Disentangling the effects of external perturbations on coexistence and priority effects

bv;m|-m]Ѵbm]|_;;==;1|vo=;Š|;um-Ѵr;u|†u0-|bomvom

1o;Šbv|;m1;-m7ruboub|‹;==;1|v

_†Ѵb-m]"om]

Ɛ

Պ|!†7oѴ=ĺ!o_u

2

Պ| -ˆb7(-vv;†u

3

Պ|";u]†;b"--ˆ;7u-

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0v|u-1|

Ɛĺ  l-fou 1_-ѴѴ;m]; bm ;1oѴo]b1-Ѵ u;v;-u1_ bv |o b7;m|b=‹ |_; |oѴ;u-m1; o= ;1oѴo]bŊ 1-Ѵ1oll†mb|b;v|o;Š|;um-Ѵr;u|†u0-|bomvĺo7;um1o;Šbv|;m1;|_;ou‹Ő$ő_-v 0;;m‰b7;Ѵ‹-7or|;7-v-=u-l;‰ouh|obmˆ;v|b]-|;|_;|oѴ;u-m1;|or;u|†u0-|bomv bmu;Ѵ-|bˆ;u;7†1|bomvo=r;u1-rb|-]uo‰|_u-|;vķo=|;m†vbm]l;|ub1v|_-|;ŠrѴb1b|Ѵ‹ ;Ѵblbm-|;|_;bm7;r;m7;m|uoѴ;o=bm|ubmvb1]uo‰|_u-|;vĺou;u;1;m|Ѵ‹ķ|_;v|u†1Ŋ |†u-Ѵ-rruo-1_Ő"ő‰-vbm|uo7†1;7|obmˆ;v|b]-|;|_;|oѴ;u-m1;o=1oll†mb|b;v|o r;u|†u0-|bomvbmbm|ubmvb1]uo‰|_u-|;v-v-=†m1|bomo=|_;v|u;m]|_o=bm|u-vr;Ŋ 1b=b1-m7bm|;uvr;1b=b11olr;|b|bomĺ;1-†v;|_;;Š|;um-Ѵr;u|†u0-|bomv-u;Ѵbh;Ѵ‹ |o_-rr;mbm0o|_bm|ubmvb1]uo‰|_u-|;v-m71olr;|b|bomv|u;m]|_vķmo=u-l;‰ouh -Ѵom;1-m=†ѴѴ‹7bv;m|-m]Ѵ;|_;;==;1|vo=;Š|;um-Ѵr;u|†u0-|bomvĺ Ƒĺ ;u;‰;1ol0bm;$-m7"|o7bv;m|-m]Ѵ;|_;|oѴ;u-m1;bm1o;Šbv|;m1;-m7 ruboub|‹;==;1|vo=-r-buo=1olr;|bm]vr;1b;v‰_;mv†0f;1||or;u|†u0-|bomvbm bm|ubmvb1]uo‰|_u-|;v-m71olr;|b|bomv|u;m]|_vĺ$_uo†]_|_bv1ol0bm-|bomķ‰; u;ˆ;-Ѵ |_; ;l;u];m1; o= - h;‹ |u-7;Ŋo==Ĺ bm1u;-vbm] |_; |oѴ;u-m1; |o r;u|†u0-Ŋ |bomv bm bm|ubmvb1 ]uo‰|_ u-|;v |‹rb1-ѴѴ‹ 7;1u;-v;v |_; |oѴ;u-m1; bm 1olr;|b|bom v|u;m]|_vķ-m7ˆb1;ˆ;uv-ĺ †u|_;ulou;ķ|_bv|u-7;Ŋo==bvv|uom];u†m7;u1o;Šbv|Ŋ ;m1;|_-m†m7;uruboub|‹;==;1|vĺ

