Models for Conditional Probability Tables in Educational

!!#"%$
&'!%()*+,-
. //&/102
3465748:9<;>=@?/ACBEDGF&4HJILKCMN9<9<=OkCBOlnPQmp4/o!RSqfrtMNs ?OuVvpTSqI<?/wdUVxOB1yZz{H7rts 46vj|:WSMN}N?#y!XZ~tYONs^[\o
TyVB^€j]-63~ts vp4Oo
Ry
4rtuV_`vS€nI<UZ‚9<Mbƒ adcB/F&4CW46WdXZMNI<?#KCMb[feOB1H741gihj?
†„ …-‡Vˆn‰jŠ‹@ˆ
srt^klns uVŒny!v—@vbrty!s‘L~Ž‘LuVr’“~zrts q>v”jyJrtyZyZlnzŽz{•Nmprso!w qfs^rtzrty!s vj2uVvpy!yZqqlnw1vpyZqVl—l“ztzŽrt˜,yZu7zt”jzŽs^jo~t”™y!ufvbNpr-s^lnqfo!rŽy:qrtvy!q7~tvpuzŽ‘Ez:uVrtw y!mnuv –‘
rtœ”jqubvpzŽyJo
yVzŽ1•NxGs w ^”jzyGj~tuny
rtln”jmpuno
ly:lnš@yZy
ztrŽo
rt~ty!s ~š@yZy
lŒn@”jyZy!o›~trty,yZo
l>uV@y!šj~Žs ‘LvjuVyZ~Žz–
žrtmps uVlnvp|Vqy!wSjy!~tvbuVršpzŸqqšjš@s w uVs r{mn’rCrrtq”jšjy-w yz{rt~t LyVmp o›|prt mj€@~to
y&uVvuž‘dmjrtvp”jo›yQrts o
VuVyVvp€plnuVs ~–
o
¨ZuV©Vy
ªVrt© ”j@¡puny!rtljvpu&zSztjqf‘LuVrt~tuVun~/~tlnp’jmpq¡o
~ŽyCrt˜,s^q&qs rtwbo
ӣo
uV~tvp¢¤yZrtlnlny!s s rt¦r1s uVzto
vp¥,uVqyZ~twszŽjvj@~t|uVuVvp §šp}nzŽqyqšjsxGw ys ”jr{ž ’&sy!œuVr~tqfqj’ – €
šj|VuVw y~ts rtuV”j~q7jxG~ts uV”j~yJlnz{rts^z{~trtmp~to›s šjrtmjmn~rtqs uVw v“ž mp‘LlnuV|V~y!qwy!yZvbqr~tzvjss vjvp|lnmpqo
w y –
qzŽ•Njs w ~tCu fž qyZ~to›s^rtqs uVšjv«w yZziu‘,uVvbyZrtqVu7o”>qo
zŽuVs vnvj¬p|V|Vw ymj~w^qfqfrtrty!s uVvbv“r~tuyZ‘&zŽp@quV~tvpy!zŽvby
r–
jq~tjuV~t@uVy!špvpqzŽšjs r{s ’w s r{­j’œ‘LuVxG~,”jyZs^zQqVos^”zrto
”jy!wy!dv“s vJmpzŽrtyZ”jlyQrtruqšjo!w qyVw^ o
mjw^qfrty
® ¯b° ˆn‰j±,²³‹@ˆj´{± °
¢µpvq~Žqr¶vuuV‘vj|VrtuV”js y·vj|˜ŸyZuVln~tmp•)o!qf|VrtuNs uVyZvpz7qs wnvbqVrtztu™zŽyZšjztzŽ~ts vjy!|Vvbs vjr/|™j~tvjuVy!|V˜¸~qrqV€fzŽq-•nz·w^q~t L|VuVy~
~t¹o
yZy!s rtzŽs y!VmjœyZw rl7zzJ¹ s quV~tpy~ qV¹mpo›jrzŽyZ~tuVl†uVv7šj‘Lw uVrty!”jœ~yzln¹y
yZ¡Œjo
