ ƕķƓƑѵ "(v oˆ;uѴ-rr;7 0;|‰;;m ;Šr;ubl;m|vķ -| ‰_b1_ ‰; 1o†Ѵ7 †v; - |o|-Ѵ o= ƐѵķѵƐƏ ];mo|‹r; 1olr-ubvomvĺ = |_ov;ķ omѴ‹ ѵƖĺƖѷ l-|1_;7ķ ‰b|_ l-|1_bm] u-|;v

  & !   Ɛ Պ 11†u-1‹o=;uuouu-|;;v|bl-|;vĺ"_o‰m-u;|_;;v|bl-|;7;uuouu-|;vu;Ѵ-|bˆ;|o|_;|u†;;uuouu-|;vŐu;7Ѵbm;őo=ƐƏƏu;rѴb1-|;v =ou7b==;u;m|v-lrѴ;vvbŒ;vnŐv_o‰mom|orőķ|_;|‰o;uuouu-|;vƏĺƐ-m7ƏĺƏƐŐ=buv|-m7Ѵ-v||‰o1oѴ†lmvķu;vr;1|bˆ;Ѵ‹ő-m77b==;u;m|m†l0;uv o=†mѴbmh;7Ѵo1bĺ$_;_oubŒom|-Ѵ7-v_;7Ѵbm;vbm7b1-|; Ƒķ|_;bm|;uˆ-Ѵ‰b|_bm‰_b1_-m;v|bl-|;bvѴ;vv|_-m-=-1|ouo=|‰o-‰-‹=uol|_; |u†;ˆ-Ѵ†;Őbĺ;ĺķ‰b|_bm_-Ѵ=-m7|‰o|bl;v|_;|u†;ˆ-Ѵ†;őĺ"bl†Ѵ-|bomv‰;u;];m;u-|;7=ou|_;|u†|_v;|Ő|oruo‰őķ|_;bm7bˆb7†-Ѵu;rѴb1-|;Ő|‰o u;rѴb1-|;vr;uv-lrѴ;ķlb77Ѵ;uo‰ő-m7ror†Ѵ-|bomv-lrѴ;vlo7;ѴvŐ0o||oluo‰őŒoѴo†u=b]†u;1-m0;ˆb;‰;7-|‰bѴ;‹omѴbm;Ѵb0u-u‹ĺ1olœ ●●●●●●● ●●●●●●● ●●●●●●● −0.4 0 0.4 n = 1 n = 10 n = 100 ●●●●● ●● ●●●●●●● ●●●●●●● n = 1 n = 10 n = 100 ● ●●●●●● ●●●●●●● ●●●●●●● n = 1 n = 10 n = 100 ●●●●●●● ●●●●●●● ●●●●●●● n = 1 n = 10 n = 100

Truth Set

●●●●●●● ●●●●●●● ●●●●●●● −0.4 0 0.4 n = 1 n = 10 n = 100 ● ●●●●●● ● ●● ● ● ●● ●● ● ●●●● n = 1 n = 10 n = 100 ●●●●●●● ●● ●●●●● ●●●●●●● n = 1 n = 10 n = 100 ●●●●●●● ● ●●●●●● ● ● ● ●●●● n = 1 n = 10 n = 100

_Replicates

● ●●●●●● ●●●●●●● ●●●●●●● 100 1,000 10,000 100 1,000 10,000 100 1,000 10,000 −0.4 0 0.4 n = 20 n = 100 n = 200 ● ● ●● ●●● ● ●●●●●● ●●●●●●● 100 1,000 10,000 100 1,000 10,000 100 1,000 10,000 n = 20 n = 100 n = 200 ●●● ●●●● ●●●●●●● ●●●●●●● 100 1,000 10,000 100 1,000 10,000 100 1,000 10,000 n = 20 n = 100 n = 200 ● ● ●●● ●● ● ● ●●●●● ●●●●●●● 100 1,000 10,000 100 1,000 10,000 100 1,000 10,000 n = 20 n = 100 n = 200

Pop. sample

ε

0

= 0.1

#loci

ε

1

= 0.1

#loci

ε

0

= 0.01

#loci

ε

1

= 0.01

#loci log10 est/tr ue log10 est/tr ue log10 est/tr ue   & !   Ƒ Պ bv|ub0†|bomo=|_;u;Ѵ-|bˆ; 0b-v‰_;mbm=;uubm];uuouu-|;v=uol- |u†|_v;|];m;u-|;7‰b|_m;Š|Ŋ];m;u-|bom v;t†;m1bm]7-|-‰b|_-vr;1b=b1l;-m 7;r|_ĺ-1_Ѵbm;bm7b1-|;v-t†-m|bѴ;l v†1_|_-|-vl-ѴѴ;u0b-v‰-vo0v;uˆ;7 bm-=u-1|bomlo=ƐƏ6vbl†Ѵ-|bomvo=ƐƏ4 _oloŒ‹]o†v-m7ƐƏ4_{_;|;uoŒ‹]o†vѴo1b} ‰b|_ε₀ = ε₁ƷƏĺƏƐŒoѴo†u=b]†u;1-m0; ˆb;‰;7-|‰bѴ;‹omѴbm;Ѵb0u-u‹ĺ1olœ 0 5 10 15 20 25 30 0.001 0.003 0.01 0.03 0.1 0.3 1 3 10 Relativ e bias of ε0 Depth 50% 55% 60% 70% 80% 90% 95% 99% ε0= 0.01 0 5 10 15 20 25 30 0.001 0.003 0.01 0.03 0.1 0.3 1 3 10 Relativ e bias of ε1 Depth 50% 55% 60% 70% 80% 90% 95% 99% ε1= 0.01