ƒĺ ); |;v| |_bv 1ol0bm;7 =u-l;‰ouh om 1olr;|bm] r-buv o= ƐѶ -Ѵb=oumb- -mm†-Ѵ rѴ-m|vr;1b;vĺ ou0o|_1o;Šbv|;m1;-m7ruboub|‹;==;1|vķ‰;=bm7|_-||_;|oѴ;u-m1; |or;u|†u0-|bomvbmbm|ubmvb1]uo‰|_u-|;vbvl-ŠblbŒ;7bmv|;-7o=|_-||or;u|†u0-Ŋ |bomvbm1olr;|b|bomv|u;m]|_vbm|_;v|†7b;7-mm†-ѴrѴ-m|1oll†mb|b;vĺ Ɠĺ Synthesisĺ†u1ol0bm;7=u-l;‰ouho=lo7;um1o;Šbv|;m1;|_;ou‹-m7v|u†1|†u-Ѵ -rruo-1_bѴѴ†v|u-|;v|_-|b|bvrovvb0Ѵ;|o7bv;m|-m]Ѵ;|_;blr-1|o=7b==;u;m|;ŠŊ |;um-Ѵr;u|†u0-|bomvom|_;r;uvbv|;m1;o=vr;1b;vĺlrou|-m|Ѵ‹ķo†u=bm7bm]vv_o‰ |_-|vr;1b;vbm|;u-1|bomvl-‹u;ˆ;-Ѵ‰_;|_;u1oll†mb|b;v-u;7olbm-|;7;b|_;u 0‹ 1_-m];v bm bm|ubmvb1 ]uo‰|_ u-|;v ou 0‹ 1olr;|b|bom v|u;m]|_vĺ ˆ;u-ѴѴķ |_bv 1ol0bm;7=u-l;‰ouh1-mor;m-m;‰r;uvr;1|bˆ;|o†m7;uv|-m7-m7ru;7b1||_; u;vromv;o=ror†Ѵ-|bomv|o1_-m]bm];mˆbuoml;m|-Ѵ1om7b|bomvĺ K E Y W O R D S 1o;Šbv|;m1;ķ1olr;|b|bomv|u;m]|_vķbm|ubmvb1]uo‰|_u-|;vķlo7;um1o;Šbv|;m1;|_;ou‹ķ ruboub|‹;==;1|vķv|u†1|†u-Ѵ-rruo-1_ķ|oѴ;u-m1;|or;u|†u0-|bomv 1

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Published in "Journal of Ecology (): 1365-2745.13349, 2020"

which should be cited to refer to this work.

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&m7;uv|-m7bm] |_; 1om7b|bomv Ѵ;-7bm] |o vr;1b;v 1o;Šbv|;m1; -m7 ruboub|‹;==;1|v_-vѴom]0;;m-1;m|u-Ѵu;v;-u1_|orb1bm1oll†mb|‹ ;1oѴo]‹Ő †h-lbķƑƏƐƔĸ;ˆbm;ķ-v1olr|;ķ7Ѵ;uķşѴѴ;vbm-ķƑƏƐƕĸ oubmķ ƑƏƏƖĸ (;ѴѴ;m7ķ ƑƏƐѵőĺ o;Šbv|;m1; o11†uv ‰_;m l†Ѵ|brѴ; vr;1b;vr;uvbv|‰b|_bm|_;v-l;Ѵo1-|bom=ou-1om|bm†o†vr;ubo7o= |bl;Ő-v;ķƑƏƏƏĸo=0-†;uş"b]l†m7ķƐƖƖѶőĺm1om|u-v|ķruboub|‹ ;==;1|v o11†u ‰_;m |_; 7‹m-lb1v o= |_; 1oll†mb|‹ -u; ]oˆ;um;7 0‹|_;ou7;uo=vr;1b;v-uubˆ-ѴvŐ_-v;ķƑƏƏƒĸ †h-lbķƑƏƐƔĸ"om]ķ Ѵ|;ul-||ķ ;-uv;ķ ş "--ˆ;7u-ķ ƑƏƐѶőĺ $_; l-foub|‹ o= |_;ou;|b1-Ѵ v|†7b;v_-ˆ;-77u;vv;7|_bv|orb10‹=o1†vbm]om|_;m;1;vv-u‹-m7ņ ouv†==b1b;m|1om7b|bomv1olr-|b0Ѵ;‰b|_1o;Šbv|;m1;ouruboub|‹;=Ŋ =;1|v -vv†lbm] |_-| lo7;Ѵ r-u-l;|;uv Ő;ĺ]ĺ bm|ubmvb1 ]uo‰|_ u-|;v -m71olr;|b|bomv|u;m]|_vő-u;=bŠ;7Ő-u-0࢙vķ Ľm7u;-ķş"|†lrķ ƑƏƐѶĸ0†|v;;(-m7;ul;;uķƐƖƕƔőĺom;|_;Ѵ;vvķlo7;Ѵr-u-l;|;uv Ő;b|_;ul;1_-mbv|b1our_;mol;moѴo]b1-Ѵő1_-m];bmu;vromv;|o†mŊ -ˆob7-0Ѵ; ;Š|;um-Ѵ r;u|†u0-|bomv Ő buŒo ;| -Ѵĺķ ƑƏƐƓĸ ;ˆbmvķ ƐƖѵѶĸ "1_;==;uv ;| -Ѵĺķ ƑƏƐѵĸ $†1h;u ş †h-lbķ ƑƏƐƓőķ Ѵ;-7bm] |o |_; m-|Ŋ †u-Ѵt†;v|bomo=_o‰uo0†v|1o;Šbv|;m1;-m7ruboub|‹;==;1|v-u;|o 1_-m];v bm lo7;Ѵ r-u-l;|;uvĺ †u -0bѴb|‹ |o -77u;vv |_bv t†;v|bom _-v 0;;m v_-r;7 0‹ |‰o 7b==;u;m| =u-l;‰ouhvŌlo7;um 1o;ŠbvŊ |;m1;|_;ou‹Ő$ĸ_;vvomķƑƏƐѶő-m7|_;v|u†1|†u-Ѵ-rruo-1_Ő"ĸ "--ˆ;7u-ķ!o_uķ;|-ѴĺķƑƏƐƕőĺ