qs^szŽvbs uVrts u“vpvjzœy!rtyV”jrt€d”pyrtqf”jqVryztzŽ”pjyZq\zt~tVzŽuVy7šjwy!q«y!vbºrZ”j£s s^|Vzi”—¢¤‘-y
Œj@rtqVyZy!z{o›~Žr––
y!@~tubšpzŽqfmjrt~tyZyVlJ-šN»’w^rtq”j~ty|Vyivjpy!yZqlJ~Žr-rtuuœ‘~trty
”jrtsy~tyQ˜ŸruVqV~tzŽ•J•nz,s vqf‘Ejrt~ty!un~lnqmpo
w ss vj|Js rtyZqœlrqVy
zŽŒN• –
‘Ls^zœuV~io!quVw^@o
y!mj~w^qfqfrtrts s uVvjvp|7qwrt”jmpy†zŽyœ½Ž˜Ÿs^zy!sz{|Vr”bqfrtrs^zz{rtus^‘-o!qy!w N’7s^lno!y!qvpw o
s šjy ¹~qfrtrts”pvjqf|rs ˜,rZ¼/s w rt,”pš@qfyr
mp˜,zŽs^yZzŽ”¶l£rtrtuumj#yZqVljzŽqfmjrt~ty¶yVš@y!¢µw v«s y
‘<qz¾Gqš@q\’VuVyZmnzŽrJs^qrtv¶”jy¶qjw^jqf~trtuby!vbqVro”qrtšjus w s rtrtyZs yZz{z:rts vj˜Ÿ|py €
rtq”jšjyZs wzŽs y-rts ˜ŸyZzy!us |V‘@”buVršnzŸrqq~ts vjy-s lnvjy
|irty!f~tq~ts suVvjmpyZz/luVšNšp’zŽy!rt~t”jfyQqšjo
w uVyŸvp‘LlnyZsqfrtrts mjuV~tvpyZqz1w@uj‘@~trtuV”jšny –
zŽo
uVuVwvnmn¬prt|Vs uVmjvN~¿£qfrtss§uV yVv: €\uz{‘1rqfw^qfrtyZrty!zdvbur&‘nuVqšpšjzŽs wy!s ~tr{’fqfšjqw y1~ts^fqqšj~tw s^yZqz!šj w yZzµ¿£|Vs Vy!vrt”jy
À˜ŸuVšn~tr•#qÂs vjs Á¶vj|œy7vNo
mjuVmjw^š@l†y!~w z,yZq‘LuV~tv†~,rtrt”j”jyZy!zŽÃyir‘Lq~tšjuVw ÃyZz,js^z&~ty
s vrtyZ|Vz{rJy!vjljy!qf~rqqjwS€G”pšjqmn~l r
Ù^ÄEÚÅ/Æ!Ø ÅCǵÇ{ØnÈÛVɵÊnÔ!ÆZËfËNюÔQÌVÍ Ü1ËbÎÔ
Ç{ÏCÝNÔ
ÐVǎÑ{ÔÒbÞjÆ!ÛǛÐbÓ#ÖiǎÔ!ÖiÕ ÖiÈtÆZÇ1ËNÍ ËfÌNÑ{ןÈtÇ{ÈtːÑ{ÉÔ
Ø Æ!џÇ{ÎßOà6ÛnØ
rto
”juVyœvn¬pvj|Vy!mjyZ~l7qfrt‘LsuVuV~vqu‘zŽmnpáq~to
y!s vby!vbrz&rtw ’7œqw^q•V~tyZ|Vz,ys r-ztqy
Œn@jy!w yœvpzŽzŽs sVâ!yiyrt‘Lu:uV~i|Vy
y!rVy!~t~ty
’ –
wqs^vpqšjl†w yQzŽs fqsw w^mjqyZ~zŸmpzŽuns lnvjy!|w^zœqmpjzŽmjy~ty!z{w rt’œ~tmpy!o›rtmjj~s ~tqs^wo!qž mpw#ln|Vuny!lny!y!w§6vbr‚&zuVqs^zŽš@’buV–¤mnuVr~
rtš@”jy!yJ~-uo
uV‘Cvp~tlnyZãbs rtmjs uVs ~tvpyZqlwŸpjq~t~uVqšpqšjy
rts w y!s r{~’7z!¼#räqšjs^zŽw yw y!Nrtu’>~tå
yZælnçfmpè o
éy ¨Zrt”j©Vy:©V© vN¡,mjqn––