http://doc.rero.ch

bm1u;-vbm] ‰b|_ ! Ŋv;t 7;r|_ Ő b]†u; ƒ-őĺ "|ubhbm]Ѵ‹ķ ! Ŋv;t ];mo|‹r;v‰;u;l†1_Ѵ;vvo=|;m_;|;uoŒ‹]o†v|_-m"];mo|‹r;v Ő b]†u;ƒ0őķ;vr;1b-ѴѴ‹-|Ѵo‰7;r|_ĺmѴbm;‰b|_|_;v;o0v;uˆ-|bomvķ ‰;bm=;uu;7r;uŊ-ѴѴ;Ѵ;];mo|‹rbm];uuouu-|;vƻƐƏѷ‰_;m;ˆ;u! Ŋ v;t7;r|_‰-vƽƒƔ-m7‰_;m†vbm]-lo7;Ѵ-vv†lbm]-vbm]Ѵ;;uuou u-|;Őε₀ = ε₁ őķ7ubˆ;m0‹-m;Š1;r|bom-ѴѴ‹_b]_;uuouu-|;-||u†Ѵ‹_;|-;uoŒ‹]o†vvb|;vε1Ő b]†u;Ƒ1őĺ $_;v;-u;v†urubvbm]Ѵ‹_b]_;uuouu-|;vķr-u|b1†Ѵ-uѴ‹‰_;m1omvb7-;ubm]|_-|v;t†;m1bm];uuouu-|;vo=ѴѴ†lbm-l-1_bm;v-u;;v|bl-|;7 -|ƺƐѷŐb;Ѵv;mķ-†ѴķѴ0u;1_|v;mķş"om]ķƑƏƐƐőĺlrou|-m|Ѵ‹ķ|_; 0b-v|o‰-u7v_oloŒ‹]o†v];mo|‹r;1-ѴѴvbvmo|vblrѴ‹;ŠrѴ-bm;70‹ Ѵo‰7;r|_ĺm7;;7ķ! Ŋv;tv|bѴѴu;v†Ѵ|;7bmѴ;vv|_-m_-Ѵ=-vl-m‹ _;|;uoŒ‹]o†v 1-ѴѴv -| 7;r|_v ƾƓƏƵķ ‰_b1_ -u; †v†-ѴѴ‹ 1omvb7;u;7 lou; |_-m v†==b1b;m| =ou -11†u-|; ];mo|‹r; 1-ѴѴbm] Őb;Ѵv;m ;| -Ѵĺķ ƑƏƐƐőĺmv|;-7ķo†uu;v†Ѵ|vv†]];v|-mbm_;u;m|0b-vbm|_;! Ŋv;t 7-|--m-Ѵ‹v;7_;u;ĺ

); 1om=bul;7 o†u v†vrb1bom 0‹ -m-Ѵ‹vbm] -ѴѴ;Ѵb1 bl0-Ѵ-m1; -| vb|;v|_o†]_||o0;_;|;uoŒ‹]o†v0-v;7om|_;"];mo|‹r;vķѴblb|-bm]|_;-m-Ѵ‹v;v|o];mo|‹r;v1oˆ;u;7-|†r|oƔƏƵ|o-ˆob7vr†ubo†v -Ѵb]ml;m|vŐ b]†u;"ƒőĺmѴ‹-vbm]Ѵ;-ѴѴ;Ѵ;‰-v=oubmv|-m1;o0v;uˆ;7 -|ѵƖѷo=-ѴѴ_;|;uoŒ‹]o†v];mo|‹r;v‰b|_7;r|_ƾƔƵķ-=u-1|bom|_-| 7uorr;7|oѵƏѷ-m7ƔƑѷ=ou];mo|‹r;v‰b|_7;r|_ƾƑƏƵ-m77;r|_ ƾƒƏƵķu;vr;1|bˆ;Ѵ‹ķbm7b1-|bˆ;o=-ѴѴ;Ѵb17uoro†|-|-Ѵ-u];v1-Ѵ;ĺ

o‰;ˆ;uķ o†u ;v|bl-|;v u;Ѵ‹ om |_; -vv†lr|bom |_-| |_; " 7-|-u;=Ѵ;1||u†;];mo|‹r;vĺ$_bvbv0-v;7om]oo7;ˆb7;m1;ĺ buv|ķ bm7|h; ;| -Ѵĺ ŐƑƏƐƓő -77b|bom-ѴѴ‹ v;t†;m1;7 |_; lo|_;u |u;;v o= -ѴѴ bm7bˆb7†-Ѵv 1omvb7;u;7 _;u; -m7 ;v|bl-|;7 rov|;ubou ];mo|‹r;v †vbm]-_b;u-u1_b1-Ѵ-m1;v|u‹lo7;Ѵ|_-|bm1ourou-|;7=-lbѴb-Ѵu;Ѵ--|bomv_brv‰b|_lo|_;uv-m7-lom]vb0Ѵbm]vĺ$_;v;†r7-|;7;v|bl-|;v