o7;um 1o;Šbv|;m1; |_;ou‹ Ő_;vvomķ ƑƏƏƏķ ƑƏƐѶő _-v 0;;m ‰b7;Ѵ‹-7or|;7-v-=u-l;‰ouh|obmˆ;v|b]-|;|_;1om7b|bomvѴ;-7Ŋ bm] |o vr;1b;v 1o;Šbv|;m1; -m7 _-v lou; u;1;m|Ѵ‹ 0;;m ;Š|;m7;7 |o ruboub|‹ ;==;1|v Ő †h-lbķ ou7;1-bķ ş v|Ѵbm]ķ ƑƏƐѵĸ u-bm];uķ ;||;mķ bѴ0;u|ķ ş †h-lbķ ƑƏƐƖĸ ; ş ;||;mķ ƑƏƐѶĸ ;ˆbm; ş bѴѴ;!bv-l0;uvķ ƑƏƏƖĸ ou7;1-bķ oѴbm-ubķ "|-_Ѵ_;0;uķ uovvķ ş Ľm|omboķƑƏƐƔőĺmr-u|b1†Ѵ-uķ$v_o‰v|_-|1o;Šbv|;m1;o11†uv ‰_;m|_;;==;1|vo=mb1_;oˆ;uѴ-r;Š1;;7|_;;==;1|vo=0b-vbm]|_; =b|m;vvu-|boom|_;bm=;ubouvr;1b;vĺbh;‰bv;ķ$_-vv_o‰m|_-| ruboub|‹;==;1|vo11†u‰_;m|_;;==;1|vo=7;v|-0bѴbŒbm]l;1_-mbvlv Őv†1_-vrovb|bˆ;=u;t†;m1‹7;r;m7;m1;ő;Š1;;7|_;;==;1|vo=0b-vŊ bm]|_;=b|m;vvu-|bo=ou|_;v†r;ubou1olr;|b|ouŐ;ş;||;mķƑƏƐѶĸ "1_u;b0;uķ+-l-lb1_bķş"|u-†vvķƑƏƐƖőĺlrou|-m|Ѵ‹ķ$-ѴѴo‰v†v |o †m7;uv|-m7 |_; uo0†v|m;vv o= 1o;Šbv|;m1; |o u-m7ol r;u|†u0-Ŋ |bomv bm u;Ѵ-|bˆ; u;7†1|bomv bm r;u 1-rb|- ]uo‰|_ u-|;v Ő-u-0࢙v ;| -Ѵĺķ ƑƏƐѶőĺ  r-bu o= 1olr;|b|ouv 1-m 0; Ѵo1-|;7 bm |_; r-u-l;|;u vr-1;Őo=u;Ѵ-|bˆ;u;7†1|bomvbmr;u1-rb|-]uo‰|_u-|;őu;Ѵ-|bˆ;|o|_; 0o†m7-u‹0;|‰;;m1o;Šbv|;m1;-m7;Š1Ѵ†vbomĺ$_;=†u|_;ubm|o|_; 1o;Šbv|;m1;u;]bom-r-buѴb;vķ|_;lou;uo0†v|1o;Šbv|;m1;‰o†Ѵ70; |o1_-m];vbm|_;-ˆ;u-];=b|m;vvoumb1_;oˆ;uѴ-ro=|_;1olr;|bŊ |ouvĺm-Ѵo]o†vru;7b1|bomv1-m0;l-7;=ouruboub|‹;==;1|vĺ+;|ķ|_; l;|ub1vbm$Őv†1_-vmb1_;oˆ;uѴ-r-m7=b|m;vvu-|boő-u;o=|;m1-ѴŊ 1†Ѵ-|;70-v;7om1olr;|b|bom1o;==b1b;m|vv1-Ѵ;70‹bm|ubmvb1]uo‰|_ u-|;vķ ‰_b1_ ;ŠrѴb1b|Ѵ‹ ;Ѵblbm-|; |_; bm7;r;m7;m| uoѴ; o= bm|ubmvb1 ]uo‰|_ u-|;v ŐbѴѴ;!bv-l0;uvķ 7Ѵ;uķ -uroѴ;ķ ;ˆbm;ķ ş -‹=b;Ѵ7ķ ƑƏƐƑĸ࣐u;ŒŊ!-lovķ-|झ-vķॕl;ŒŊr-ub1boķşo7o‹ķƑƏƐƖőĺ