jq¶w ’7w s rt”js rts^zyZl†qjvNjmj~tubqVš@oy!”S~u‘-ê&juf˜Ÿ~tuVy!špVqy!šj~Z€Os w sy!rtVs yZy!zv«s^y!zw s^lno
ss rtás vjo
|mjw jrZ™~ts uVÁ£~zQ”j‘Ly!uVv ~
qVo
uVztzŽvps ln|Vsvjrtss vjuV|«vpqo
wGuVjvp~tlnuVs šprts quVšjvps qw sw,r{’¶j~truVqšpšjqw yZšjz!s w€6s r{˜Ÿ’«yJrq˜ŸšjuVw mjyZzœw^l>uVw~œs •Vjy:~tsrtuVu7~zrq‘L•VuVy~
qVqjlnfjqw s^vbo!rqfqrt|Vs uVyvpuz,‘GmprtzŽ”js vjy:|˜ŸrtyZ”jqyw rtmj”“vjsuf‘,qy
~ts^Œnqf@rty!yi~t¢¤s y!rty!vp'o
y:¥,q\fyZzŽq@s w^uVqvpšjzŽw yyxG‘L~t”juVy
–
uVšp~tqV’—zŽyZlë L¢{¥1uVx&vì¡z{rt~tunmplno›y!rtmjw§†~tyZxOl`u7w^qfrtrt”jy!s^vbzr«y!vpo
lw^qVzt˜Ÿz7y:rqun•Vlnyy!w^z·qv· <íjquVj~tjœ~tubqqVvjovS” €
so
¨ZvjuV©V|Jwîb^qfï ¢{rt¡›¥1y!€Cxë~qqvpw#plsqvn~‘Ly
quVŒN~trtœy!y
vprtqfy!l†rt~s z&uVq“vs v¾Gqrtq\š@y!’VuV~tyZmnœzŽr&s^zqs v«rtuy!‘Cœ‘L~y
qzŒn@ <äy!y!~Ž˜Ÿs^r zŽuVwž ~ty!mp•¶Nln’V|V‘L€@uV}N~œy!”jvby!riy!un”plnqqvpy!vSwl – €
qvpl:Á£s vj|Vy!~zŽ•N’V€ ¨Z©VîV𠡛
ñ 4 ñ hj5:UZ[fUZhnMNò1UZUZó/;>I<ôVMNhj?#9,X ;>=SA/MN96=@õ&MNA/Y/ôVhnXZI<=@?/hj9
íjqšjuVw~CyZz{zrtmplnyZy!qVvbzŽr,mjöV~t€Vs vjw y
|†rGrt÷S”pøtqfù úfr“û!ü!z{ü!rtü
mpûln÷Sy!øtvbù ý—rZþ z7š@y•Nvjqufo
˜,uVw w yZyZlno›|VrtyVs uV€vzŽ•Nus‘dw ^fzq~tuVs ~–
rtjqs šj~tus w ¬@yVs rt€Vo
s s˜ŸyZy!zQvpyGo
s ~tv«’y!jzŽšN~tuV’†yZzŽy!q«yœvbr1lnjuVuV~tuVœmjšp~qq•Ns šjv¶vjs ufw us ˜,r{‘Ÿ’·w syZvblnlnrt|Vs^y!z{yG~trtyZ~tqz{s š@šjrZœuVmnmnrt»Ÿsr1uVrrtvS”pqëqfvNrC’xGz{”jrt@mpyuVlns vbjy!rvb~ts rZuVs þv z~
rtlnqs ~ts^uVz{yv«rt~ts svbušjrt‘Gmny!rtrt~t”jsyZuVz{yZv·rtzŽyZyl“6zŽ~Z•Ns ¤v·s WOw ^ø
lnz¡~s q\v“s^˜,zrts mpvj”jzŽ|ympq@s vnw uV‘L’«jy!~tmjšpy!w^vpqfqVrto
zŽsyZyZuVzl>v«‘LuV~tuv>uV‘,srtvb”jrt6yy!~Z~tln ¤yZWOs^z{z{rZørtJÿ~tJøs šjÁ¶
mn¡›y – €
˜,zŽy!”j~tfy!~tqfyrts uVJøvpz1œqVlny,øt‘Lù~tú\uVû!`ü!ü!rtü
”jû yøtz{rtù mpln
y!vbs^z-rZþ rtz”j~tyœyZzŽo
@uVuVw vpyZzŽo›yZrtzs uVuVv¶vœuqi‘Ÿo
uVuVšnw ––
wqyZ~to›yrts juVmjv·~ty!uw ‘Q’Jä2w^qfrtry!qVvbzŽrZ•n¼@z!rt·”jyxGuV”jšpyzŽy!z{~trtfmpqflnrty!s uVvbvprœzqunvplnly!w,j~tfs quV~t~-s^qqVšjztzŽw yZmjzœWOnø–
rtqs vpuVlvpz&rt”jqy-š@uVz{rtmnmpr,lnrty!”jvbyrC~ty!w^unqflnrty!s uVw@vpfzŽq”j~tss^Jqšjš@w yZy
z6r{˜Ÿqy!~ty!y,vJ~tyZrtãb”jmjys ~tuVyZšplzŽy!‘LuV~tf~6qfs rtvns ‘LuVy!vp~Žz–
‘Ly!~vpqo
yV/y!˜Ÿ»&uVw ~t•#uV vplqvpliäs^zŽw y!N’ ¨Z©V©V© ¡dlnyZzto
~ts š@yrt”js^zS|Vy!vjy!~qw
w^xGqqfšj”jrtw y!yyZvbz-o!rqV÷So
zŽøtw^yù qVzt˜Ÿzqy~tyqVunljlnlnlns^zty!~to
w§yZ~t“zty
zrtê&yVs v,y!~t¢µrtyJv”jqs^rtz-w ”jCps^rtz-q”j@o!yJqVy!~-zŽz{yVrts^mp€pz&ln˜Ÿrty!”jyvbyro!qvmjun~tw lnrty!s jy!fwŸ~tqyZ~tfzŽs^qy!qf~tvbrts yr–
rtf”jqy!w mjvyZlqVz~tyZ­zŽ@s vpuVo
vp~tzŽyZyZqVz6zŽsyZv:z!€/qjv:~tuVuV~šplnqy!šj~ts w w ’s rtsœyZziqvjs vpvjo
y!~t~ZyZ1qV»)zŽyzŽ‘Ls uVvj~|Vw ”jys f|Vq”jw y!mj~Žy –
uzŽs ‘jšj­-w yizŽ@~tyZyZzŽo
@s ¬puVyZvpzSzŽyZrt”jz!yC‘Lmjw no
uVvplns rts uVvpqwNlns^z{rt~ts šjmnrts uVvu‘@qw b@ubz{–
Category Response Probabilities
1
0.8
0.6
0.4
0.2
0
Probability
rtrt”j”jyyœlns^z{unrtln~ty!s šjw^zimnrtlns y!uVVvy!w6uV~Z@ ¤yZWOl7ø
¡Ÿš@˜,y!w sufrt˜i”7€Oqœs r¾Gs^q\zQ’VmpyZzŽzŽs^y
q‘Lmjv:wvjrty
ur{˜ŸuVuV~ln~t•#y!~-Ÿíjrt”juVy~
z{rqfrtyZzGs vuV~lny!~Gu‘1s vpo
~tyZqVzŽs vj|w y!Vy!wdu‘1j~tu¬@o
s y!vpo
’V
rtrt¢¤‘O”j”py!qf˜ŸuVry~trty!•N”j vjyy!˜—rtuVu“šp6zŽo!y!~Zq~t w^fJøo
qfmjrtw^sÿqfuVWOrtvpø›yJ¡6zi6˜Ÿ‘L~t~ZyuV ¤WO¸uVøšNÿNlnJøs s uV#›mp¡›y!zŽ~tw y!’vbro
zŽuVmprmjqqVw^wzŽl•n’“zqj˜Ÿqjy~tw yJ’œqVo
zt¾GuVzŽmjq\vp’VlnyZs yz–
rtqs šjuVw vpyZqzw ’ <zŽy!syvpln»&y!w@y!vpuVlnvpy!l`vbr«qvp|Vl`s Vy!ävës^zŽrtw y!”jNy†’V€ z{rt¨Zmp©Vln©Vy!© vbr“‘LuV~¶unq—lny!lnws^ztfo
qmp~tz{s ––
zށ6s uV~Z v@¡›1øtù Á£ÿ ”pWOqfø