1ouu;Ѵ-|;7‰b|_|_;u-‰l-Šbl†lѴbh;Ѵb_oo7];mo|‹r;;v|bl-|;vb]-moubm]=-lbѴb-Ѵ7-|--|ƏĺƖѶƔ-m77b==;u;7=uol|_ov;bmƺƏĺƏƑѷo= -ѴѴ 1-ѴѴvĺ ";1om7ķ ‰; u;v|ub1|;7 |_bv 1olr-ubvom |o " ];mo|‹r;v ‰b|_-rov|;ubouruo0-0bѴb|‹ƾƖƖѷĺ$_bu7ķ|_;=u-1|bomo=1om1ou7-m| ];mo|‹r;1-ѴѴv0;|‰;;m|_;"-m7! Ŋv;t7-|-bm1u;-v;7‰b|_ ! Ŋv;t7;r|_ĺ=|_;lbvl-|1_;v‰;u;7ubˆ;m0‹;uuouvbm|_;" 7-|-ķmov†1_7;r;m7;m1;v_o†Ѵ70;o0v;uˆ;7ĺ

ƒĺƒĺƑՊ|Պ!;rѴb1-|;v

);m;Š|0;m;=b||;7=uol|‰ov;|vo=u;rѴb1-|;Ѵb0u-ub;v|o;v|bl-|; r;uŊ-ѴѴ;Ѵ; ];mo|‹rbm] ;uuou u-|;vĺ $_; =buv| v;| 1omvbv|;7 o= |‰o u;rѴb1-|;Ѵb0u-ub;vo=;-1_o=|‰obm7bˆb7†-ѴvŐ ƏƒƖōƏƔ-m7ƒƕƒōő v;t†;m1;7-Ѵom]-ѴѴo|_;uv-lrѴ;vĺuuouu-|;v;v|bl-|;7=uol|_-| 7-|- 1ouuo0ou-|;7 |_; 1om1Ѵ†vbom o0|-bm;7 =uol |_; 1olr-ubvom

‰b|_"7-|-Ő b]†u;ƒ7őĹ;uuouu-|;v-||u†Ѵ‹_oloŒ‹]o†vvb|;vŐε0ő

‰;u;om|_;ou7;uo=ƐѷouѴ;vvķ-m7|_ov;-||u†Ѵ‹_;|;uoŒ‹]o†vvb|;v

Őε1ő‰;u;;t†-Ѵou1Ѵov;|oƔƏѷķ‰_b1_bv|_;Ѵ-u];v|ˆ-Ѵ†;rovvb0Ѵ;

under our model.

m1om|u-v||o|_;;v|bl-|;vo0|-bm;7bm1olr-ubvom|o"];m-o|‹r;vķ |_; ;uuou u-|;v -| |u†Ѵ‹ _;|;uoŒ‹]o†v vb|;v Őε₁ő 7uorr;7 |o

-0o†| ƑƏѷ -| _b]_ 7;r|_ ŐƾƑƏƵőĺ $_bv 7b==;u;m1; lb]_| bm r-u| 0; 7ubˆ;m 0‹ ;uuouv bm |_; " 7-|- vѴb]_|Ѵ‹ bm=Ѵ-|bm] ;uuou u-|; ;v|b-l-|;vĺo‰;ˆ;uķ]bˆ;m|_;_b]_t†-Ѵb|‹o=|_;"7-|-ķb|-rr;-uv lou;Ѵbh;Ѵ‹|_-||_;;uuouu-|;v=uolu;rѴb1-|;v-u;†m7;u;v|bl-|;7ĺ oѴ‹lour_bvlvbmu;v|ub1|bom1†|vb|;vou†m;t†-Ѵ!-lrѴb=b1-|bom u-|;v o= -ѴѴ;Ѵ;vķ =ou bmv|-m1;ķ -==;1| u;rѴb1-|;v v‹v|;l-|b1-ѴѴ‹ķ ‰_bѴ;