ou; u;1;m|Ѵ‹ķ |_; " Ő"--ˆ;7u-ķ !o_uķ ;| -Ѵĺķ ƑƏƐƕő ‰-v bm|uoŊ 7†1;7|obmˆ;v|b]-|;|_;u-m];o=bm|ubmvb1]uo‰|_u-|;v1olr-|b0Ѵ; ‰b|_1o;Šbv|;m1;-m7ruboub|‹;==;1|vķ-v-=†m1|bomo=|_;-0voѴ†|;

u;7†1|bomv bm r;u 1-rb|- ]uo‰|_ u-|; Ő-ĺhĺ-ĺ 1olr;|b|bom v|u;m]|_vĸ ;m1bķ "om]ķ ş "--ˆ;7u-ķ ƑƏƐѶőĺ $_; u;]bom o= 1o;Šbv|;m1; bv 7;v1ub0;70‹-m-m]Ѵ;-m1_ou;7-||_;oub]bmo=-rѴo|‰_ov;x and

y -Š;v -u; |_; bm|ubmvb1 ]uo‰|_ u-|;v o= |_; |‰o 1olr;|b|ouvĺ $_;

‰b7;u|_;-m]Ѵ;ķ|_;]u;-|;u|_;u-m];o=bm|ubmvb1]uo‰|_u-|;7b==;uŊ ;m1;v0;|‰;;m1olr;|b|ouv1olr-|b0Ѵ;‰b|_1o;Šbv|;m1;ĺ$_;-m]Ѵ; 0;1ol;v-voѴb7-m]Ѵ;ou1om;bm-_b]_;u7bl;mvbom=ou1oll†mbŊ |b;v1om|-bmbm]lou;|_-m|‰o1olr;|b|ouvŐ"om]ķ!o_uķş"--ˆ;7u-ķ ƑƏƐѶőĺm|_bv‰-‹ķ"bvvr;1b=b1-ѴѴ‹7;vb]m;7|o†m7;uv|-m7|_;uoŊ 0†v|m;vvo=-1oll†mb|‹Ō-v-=†m1|bomo=1olr;|b|bomv|u;m]|_vŌ |ou-m7ol1_-m];vbm|_;bm|ubmvb1]uo‰|_u-|;vo=|_;1omv|b|†;m| vr;1b;vĺ ;1-†v;;Š|;um-Ѵr;u|†u0-|bomv-u;Ѵbh;Ѵ‹|o_-rr;mbm0o|_|_; bm|ubmvb1]uo‰|_u-|;v-m71olr;|b|bomv|u;m]|_vŐ;b|_;uvbl†Ѵ|-m;Ŋ o†vѴ‹ouv;r-u-|;Ѵ‹őķ_;u;‰;-u]†;=ou-1ol0bm-|bomo=$-m7" =o1†v;7omr-u-l;|;u1_-m];vŐr;u|†u0-|bomvőĺ"-m7$l;-v†u; 7b==;u;m|-vr;1|vo=|_;uo0†v|m;vvo=1o;Šbv|;m1;Őruboub|‹;==;1|vőĹ "_-v|_†v=-u0;;m7;ˆ;Ѵor;7‰b|_omѴ‹r;u|†u0-|bomv|o|_;bmŊ |ubmvb1]uo‰|_u-|;vbmlbm7Ő|_;uo0†v|m;vv-v-=†m1|bomo=1olr;Ŋ |b|bomv|u;m]|_vőĸ$_-v0;;m7;ˆ;Ѵor;7‰b|_|_;b7;-o=ro|;m|b-Ѵ vbl†Ѵ|-m;o†v1_-m];vbmr-u-l;|;uvķ0†|l;u]bm]|_;lbm|o-vbm]Ѵ; r-u-l;|;uŐu;Ѵ-|bˆ;u;7†1|bomvbmr;u1-rb|-]uo‰|_u-|;őĺo|;|_-| bm|ubmvb1 ]uo‰|_ u-|;v -m7 1olr;|b|bom v|u;m]|_v -u; r_;mol;moŊ Ѵo]b1-Ѵv†ll-ub;vo=7b==;u;m|-0bo|b1-m70bo|b1=-1|ouvŐ-7o||;ş $†1h;uķƑƏƐƕĸo†Ѵvom;|-ѴĺķƑƏƐƕĸ;ˆbmvķƐƖѵѶĸ-1u|_†uķƐƖƕƏőķ -m7|_;‹rѴ-‹7b==;u;m|=†m7-l;m|-ѴuoѴ;vbmv_-rbm]|_;7‹m-lb1v o=l†Ѵ|bvr;1b;vv‹v|;lvŐ;m1bş"--ˆ;7u-ķƑƏƐѶĸ"om]ş"--ˆ;7u-ķ ƑƏƐѶ-ķƑƏƐѶ0őĺ$_;u;=ou;ķ-1_b;ˆbm]-1ol0bm-|bomo=$-m7" bv1_-ѴѴ;m]bm]0;1-†v;|_;l;|ub1vbm|_;|‰o-rruo-1_;v-u;mo|7bŊ u;1|Ѵ‹|u-mvѴ-|-0Ѵ;Ő-rr;m7bŠ"Ɣbm"--ˆ;7u-ķ!o_uķ;|-ѴĺķƑƏƐƕőĺ+;|ķ bmv|;-7o=|u-mvѴ-|bm]|_;bul;|ub1vķ‰;ruorov;|obmˆ;v|b]-|;_o‰ |_;-m]Ѵ;7;v1ub0bm]|_;bm|ubmvb1]uo‰|_u-|;v1olr-|b0Ѵ;‰b|_1oŊ ;Šbv|;m1;Őruboub|‹;==;1|vőbm"1_-m];v-v-=†m1|bomo=|_;mb1_; oˆ;uѴ-r-m7=b|m;vvu-|bobm$ĺ †u1ol0bm-|bomo=$-m7"=o1†v;vom|‰oŊvr;1b;v1olŊ r;|b|bom7‹m-lb1vĺ)_bѴ;"1-m0;†v;7=ou|‰oŊvr;1b;v-m7l†ѴŊ |bvr;1b;v 1oll†mb|b;v ‰b|_bm |_; v-l; =oul-Ѵbvl Ő"--ˆ;7u-ķ !o_uķ ;|-ѴĺķƑƏƐƕőķ_;u;‰;=o1†vom|‰oŊvr;1b;v7‹m-lb1v]bˆ;m|_-||_; 1-momb1-Ѵ =oul-Ѵbvl o= $ bv ;ŠrѴb1b|Ѵ‹ f†v|b=b;7 =ou |‰oŊ1olr;|Ŋ bm] vr;1b;v Ő-u-0࢙v ;| -Ѵĺķ ƑƏƐѶĸ _;vvomķ ƑƏƐѶĸ "om]ķ -u-0࢙vķ ş"--ˆ;7u-ķƑƏƐƖĸ"r--hş ;-;m7;uķƑƏƐѶőĺo|;|_-|$1-m -Ѵvo0;-rrѴb;7|ol†Ѵ|bvr;1b;v1oll†mb|b;vķ0†||_;=oul-Ѵbvl-m7 7;=bmb|bomv -u; 7b==;u;m| Ő-u-0࢙v ;| -Ѵĺķ ƑƏƐѶĸ "om] ;| -Ѵĺķ ƑƏƐƖőĺ ;ˆ;u|_;Ѵ;vvķ|_;u;v†Ѵ|vo0|-bm;7=ou|‰oŊvr;1b;v1oll†mb|b;v-u; ˆ-Ѵ†-0Ѵ; =ou 0o|_ |_;ou;|b1-Ѵ -m7 ;lrbub1-Ѵ u;v;-u1_ Ő-v;ķ ƑƏƏƏőĺ uol - |_;ou;|b1-Ѵ r;uvr;1|bˆ;ķ |_; 1ol0bm-|bom o= $ -m7 " mo| omѴ‹ 1o†Ѵ7 -ѴѴo‰ †v |o 7bv;m|-m]Ѵ; |_; uoѴ; rѴ-‹;7 0‹ bm|ubmvb1 ]uo‰|_u-|;v-m71olr;|b|bomv|u;m]|_vbmv_-rbm]1o;Šbv|;m1;-m7 ruboub|‹;==;1|v0†|-Ѵvo1o†Ѵ7o==;u-m;‰r;uvr;1|bˆ;|o†m7;uv|-m7 |_; |oѴ;u-m1; o= ;1oѴo]b1-Ѵ 1oll†mb|b;v |o |_; ;==;1|v o= vbl†Ѵ|-Ŋ m;o†v;Š|;um-Ѵr;u|†u0-|bomvom7b==;u;m|lo7;Ѵr-u-l;|;uvĺ uol -m ;lrbub1-Ѵ r;uvr;1|bˆ;ķ 0;1-†v; |‰oŊvr;1b;v 7‹m-lb1v _-v 0;;m -m71om|bm†;v|ou;ru;v;m||_;lov|=;-vb0Ѵ;;Šr;ubl;m|-Ѵv‹v|;l