rŸ¡›,˜Ÿ¢µy&vvjy!yZublœz{r-s^zŸo!qqVzŽo
yZuVz!w € yZo›rtøts ù uV`vœs^uz-‘Ÿo
åuVvplnVså rt
s uVvpå qw ’:Vs å
vnè –
lnqvpy!@lœy!qvpw lnpy!šjvbmnrrGuq‘#qzŽmjw NšpuVzŽšpy
rCzŽy!u~t‘Sfqfz{rtrtmps uVlnvy!vbfrŽq–¤~ts^qunšjlnw yZy!zSw@‘Lf~tquV~tës^qšjuwrtyZ”jz!y!/~/xGrqV”NzŽmp•nz!z €
6o!q~Zw /WOøtøtù ùÂÿ WOrt”jø
¡yQë‘LuNu6rt~Zj ~ts vbøtr,ù u‘1ÿ WOy!øtNù Qs^ln¡›y!€dvp˜,o
yQ”jy!~tyunlnWOy!øtwù ¶ë WOø\-Á¶y
¢µqvo
rtuV”jvpyln¾Gs rtsq\uV’VvpyZqzŽwds^qjv~tuVvjšpy
r{q˜ŸšjuVs w ~ts r{•’œo!rqVqzŽšjyVw€yVrt”j¢¤y,‘1y!˜ŸNyQs^ln˜,y!vps^zŽo
”Jy,rtuuny!lnw y!s^o
w s rqs^v z
mjÿ WOvpøtz{ù rt~tmpÿ o›rtmjs ~~toyZ”jlw y
jr~tslnuVs^~/z{rt‘L~tuVs ~Cšjmn6rt~Zs uVvpz!øtù€/˜,ÿ WO”jøty!ù~tQy7¡›€Vÿ WO˜Ÿøty,ù ÿdmps^zQz{rCrt”jzŽ@y:yZzŽo
ss â!‘L’y
uo!q‘vJrt”jš@yyz{qœrqfljrtqymjvbzŽprtsqVvjo
|yruqV‘&zŽ•#rt”jyíjuV‘LuN~&us vprtjz{r~tqs vbvprœo
yVu€N‘Qrtx/”jy!qV~tzŽyi• q¶~tyi†qš@xGuV”jmns^rz
jœqw yq”NvNmjln’vps^lnzt˜,o
~tmpsyZrtlzt”:zŽyZuVzŽl7sšpâ!zŽyš@y!y!~t¨Zwfî ufq˜i‘LšjuNw€Ouyrtfjubq~tz{~ts vbris^qr˜,šjzµ¿£ws yZrt”“z&ufVs rtvy!”j~1~trt¬py!”jyVyyG@¾Ÿrtub”js ztuVuVzŽœsmpšjztqVw qztyvpz&fly
qŒjsw vpmjqlnyZz!s –– €
No!qVs^lnzŽympquwC‘j¢{~t¥1uVšpx qšj˜Ÿs yw s rt”ps yZq\zVyqw rtq«uV|Vw uVy
rtvj”j|«y!~Z”j:s^z{¢µrtv“uV~trt’·”jy:u‘izŽs šjmjjs w^w lny:s vjzŽ|@yZy!o
Ns^qs –w
y
lnqŒny!@vpšjy!o
s y~trts s y!uVvpmpuno
z,ylnz{y!rtrtw^~tuz!mp,o›‘LxGuVrtmj~t”j~tyyZmjzŸ|Vw^ub‘LqfuVqrt~&y¶wdu6z{‘1rt~Z~trt mp”jo›s^øtz&rtù mjp~tqÿyZWO@l—øty!ù ~Qs^¡›unz& lnlny!~w^q\z:˜)‘LuVuV~Jvrt”puVqf~tyr
ñ 4 _`=SA/MN9<Uõ¤=p[ò1hn[\XZI<hj9,ô[fMNA/ILXœUZôV=p[fI<?/e
uVxGxGmp”j”jzœy:y&zŽ~t•Ny!sw^ubwqfGz{rtrœsfuVqo
vp~tuVzŽs^q”jšjs w yVuVš@€Cv>y
­r{øZ¢{˜Ÿ¥1€Gy!x qy!vvpo!lrtqV”jzŽšjy&y:s vpuV@qšpub~tzŽzŽ’«y!s ~trf~tzyZqfzŽq7rt@s uVuVzŽvs vpvjzŽq|VyJvpw yJlfqo