  & !   ƒ Պ v|bl-|;vo=];mo|‹rbm];uuouvbm! Ŋv;t7-|-ĺŐ-ő-Šbl†lѴbh;Ѵb_oo7;v|bl-|;Őőo=|_;=u;t†;m1‹o=];mo|‹r;v ;v|bl-|;7=uol"-m7! Ŋv;t7-|-|_-|l-|1_-v-=†m1|bomo=! Ŋv;tv;t†;m1bm]7;r|_ĺ$_;]u;‹u;]bombm7b1-|;v|_;u-m];o= =u;t†;m1b;v‰b|_bm|‰oѴo]ŊѴbh;Ѵb_oo7†mb|vo=|_;ĺŐ0ő;v|bl-|;o=|_;=u;t†;m1‹o=_;|;uoŒ‹]o†v1-ѴѴv‰b|_! Ŋv;t-lom]-ѴѴ 1-ѴѴvo=-r-u|b1†Ѵ-u7;r|_oˆ;uѴ-rrbm]‰b|_|_;"7-|-ĺu;‹u;]bom-vbmĺ$_;_;|;uoŒ‹]ovb|‹o0v;uˆ;7-lom]-ѴѴoˆ;uѴ-rrbm]" ];mo|‹r;vbv]bˆ;m-v7-v_;7Ѵbm;ĺŐ1ő;uŊ-ѴѴ;Ѵ;! Ŋv;t];mo|‹rbm];uuouu-|;v=ou_oloŒ‹]o†vŐε0ķ0Ѵ-1hor;mv‹l0oѴvő-m7_;|;uoŒ‹]o†v Őε₁ķ0Ѵ†;=bѴѴ;7v‹l0oѴvő];mo|‹r;v;v|bl-|;7†vbm]-"|u†|_v;|ķѴblb|;7|o7;r|_1Ѵ-vv‰b|_-|Ѵ;-v|ƐƏƏ1olr-ubvomvĺv|bl-|;v=ou- lo7;Ѵ-vv†lbm]ε0= ε1-u;v_o‰m‰b|_‹;ѴѴo‰1Ѵov;71bu1Ѵ;vĺŐ7ő;uŊ-ѴѴ;Ѵ;! Ŋv;t];mo|‹rbm];uuouu-|;vo0|-bm;7=uol|‰ou;rѴb1-|;vo= ƏƒƖōƏƔ-m7ƒƕƒō;-1_Ő1bu1Ѵ;vő-m7|‰o-m7|_u;;u;rѴb1-|;v=uolƐ-m7;|ķu;vr;1|bˆ;Ѵ‹Ő|ub-m]Ѵ;vőķѴblb|;7|o7;r|_1Ѵ-vv‰b|_-|Ѵ;-v| ƐķƏƏƏvb|;vĺoѴo†uv-vbmŒoѴo†u=b]†u;1-m0;ˆb;‰;7-|‰bѴ;‹omѴbm;Ѵb0u-u‹ĺ1olœ ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ● ●●● ● ●●● ●●●●●●● ●●● ● ●●●●●●●●●●●●●●● ●● ● ● ●● ● ●● ● ● ●●●●●●●●●●●●●●●● ● ● ●● ● ● ● ● ● ● ●● ●● ●●● ●●●●● Matching Genotypes 1 10 20 30 40 50 60% 65% 70% 75% 80% 85% 90% Depth ● ● ● ●●●_●●●● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Heterozygosity 1 10 20 30 40 50 0% 5% 10% 15% 20% 25% 30% 35% 40% Depth ● ● ● ●●● ● ●● ● ● ●● ● ● ● ● ●_● ● ●● ● ●● ● ●●● ● ●●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● Heterozygosity GBS

Genotyping Error Rate from T

ruth Set 1 10 20 30 40 0.1% 0.2% 0.5% 1% 2% 5% 10% 20% 50% Depth

Genotyping Error Rates from Replicates _0.1%

0.2% 0.5% 1% 2% 5% 10% 20% 50% 1 10 20 30 40 Depth (a) (b) (c) (d)

http://doc.rero.ch

|_; v|-|bv|b1-Ѵ bm=;u;m1; l†v| -vv†l; bm7;r;m7;m1; o= ;uuouv 0;-|‰;;mu;rѴb1-|;vĺ

$o ˆ;ub=‹ |_-| _b]_ ;uuou u-|;v -u; mo| vr;1b=b1 |o |_; ! Ŋv;t u†mr;u=oul;7om|_;v;_‹0ub7vķ‰;1-uub;7o†|-v;1om7! Ŋv;t ;Šr;ubl;m|bm1Ѵ†7bm]|‰o-m7|_u;;u;rѴb1-|;vo=-r†u;P. alba indi-ˆb7†-ѴŐƐő-m7-r†|-|bˆ; ƐP. albaƵP. tremula_‹0ub7Ő$őķu;vr;1-|bˆ;Ѵ‹ĺ $_bv ;Šr;ubl;m| u;v†Ѵ|;7 bm ѵƖƓķƏƒƐ ŐSD ƐѶƕķƖƔƕő u;-7v r;u v-lrѴ;|_-|r-vv;7t†-Ѵb|‹|ubllbm]-m7l-rr;7-]-bmv||_;u;=;u-;m1;];mol;o=P. trichocarpa‰b|_t†-Ѵb|‹ƾƑƏĺ;uŊ-ѴѴ;Ѵ;;uuouu-|;v ;v|bl-|;7=uol|_bv7-|-‰;u;bm7;;7Ѵo‰;uķ‰b|_;uuouu-|;v-||u†Ѵ‹ _oloŒ‹]o†vvb|;vŐε0 őom|_;ou7;uo=ƏĺƑѷ-m7|_ov;-||u†Ѵ‹_;|-;uoŒ‹]o†vvb|;vŐε₁őv|-u|bm]o†|-|ƔƏѷ-m77uorrbm]|o-0o†|ƒѷ-| -7;r|_o=ƑƔƵŐ b]†u;ƒ7őĺo‰;ˆ;uķ|_;v;Ѵo‰;u;uuouvv|bѴѴrobm||o -r-u|b1†Ѵ-ubvv†;bm1-ѴѴbm]_;|;uoŒ‹]o†v];mo|‹r;vĹo=-ѴѴ|u†Ѵ‹_;|-;uoŒ‹]o†vvb|;v‰b|_7;r|_ƾƑƔƵbmo†u7-|-ķƻƔѷ-u;;Šr;1|;7|o0; 1-ѴѴ;7_oloŒ‹]o†vŐ|_;Ѵo‰;uo†|r†|o=|_bvv;t†;m1bm];Šr;ubl;m| 7o;vmo|-ѴѴo‰†v|ol-h;u;Ѵb-0Ѵ;v|-|;l;m|v=ou_b]_;u7;r|_vőĺ