2

Ő7Ѵ;uķ -f-u7oķѴ;bm_;vv;Ѵbmhķşu-=|ķƑƏƐƒĸblѴ;uķ"|o†==;uķ-bķ ş -‹=b;Ѵ7ķ ƑƏƐѶĸ -u7bm-†Šķ -u|ķ ş Ѵ;Š-m7;uķ ƑƏƐѶĸ _† ;| -Ѵĺķ ƑƏƐѵĸ;ul-bmķ-‹=b;Ѵ7ķşbѴ0;u|ķƑƏƐѶĸo7o‹ķu-=|ķş;ˆbm;ķ ƑƏƐƓĸu-bm];u;|-ѴĺķƑƏƐƖĸu-=|ķo7o‹ķş;ˆbm;ķƑƏƐƔĸ;ˆbm;ş bѴѴ;!bv-l0;uvķƑƏƏƖĸbķ$-mķ+-m]ķ-ķşb-m]ķƑƏƐѶĸ-‹=b;Ѵ7ş ;ˆbm;ķƑƏƐƏĸou7;1-b;|-ѴĺķƑƏƐƔĸ-u‰-mbķѴ;Š-m7uo†ķ-hѴ;‹ķ -uuoѴѴķş-u7bm-Ѵ;ķƑƏƐƒĸ࣐u;ŒŊ!-lov;|-ѴĺķƑƏƐƖőķ|_bv1ol0bm-Ŋ |bom o= |_;ou;|b1-Ѵ |ooѴv 1-m 0; ;-vbѴ‹ -rrѴb;7 |o ]-bm m;‰ bmvb]_|v -0o†| |_; uo0†v|m;vv o= ;1oѴo]b1-Ѵ 1oll†mb|b;v |o 1_-m]bm] ;mˆbŊ uoml;m|-Ѵ1om7b|bomvĺ

$_; l-m†v1ubr| bv ou]-mbŒ;7 -v =oѴѴo‰vĺ buv|ķ 0†bѴ7bm] †rom |‰oŊ1olr;|bm] vr;1b;v 7‹m-lb1vķ ‰; 0ub;=Ѵ‹ bm|uo7†1; |_; =†m7-Ŋ l;m|-Ѵvo=$-m7"ĺ);v_o‰‰_‹;-1_=u-l;‰ouh-Ѵom;1-mŊ mo|=†ѴѴ‹7bv;m|-m]Ѵ;|_;uoѴ;vrѴ-‹;70‹bm|ubmvb1]uo‰|_u-|;v-m7 1olr;|b|bomv|u;m]|_vĺ$_;mķ‰;v_o‰_o‰|_;l;|ub1v=uol$Ō |_;v|-0bѴbŒbm]-m7;t†-ѴbŒbm]l;1_-mbvlvŌu;Ѵ-|;|o|_;voѴb7-m]Ѵ; o= "ĺ 1_b;ˆbm] |_bv 1ol0bm-|bom o= |ooѴv u;t†bu;v 0o|_ -7ˆ-m1Ŋ bm]"|ovbl†Ѵ|-m;o†vѴ‹ˆ-u‹l†Ѵ|brѴ;r-u-l;|;uvŐ-vbm$ő-m7 u;ˆbvb|bm] $ |o †m|-m]Ѵ; |_; 1om|ub0†|bom o= lo7;Ѵ r-u-l;|;uv Ő-v bm "őĺ lrou|-m|Ѵ‹ķ ‰; v_o‰ |_-| |_; ;t†-ѴbŒbm] l;1_-mbvl Ő0-v;7 om =b|m;vv u-|boő ;Š_b0b|v - h;‹ |u-7;Ŋo== 0;|‰;;m |oѴ;uŊ -m1; |o r;u|†u0-|bomv bm bm|ubmvb1 ]uo‰|_ u-|;v -m7 bm 1olr;|b|bom v|u;m]|_ĺ);v_o‰|_-||_bv|u-7;Ŋo==bvv|uom];u†m7;u1o;Šbv|;m1; |_-m†m7;uruboub|‹;==;1|vĺ;Š|ķ‰;-rrѴ‹o†uv|†7‹|o-m;lrbub1-Ѵ 7-|-v;|o=-mm†-ѴrѴ-m|-vv;l0Ѵ-];vĺ);v_o‰|_-|bm|_;v;;Šr;uŊ bl;m|-Ѵv‹v|;lvķ|_;|oѴ;u-m1;|or;u|†u0-|bomvbmbm|ubmvb1]uo‰|_ u-|;vŐ0†|mo|bm1olr;|b|bomv|u;m]|_vőbvl-ŠblbŒ;7ĺ-v|ķ‰;ruoŊ ˆb7;-7bv1†vvbom-0o†||_;Ѵblb|-|bomv-m7=†|†u;u;v;-u1_-ˆ;m†;v 7;ubˆ;7=uolo†u‰ouhĺ

ƑՊ|Պ$ ) Ŋ  $"  " + "