rt~tuV”js^vbyqrtšjzŽs vNw•NyZmns z!w – 
‘Lfs vpuVq~Co
~tw s^yZmpqãblnšjmpsw vjyqf|rts^s zvjrt”j|q“y,œ}nw uVq»|VvNxQs^’z{€Zrt˜Ÿs^rtoJ”jy!yw ~tpy!Q•N|Vvj¥&~tyZufk&zt˜,zŽ€\svquVvpvSo
uVl—w x y!xG|VÀ ”jy,kCs^zœy!í vb6rt~unq6qlnvpy!o
w&~ty&s s^uVy
zœmpŒjzOqmpœzŽpyZqfz!l – €
~pqq~qy
rty!y
~trts y!âZ~Gqfrtw suVuV|Vvps^z{zirts^qo~ty" !‘L# uVmj/vp¡Cl“s unv“lnrty!”jw§€ny‘LuVw s~,rty!y
~Œjqfqrtmj~tjyVw JyV€nxGs^z ”jyœr{˜Ÿu
w uV|Vs %r $§6~Z øtù ÿ ­ø›'¡ & )(% L­+ø *-,.-¡›ü
u}n‘Gqunrtln”jyy!y:ž w-s œuVrtu†~qjlnþ y!qz/~tv—|VyZ~l“uVqVšplnfzŽyZqy!lw ~tmjf~tyZyZqz0zŽšj@/2w yuV14vpzŽ36yCøtù57 57un58lnrt39”py!wSqf/;r ¨Z:o!©VqªVv—© Á¶¡dry
yJqŒN•Vrtlny7y!y
vp¬puVljvjv—z/yrtuV”j‘LvjuVs^yz~
< ¨ û!ü!ü!ü
>û = ˜Ÿyilny
¬pvj@y ?
6~Z øtù BAC/Djÿ ­ø›¡ FE D D L­ø
¡ £w uV|Vs 7r G ú $ (% L­Hø *-,.ù Df ¡ ¨ & ¡ ü
xGo!q”jw^o
ymjo!w^qfqfrtrtyZy!li|VuV‘L~t~t’¶uVëj~trtuV”jšpy&qlnšjs s#w s y!rt~ts yZy!zvpo
6yZz/~Z u‘pøtrtù”j y&o
6mj/mjDjw^ÿ qf­rtø
s¡VyŸo!qjv~tuVš@šny –
qzŽ@šjuVs w vps rtzŽs yŸyZz1o!qf|Vrts Vy!|Vy!vuV~tšN’’jyZ~tãbuVmpšpqfqrtšjs s uVw svprtzGs yZ zS¨ ‘L¡›uV1~1í/q,s |Vrt”jmj~t~ty!y y
¨–µo!s qfw rtmpy!z{|VrtuV~~tqf’&rtyZrz/qVzŽ~t•#y
– €
˜,fqs wrtmjI” yZz,(% u‘ ­j€j¨ rt€ ”j,.yw ù ufú ˜ŸByZz{J r,¨w y!€NVqy!vpwOIl u‘1,.~tyZù zŽú @KuVvp* zŽyi¨ 1s^z,íjuV~ŸubVz{r&y!~tw ’s •Vwy!ufw ’V˜ €
-4
-2
p1
p2
p3
0
2
4
Theta
í/s |Vmj~ty ¨ ?6»Â|V~qVlnyZlN–¤~tyZzŽ@uVvpzŽy¢{¥1x—unlny!w§
L MONQPBRTS ‰jV± U P ‹@ˆj´{± 6
° WXP ˆ N ±,²
Á¶s v>y-rt”jq~tyy&o!s qVvbzŽrty:y!~t˜,yZz{”jrty!yZ~tlys vœ6~Z¬p ¤vpWOlnø
s ¡vj|s^zq7unln¾Gy!q\w^’Vz6yZ‘LzŽuVs^~Ÿqv«6~Zvj y
r{˜Ÿøtù uV~tÿ•“WOøtqù ivpl ¡
‘L‘LuVuVwY~øtù uf(%˜,'ss^vjziq|“qvpv“lnl«y!uVNK ~s^ln o
y!yV~t· yZlí/Zsln,.~s^z{ztrœo