ƒĺƓՊ|Պv|bl-|bomo=];mol;Ŋ‰b7;-m7

interspecific ancestry

); bmˆ;v|b]-|;7 |_; blr-1| o= ];mo|‹rbm] ;uuouv bm o†u ! Ŋv;t 7-|- om |_; bm=;u;m1; o= ];mol;Ŋ‰b7; -m1;v|u‹ q -v ‰;ѴѴ -v

bm|;u-vr;1b=b1 -m1;v|u‹ Q₁₂ķ ‰_b1_ u;=Ѵ;1|v |_; ruorou|bom o= Ѵo1b o=

_;|-;uovr;1b=b1-m1;v|u‹ĺ);;v|bl-|;7|_;v;-m1;v|u‹1olrom;m|v‰b|_ ;m|uor‹=uolƑƒƏķѶƏƔ"(vķ-m71olr-u;7|_;l|o;v|bl-|;v=uol "o0|-bm;70‹bm7|h;;|-ѴĺŐƑƏƐƓőĺ $_;lo7;ѴblrѴ;l;m|;7bm;m|uor‹-11o†m|v=ou|_;];mo|‹rbm] †m1;u|-bm|‹u;=Ѵ;1|;7bm|_;];mo|‹r;Ѵbh;Ѵb_oo7vĺo‰;ˆ;uķ|_;u-‰ ];mo|‹r;Ѵbh;Ѵb_oo7vo0|-bm;7=uolo†u! Ŋv;t7-|--u;lbvѴ;-7bm]Ĺ =ouvb|;v‰b|_1omvb7;u-0Ѵ;7;r|_ķ|_;! Ŋv;t];mo|‹r;Ѵbh;Ѵb_oo7v o=|;mv†]];v|-Ѵlov|1;u|-bm|‹=ou‰uom]];mo|‹r;vĺ=-ѴѴ];mo|‹r;v ‰uom]Ѵ‹1-ѴѴ;7-v_oloŒ‹]o†v-|7;r|_ƾƒƏƵŐf†7];70‹|_;1olr-u-bvom|o"7-|-őķƖƏѷ_-7-ˆ-ub-m|t†-Ѵb|‹o=ƕƕoulou;ĺˆ-ub-m| t†-Ѵb|‹o=ƕƕblrѴb;v|_-|b|bvlou;|_-mƔ0bѴѴbom|bl;vѴ;vvѴbh;Ѵ‹|oo0-v;uˆ;|_;o0|-bm;77-|-=uol-_;|;uoŒ‹]o†v|_-m_oloŒ‹]o†vvb|;ĺ

v - u;v†Ѵ|ķ -m1;v|u‹ ;v|bl-|;v 7b==;u;7 1omvb7;u-0Ѵ‹ 0;|‰;;m |_; " -m7 ! Ŋv;t 7-|- v;|v Ő b]†u; Ɠőĺ m|;u;v|bm]Ѵ‹ķ |_; ;v|b-l-|;vo=|_;];mol;Ŋ‰b7;-m1;v|u‹q‰;u;l†1_Ѵ;vv-==;1|;70‹ ];mo|‹rbm] ;uuouv |_-m |_; ;v|bl-|;v o= |_; bm|;uvr;1b=b1 -m1;v|u‹

Q₁₂ĺ$_bvbvu;-7bѴ‹;ŠrѴ-bm;7ķ_o‰;ˆ;uķ0‹|_;7bu;1|bom-Ѵb|‹o=|_;

lov| 1ollom ;uuouķ ‰_b1_ bv |o ‰uom]Ѵ‹ bm=;u _oloŒ‹]o†v ];mo-|‹r;v-|_;|;uoŒ‹]o†vvb|;vĺ);=o†m7|_;v;;uuouv7ou;v†Ѵ|lou; =u;t†;m|Ѵ‹bm-_oloŒ‹]o†vu;=;u;m1;|_-m_oloŒ‹]o†v-Ѵ|;um-|bˆ; 1-ѴѴŐѵƔĺƏѷőķr-u|b1†Ѵ-uѴ‹-|Ѵo‰7;r|_ŐѶƓĺƔѷ-|7;r|_ƽƔƵķƓƖĺƖѷ-| 7;r|_ƾƑƏƵőĺo‰;ˆ;uķ|_bv7b7mo|bm|uo7†1;-0b-vbmq|o‰-u7vom; o=|_;vr;1b;vvbm1;‰;†v;7|_;v;t†;m1;o=|_;o†|]uo†rP.

tricho-carpa-vu;=;u;m1;ĺ$_;;v|bl-|;vo=Q₁₂ ķ_o‰;ˆ;uķ‰;u;ˆ;u‹v;mvb-|bˆ;|o-m†m7;u;v|bl-|bomo=_;|;uoŒ‹]ovb|‹ĺ