ƑĺƐՊ|Պ ‹m-lb1v

-m‹ ror†Ѵ-|bom 7‹m-lb1v o= |‰oŊ1olr;|bm] vr;1b;v _-ˆ; 0;;m ruorov;7Ő;ĺ]ĺ-v;ķƐƖƖƖĸ$bѴl-mķƐƖѶƑĸ$†u1_bmķƑƏƏƒőĺu]†-0Ѵ‹ķ |_; vblrѴ;v| 7‹m-lb1v bv |_; 1Ѵ-vvb1 o|h-ŋ(oѴ|;uu- Ő(ő 7‹m-lb1v Ő-v;ķ ƐƖƖƖőĺ $_; =oul†Ѵ-|bom o= ( u;-7v -v Őo|_;u ;t†bˆ-Ѵ;m| r-Ŋ u-l;|;ubŒ-|bomvou=oul-Ѵbvlv1-m0;=o†m7bmrr;m7bŠ"Ɛőĺ

‰_;u;|_;ˆ-ub-0Ѵ;N_iu;ru;v;m|v|_;-0†m7-m1;o=vr;1b;viķ|_;r-Ŋ u-l;|;uvr_i > 0 and αii > Ə1ouu;vrom7|o|_;bm|ubmvb1]uo‰|_u-|;-m7

|_; v;Ѵ=Ŋu;]†Ѵ-|bom Őou bm|u-vr;1b=b1 1olr;|b|bomő o= vr;1b;v iķ u;vr;1Ŋ |bˆ;Ѵ‹ķ-m7α12 > 0 and α21 > Ə-u;|_;1ouu;vrom7bm]bm|;uvr;1b=b11olŊ

r;|b|bomv|u;m]|_vŐ-ĺhĺ-ĺ-0voѴ†|;u;7†1|bomvbmr;u1-rb|-]uo‰|_u-|;őĺ lrou|-m|Ѵ‹ķ7;vrb|;|_;vblrѴb1b|‹o=(7‹m-lb1vķ-ѴѴ|_;l-bm u;v†Ѵ|v_;u;-rrѴ‹|o-l†1_Ѵ-u];u1Ѵ-vvo=|‰oŊ1olr;|bm]vr;1b;v 7‹m-lb1vķ bm1Ѵ†7bm] v-|†u-|bm] 1olr;|b|bom 7‹m-lb1v Őu-†;u ş

-v|bѴѴoŊ_-ˆ;ŒķƑƏƐƐőķ|bl;7bv1u;|;(7‹m-lb1vŐ"--ˆ;7u-ķ!o_uķ ;| -Ѵĺķ ƑƏƐƕőķ 1omv†l;uŊu;vo†u1; 7‹m-lb1v Ő;||;mķ _-lbķ ;ķ ş †h-lbķƑƏƐѶĸ"om];|-ѴĺķƑƏƐƖő-m7-mm†-ѴrѴ-m|7‹m-lb1vŐo7o‹ş ;ˆbm;ķƑƏƐƓĸ-u|ķ$†u1o||;ķş;ˆbm;ķƑƏƐƖőĺo|;|_-||_;v|u;m]|_ o=vr;1b;v1olr;|b|bombm|_;v;7‹m-lb1v1-m-Ѵvo0;;Šru;vv;7bm |;ulvo=momѴbm;-u=†m1|bom-Ѵu;vromv;vŐ;m1bş"--ˆ;7u-ķƑƏƐѶőĺ

ƑĺƑՊ|Պo;Šbv|;m1;

$_;m;1;vv-u‹-m7v†==b1b;m|1om7b|bomv=ou|_;1o;Šbv|;m1;o=|_; |‰o1olr;|bm]vr;1b;v-u;]bˆ;m0‹|_;|‰o=oѴѴo‰bm]bm;t†-Ѵb|b;v Ő"om]ş"--ˆ;7u-ķƑƏƐѶ0ĸ(-m7;ul;;uķƐƖƕƔőĹ

$_; |‰o bm;t†-Ѵb|b;vķα21/α11 < r2/r1 and r2/r1 < α22/α12ķ ]u-m|

|_-|vr;1b;vƐ-m7Ƒ1-ml†|†-ѴѴ‹bmˆ-7;]bˆ;mr₂/r1Ō‰_-|‰;1-ѴѴ

|_; u-|bo o= bm|ubmvb1 ]uo‰|_ u-|;vĺ m - |‰oŊ7bl;mvbom-Ѵ v‹v|;lķ |_bv rovvb0bѴb|‹ ]u-m|v |_-| vr;1b;v 1-m _-ˆ; rovb|bˆ; -0†m7-m1; -| ;t†bѴb0ub†lķˆbŒĺfeasibilityŐ-v;ķƑƏƏƏőĺomv;t†;m|Ѵ‹ķ|_;v;|‰obmŊ ;t†-Ѵb|b;vblrѴ‹|_;|_bu7bm;t†-Ѵb|‹α21/α11 < α22/α12ķ‰_b1_;mv†u;v |_-||_;7‹m-lb1v‰o†Ѵ71omˆ;u];|o|_;;t†bѴb0ub†lv|-u|bm]=uol -m‹bmb|b-Ѵvr;1b;v-0†m7-m1;ķˆbŒĺglobal stabilityĺo|;|_-||_;|_bu7 bm;t†-Ѵb|‹1-m0;7;7†1;7=uol|_;=buv||‰obm;t†-Ѵb|b;vķ0†||_;bmŊ ˆ;uv;bvmo||u†;ĺ;1-†v;|_;v;1om7b|bomv]†-u-m|;;|_;;Šbv|;m1; o=-†mbt†;ķv|-0Ѵ;ķ=;-vb0Ѵ;ķ=bŠ;7robm|ķvr;1b;v1o;Šbv|;m1;bvmo| 7;|;ulbm;70‹|_;ou7;uo=vr;1b;v-uubˆ-Ѵĺ

$u-7b|bom-ѴѴ‹ķ |_;v; bm;t†-Ѵb|b;v _-ˆ; 0;;m ]u-r_b1-ѴѴ‹ bѴѴ†v|u-|;7 om |_; v|-|; Ő-0†m7-m1;ő vr-1; o= |_; v‹v|;l ]bˆ;m 0‹ t†-|bom Ɛ Ő-v;ķ ƑƏƏƏőĺ oѴѴo‰bm] |_bv 1Ѵ-vvb1 u;ru;v;m|-|bomķ b]†u; Ɛ v_o‰v _o‰|_;r-u-l;|;uv_-ˆ;|o0;1ol0bm;7v†1_|_-||_;|‰omomŊ|ubˆb-Ѵ Œ;uoŊ]uo‰|_bvo1Ѵbm;v=-ѴѴbmvb7;|_;1o;Šbv|;m1;-u;-ĺ ou]bˆ;m];m;ub1 ˆ-Ѵ†;vo=K₁ = r1/α11 and K2 = r2/α22Ōhmo‰m-v1-uu‹bm]1-r-1b|b;vķ|_;

bm;t†-Ѵb|‹r₂/r₁ < α₂₂/α₁₂bv;t†bˆ-Ѵ;m||o_-ˆbm]vr;1b;vƐŒ;uoŊ]uo‰|_ bvo1Ѵbm;1uovvbm]|_;N₂-Šbv-0oˆ;vr;1b;vƑŒ;uoŊ]uo‰|_bvo1Ѵbm;ķ-m7 vblbѴ-uѴ‹ =ou |_; bm;t†-Ѵb|‹α21/α11 < r2/r1ĺ $_; ]Ѵo0-Ѵ v|-0bѴb|‹ 1om7bŊ

|bomα21/α11 < α22/α12 bv ;t†bˆ-Ѵ;m| |o _-ˆbm] |_; vѴor; o= vr;1b;v Ɛ

Œ;uoŊ]uo‰|_ bvo1Ѵbm; v|;;r;u |_-m |_; om; o= vr;1b;v Ƒ vo |_-| |_;‹ 1uovv‰b|_bm|_;1o;Šbv|;m1;-u;-Ő-v;ķƑƏƏƏőĺo|;|_-||_;0ou7;uv om |_; -Š;v o= b]†u; Ɛ Ő-v ‰;ѴѴ -v |_; u;]bom ‰_;u; |_; |‰o Œ;uoŊ ]uo‰|_bvo1Ѵbm;v‰o†Ѵ71uovvo†|vb7;|_;rovb|bˆ;-0†m7-m1;vt†-7Ŋ u-m|ő1ouu;vrom7|o|_;1-v;o=†m=;-vb0Ѵ;;t†bѴb0ub-ķ‰_;u;om;vr;1b;v o†|Ŋ1olr;|;v|_;o|_;uvr;1b;vŌ-Ѵvohmo‰m-v0ou7;u;t†bѴb0ub-ĺ†u; m;†|u-Ѵb|‹Ѵb;vbm|_;bm|;uv;1|bom0;|‰;;m|_;v|-0bѴb|‹ŋbmv|-0bѴb|‹0ouŊ 7;u-m7|_;=b|m;vv;t†bˆ-Ѵ;m1;Ѵbm;Ő"om];|-ѴĺķƑƏƐƖőĺ

ƑĺƒՊ|Պuboub|‹;==;1|v

b]†u; Ɛ -Ѵvo v_o‰v _o‰ |_; r-u-l;|;uv v_o†Ѵ7 0; 1ol0bm;7 v†1_ |_-| |_; 7‹m-lb1v ;Š_b0b| ruboub|‹ ;==;1|v Ő-v;ķ ƑƏƏƏőĺ !;1-ѴѴ |_-| ŐƐő ⎧ ⎪ ⎨ ⎪ ⎩ dN1 dt = N1(r1−𝛼11N1−𝛼12N2) dN2 dt = N2(r2−𝛼21N1−𝛼22N2), ŐƑő 𝛼21 𝛼11< r2 r1< 𝛼22 𝛼12 . 3

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