$oblruoˆ;|_;v;;v|bl-|;vķ‰;ruorov;|o7bu;1|Ѵ‹-11o†m|=ou |_; ;Ѵ;ˆ-|;7 ];mo|‹rbm] ;uuou u-|;v bm ! Ŋv;t 7-|- 0‹ -7f†v|bm] |_;];mo|‹r;Ѵbh;Ѵb_oo7v-11ou7bm]|o|_;o0v;uˆ;7];mo|‹rbm]†m-1;u|-bm|‹ĺ‹|u;-|bm]|_;];mo|‹r;1-ѴѴv-v7-|-ķ‰;1-m7;|;ulbm; |_;ruo0-0bѴb|b;vŐg|γőo=o0v;uˆbm]-! Ŋv;t];mo|‹r;1-ѴѴg]bˆ;m |_;|u†;];mo|‹r;γ;b|_;u0‹†vbm];v|bl-|;vo=|_;r;uŊ-ѴѴ;Ѵ;;uuou u-|;vε₀ķε₁ķou;lrbub1-ѴѴ‹=uol|_;1olr-ubvom|o-|u†|_v;|ĺ&vbm] |_;Ѵ-||;u-rruo-1_omo†u7-|-Őbm7bˆb7†-ѴѴ‹=ou;-1_7;r|_őu;v†Ѵ|;7

bm;v|bl-|;vo=q and Q12|_-|‰;u;l†1_1Ѵov;u|o|_ov;o0|-bm;70‹

bm7|h;;|-ѴĺŐƑƏƐƓĸ b]†u;Ɠőĺ

"ol; 7b==;u;m1;v 0;|‰;;m |_; robm| ;v|bl-|;v o= Q₁₂ u;l-bmķ

ruo0-0Ѵ‹ 7†; |oĹ Ő-ő 7b==;u;m1;v bm |_; lo7;Ѵv -m7 |_;bu bm=oul--|bomŊv_-ubm] -lom] bm7bˆb7†-Ѵvķ -v bm7|h; ;| -Ѵĺ ŐƑƏƐƓő †v;7 bm=ou-l-|bom -0o†| l-|;um-Ѵ rѴ-m|v -m7 vb0v_brv -v r-u| o= |_; lo7;Ѵĸ -m7 Ő0ő |_; ;Š|;m| |o ‰_b1_ bm=oul-|bom bm †m1;u|-bm ];mo|‹r;v ‰-v o†|‰;b]_;7 0‹ _b;u-u1_b1-Ѵ rubou ruo0-0bѴb|b;v u;Ѵ-|;7 |o -m-1;v|u‹ĺ om;|_;Ѵ;vvķ |_;v; u;v†Ѵ|v 7;lomv|u-|; |_; blrou|-m1; o= -11o†m|bm] =ou †m1;u|-bm|‹ bm ];mo|‹rbm] 7-|- vbm1; |_; ;v|bl-|;v o=bm|;uvr;1b=b1-m1;v|u‹‰b|_-m7‰b|_o†|1ouu;1|bomѴ;-7|o-ˆ;u‹ 7b==;u;m| 0boѴo]b1-Ѵ bm|;uru;|-|bomĺ )b|_ 1ouu;1|bomķ |_; _‹0ub7 bm-7bˆb7†-Ѵv-rr;-u|o0;lov|Ѵ‹ ;-uѴ‹];m;u-|bom_‹0ub7vķv†]];v|bm] l;-mbm]=†Ѵ u;ruo7†1|bˆ; bvoѴ-|bom 0;|‰;;m |_; vr;1b;vĺ )b|_o†|

1ouu;1|bomķ |_; Ѵ-u]; m†l0;u o= bm7bˆb7†-Ѵv ‰b|_ Ѵo‰ Q₁₂ 0†|

bm|;u-l;7b-|; ˆ-Ѵ†;v o= q v†]];v|v 1omvb7;u-0Ѵ; ];m; =Ѵo‰ 0;|‰;;m |_;

  & !   Ɠ Պ olr-ubvomo=];mol;Ŋ ‰b7;Őtő-m7bm|;uvr;1b=b1Ő ₁₂ő-m1;v|u‹ ;v|bl-|;vo=Ɛƒѵbm7bˆb7†-Ѵvo0|-bm;7 =uol"7-|-Őbm7|h;;|-ѴĺķƑƏƐƓő-m7 ;v|bl-|;v=uol! Ŋv;t7-|-Ő0Ѵ-1h 1bu1Ѵ;vő†vbm];b|_;u|_;u-‰ŐѴ;=|r-m;Ѵő ou1ouu;1|;7Őub]_|r-m;Ѵő];mo|‹r; Ѵbh;Ѵb_oo7vĺu;‹Ѵbm;v1omm;1|ˆ-Ѵ†;v o0|-bm;7=ou|_;v-l;bm7bˆb7†-Ѵ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●_●● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●_● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●●● ●● ●●● ●●●●●●●●●●●●● ● ● ●●●●●● ● ● ● ●● ●●●● ● ●●● ●●● ●● ●●● ●●● ● ●●●●●●●● ● ● ●● ● ●● ● ●●● ● ● ●● ●●●●●● ● ● ● ● ●● ●● ●●●●●●●●●●●●●●● ●●●●●●● ● ● ● ● ● ● ● ● ●● ● ●● ● 0.0 0.2 0.4 0.6 0.8 1.0 Genome− wide ancestry q 0.0 0.2 0.4 0.6 0.8 1.0 Interspecific ancestry Q12 ● GBS raw RAD−seq ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●_● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●_● ● ● ● ● ● ● ● ● ● ● ●●_● ●_● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●_● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.0 0.2 0.4 0.6 0.8 1.0 Genome− wide ancestry q

● GBS corr. RAD−seq

vr;1b;vķ -m bm|;uru;|-|bom -| o77v ‰b|_ u;1;m| ‰ouh Ő_ubv|; ;| -Ѵĺķ ƑƏƐѵķƑƏƐƕĸ-1-‹-Ŋ"-mŒ;|-ѴĺķƑƏƐƐőĺ

ƒĺƔՊ|Պm=;u;m1;o=Ѵo1†vŊvr;1b=b1-m1;v|u‹

);m;Š|;ˆ-Ѵ†-|;7|_;blr-1|o=];mo|‹rbm];uuouvomѴo1-Ѵ-m1;v|u‹ bm=;u;m1;ĺ ‹0ub7 Œom;v 0;|‰;;m P. alba and P. tremula are domi-m-|;70‹r†u;r-u;m|-Ѵbm7bˆb7†-Ѵv-m7;-uѴ‹_‹0ub7vŐlov|Ѵ‹ Ɛőķ‰b|_ omѴ‹ =;‰ -7†Ѵ| u;1ol0bm-m| _‹0ub7v Ő_ubv|; ;| -Ѵĺķ ƑƏƐѵĸ bm7|h; ;| -Ѵĺķ ƑƏƐƓőĺ ); 1_ov; ƐƏ bm7bˆb7†-Ѵv -lom] o†u v-lrѴ;v

vr-m-mbm]|_-|vr;1|u†l-11ou7bm]|oq and Q12ˆ-Ѵ†;v=uolbm7|h;;|-Ѵĺ

ŐƑƏƐƓőĹ - r†|-|bˆ;Ѵ‹ r†u; P. alba bm7bˆb7†-Ѵ Ő ƏƒƖōƏƐőķ - r†|-|bˆ;Ѵ‹ r†u; P. tremula bm7bˆb7†-Ѵ Ő ƏƒƏōƏƐőķ |‰o r†|-|bˆ; 0-1h1uovv;v |o

P. albaŐ ƏƑƏōƏƓ-m7 ƏƒƑōƏѶőķ|‰or†|-|bˆ;0-1h1uovv;v|oP.

trem-ula ŐƒƓƔōƏƑ -m7 ƒƓƔōƏƒőķ |‰o r†|-|bˆ; Ɛ _‹0ub7v ŐƒƕƒōƏƒ -m7

ƏƒƏōƏƔő -m7 |‰o r†|-|bˆ; _‹0ub7v o= Ѵ-|;u ];m;u-|bomv Ő ƏƑƑōƏƒ -m7 ƏƑѵōƏƔőĺ);|_;m†v;7!"0;uu‹Ő);]l-mm;|-ѴĺķƑƏƐƐő|o bm=;uѴo1-Ѵ-m1;v|u‹-Ѵom]1_uolovol;vƐ|_uo†]_Ɣķu;v|ub1|bm]o†u bm=;u;m1; |o |_; ѵķƓƓƔ "(v |_-| 7b7 mo| _-ˆ; lbvvbm] 7-|- bm |_; r-u;m|-Ѵu;=;u;m1;_-rѴo|‹r;v‰;|ooh=uol_ubv|;;|-ѴĺŐƑƏƐѵőĺ

mѴbm;‰b|_|_;v;;Šr;1|;7vblrѴ;-m1;v|u‹l-h;Ŋ†rvķ‰;bm=;uu;7 l-m‹Ѵ-u];-m1;v|u‹0Ѵo1hvo=|;mvr-mmbm]-Ѵlov|;m|bu;1_uolovol;v Ő b]†u;Ɣőĺ"†urubvbm]Ѵ‹ķ_o‰;ˆ;uķ‰;bm=;uu;7lov|o=|_;v;0Ѵo1hv|o

0;o=_olovr;1b=b1-m1;v|u‹ķ-m7-Ѵvobm=;uu;7l-m‹v_ou|v;]l;m|vķ ‰_b1_ -u; 7b==b1†Ѵ| |o u;1om1bѴ; ‰b|_ |_; r†|-|bˆ; -m1;v|ub;v o= o†u v-lrѴ;vŐ b]†u;Ɣőĺv-m;Š-lrѴ;ķ1omvb7;u|_;bm7bˆb7†-ѴƒƕƒōƏƒbm b]†u;Ɣ|_-|‰-v1Ѵ-vvb=b;7-v-m Ɛ_‹0ub70‹bm7|h;;|-ѴĺŐƑƏƐƓőķ0†| =ou‰_b1_‰;bm=;uu;7_olovr;1b=b1-m1;v|u‹0Ѵo1hv=ou0o|_r-u;m|-Ѵ vr;1b;vĺ"†1_-u|;=-1|v1o†Ѵ7-ubv;=uol|_;u;=;u;m1;r-m;Ѵv0;bm]|oo vl-ѴѴ|oruor;uѴ‹u;=Ѵ;1||_;_-rѴo|‹r;v=o†m7bmo†u_‹0ub7bm7bˆb7†--ѴvķѴ-u];]-rv0;|‰;;mm;b]_0o†ubm]"(vѴblb|bm]|_;ro‰;uo=|_; blrѴ;l;m|;7bm!"0;uu‹ķ0†|lov|Ѵbh;Ѵ‹0‹];mo|‹rbm];uuouv |o‰-u7v_oloŒ‹]o†v];mo|‹r;vĺ )_bѴ;!"0;uu‹7o;vmo|-11o†m|=ou];mo|‹rbm]†m1;u|-bm|‹ ˆb- ];mo|‹r; Ѵbh;Ѵb_oo7vķ |_; blrѴ;l;m|;7 1or‹bm]Ŋlo7;Ѵ -ѴѴo‰v =ouľl†|-|bomvĿķou7b==;u;m1;v0;|‰;;m|_;o0v;uˆ;7];mo|‹r;o= -m -7lbŠ;7 bm7bˆb7†-Ѵ -m7 |_; u;=;u;m1; _-rѴo|‹r;v =uol ‰_b1_ b| bv 1or‹bm]ĺ ); |_†v u;r;-|;7 |_; bm=;u;m1; 0‹ -77bm] -m ;v|bl-|; o=|_;-ˆ;u-];r;uŊ-ѴѴ;Ѵ;];mo|‹rbm];uuouu-|;o0|-bm;7†m7;u|_; |u†|_ v;| lo7;Ѵ ŐƐƒĺƕѷő |o |_; l†|-|bom u-|; r-u-l;|;uv |o -1-1o†m|=ou|_;_b]_];mo|‹rbm];uuoubmo†u! Ŋv;t7-|-Ő b]†u;Ɣőĺ 11o†m|bm] =ou ];mo|‹rbm] ;uuouv bm7;;7 blruoˆ;7 o†u ;v|bl-|;vĺ ou|_;r†|-|bˆ;0-1h1uovv;vķ=oubmv|-m1;ķ‰;1-ѴѴ;7=;‰;uv;]l;m|v _oloŒ‹]o†v=ou|_;ľ‰uom]Ŀ-m1;v|u‹ŐƐƐˆvĺƒƓő-m7|_;v;1oˆ;u;7 -vl-ѴѴ;u=u-1|bomo=|_;=buv|=bˆ;1_uolovol;vŐѵĺƐѷˆvĺƐƐĺƐѷo= |_; r-u|v -| ‰_b1_ -m1;v|u‹ 1o†Ѵ7 0; 1-ѴѴ;7őĺ "blbѴ-uѴ‹ķ ‰; 1-ѴѴ;7 - _b]_;u=u-1|bomo=|_;=buv|=bˆ;1_uolovol;v|o0;o=_;|;uoŒ‹]o†v

  & !   Ɣ Պ olr-ubvomo=Ѵo1-Ѵ-m1;v|u‹r-||;umvom1_uolovol;vƐŋƔ=ouŐ|or|o0o||olő-r†|-|bˆ;Ѵ‹r†u;P. tremulabm7bˆb7†-ѴŐĺ|u;lķ

ƏƒƏōƏƐőķ|‰or†|-|bˆ;0-1h1uovv;v|oP. tremulaŐ|u;lķƒƓƔōƏƑ-m7ƒƓƔōƏƒőķ|‰or†|-|bˆ;_‹0ub7vo=Ѵ-|;u];m;u-|bomŐ mķ ƏƑƑōƏƒ-m7 ƏƑѵōƏƔőķ|‰or†|-|bˆ; Ɛ_‹0ub7vŐ ƐķƒƕƒōƏƒ-m7 ƏƒƏōƏƔőķ|‰or†|-|bˆ;0-1h1uovv;v|oP. albaŐ-Ѵ0-ķ ƏƑƏōƏƓ-m7 ƏƒƑōƏѶő-m7- r†|-|bˆ;Ѵ‹r†u;P. albabm7bˆb7†-ѴŐP. albaķ ƏƒƖōƏƐőĺ ou;-1_bm7bˆb7†-Ѵķ!"0;uu‹u;v†Ѵ|v‰b|_ŐƳő-m7‰b|_o†|Őƴő1ouu;1|bom-u;v_o‰mĺѴ†; u;ru;v;m|vP. alba-m1;v|u‹ķou-m];P. tremula-m1;v|u‹-m7]u;‹_;|;uovr;1b=b1-m1;v|u‹ķ‰b|_7-uh;uv_-7;vv_o‰bm]_b]_;u1om=b7;m1;bm |_;-m1;v|u‹;v|bl-|;vĺ$o=-1bѴb|-|;ˆbv†-ѴbŒ-|bomķomѴ‹vb|;v‰b|_7-|--u;v_o‰mŒoѴo†u=b]†u;1-m0;ˆb;‰;7-|‰bѴ;‹omѴbm;Ѵb0u-u‹ĺ1olœ P. trem – + BC trem – + BC trem – + Fn – + Fn – + F1 – + F1 – + BC alba – + BC alba – + P. alba – + 1 2 3 4 5 Chromosomes

http://doc.rero.ch

-m1;v|u‹ŐƓƔĺƏѷˆvĺƒƕĺƑѷo=|_;r-u|v-|‰_b1_-m1;v|u‹1o†Ѵ70; 1-ѴѴ;7őĺ)_bѴ;|_;v;u;v†Ѵ|v1ouuo0ou-|;|_;blrou|-m1;o=-11o†m|-bm] =ou |_; |u†; †m1;u|-bm|‹ bm ];mo|‹r;v bm 7o‰mv|u;-l -m-Ѵ‹vbvķ |_;‹-ѴvobѴѴ†v|u-|;|_-|-l;|_o7-11o†m|bm]=ou-†mb=oul;uuou=-bѴv |o=†ѴѴ‹lb|b]-|;|_;0b-v-]-bmv|_;|;uoŒ‹]o†v];mo|‹r;vru;v;m|bm o†u! Ŋv;t7-|-v;|vĺ

ƓՊ|Պ "&""  

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