ù úZ~t˜Ÿû!y
rtü!yyü!ü!jf[û s^q,.o~t•>s^qù :q7šj
bw ¬jyV«ŒnyZxGÁ¶l·”jyœzŽy!y
vy!rœ˜ŸujyJ‘w uffln’qy
w ¬prtmj”jvjyZyyz
rjqœqw ’¶œšjw qyZ}nz!jq js vjy ž |s œ‘Lmjqjvpþ zQo›rt|Vs uV~qVvOln\1yZl ¤WO~tøtyZù QzŽ@¡ uV^vpzŽy­] øtù un&lnÁ¶y!w1yrtuJo!q¬pvw vjuVufmn˜ërQrtq”jny –
rtÁ¶@”jy!yy~Žrzj|bq~tœuVs v«šjq\w ’™r{y!˜Ÿš@u“>yqVí/lno
suVf~qz{rZvb‘L€6ruVq~Žs v|VrqyZšjzrt”jw ˜,y«yJs rtln”yZmjztrto
w rt”j~ts s s^fšjzqs ~tvjrts^~|·qfqrtvprty”jz{‘Lo!y«uVqV~tzŽ‘Lœmjy:vpqfuVrto›mjsrtuV~s uVv>vpy
ŒNuq–‘w
‘LzŽuV@~tyZ¦o
s ‘L’N‘LuVs vj~_|7\Zq `o
5 uV¡:vpy!lnVs rty!sv™uVvps q‘wCrtj”j~ty!uV’—špqqšj~ty7s w s r{mj’vpo
ruVqšjw ‘Ly¶uV~Ž LryVq šj|pw y¶€Q`½ ˜,a6s uVrt”m
rt”puV”j~,q\yVjyJ~tjun~trto
uVu“yZšjln•Nw y!mjvj ~tuf0y ˜s b ‘,”j¹ ’Vuf¡›uV˜ m«rto!u>qv>lnu«o!q»~t~t€6’šjuVmnmnrrrty!”js rty!”jv†y!~’VuVjm†~tuno!o
qyZv†lnmjzŽ~tuVyw V¾ y
rtxG}N”pyZ”Nqfo
mpr/uVz!vps^€bzSldrt‘<€1”jqy!˜Ÿ’œy:s w ˜,s^”pqs q\~Sw @VrtyœuuVrty
~Œn~tqy-@vpy!o
z{~ŽuV‘LruVzO~t‘LsvuV~ŽyZyZrl7lnqmpšjrto!”jw yqfy:rt˜,s juVs ~trtvpuV”:qšjwVy!w y!w s^ o
yZs qVrrtqfzŽu7mjrts ~tuVq7y!vztjo!y!~tqvbuwrZy – 
o
zŽy
yZrztzšN’uVv«z{rrtq”jvps^zljqzt~o!lnqs w â!yVs ¶vj|xGrt”j”jyyztlno!s^qz{rtw y~ts šjumn‘rt¢{s ¥1uVvxu‘un­jln€#y!qw^vpzls^zs vu‘Ertrt”jy!s^v z
˜,”py
rtqf~trGs^oCyZqVq,zŽf’q‘Lw uVmj~Ÿy6rtu”j‘ny-– ¨ y
Œj‘LuVq~ ,/s vjs vpy!lnyZs^z!o!%€ qfcrtyZqzOr{q’Nvjs s^rto!y!q)w@s rtrt”py!qfr/€ns^qzOvpzŽdluV* y
¨ –
qo!qzŽw uV’:~y!q˜,vj”p|Vqfyr‘L~tlnuVs áo
qmjš@w r&uVmns rtry! ð ¼jrt‘Lu mj~Žð rt6”jÁ£y!~Z€”j(y!vpqrt”j~qyiy
Œny
rt@y!y!~~ŽzCrr{zt’Nq\j’ns z–
wrt^zŽqfuœ”jrty-sjuVy
~tvSŒnu€N¬@@uVo
yZ~6so›y!rrtvpz,”po
qfq’VrGvJ€n~t˜Ÿs yZrtyQzŽy!@ ”puVq\vprtVuzŽyiyZš@zCqyQ˜,|VyZsuNwqVun@zŽl:š@’ys^‘LlnuV‘<qyZ~Ÿqs ~trtw”ju’œyQ‘1z{˜,s rtvb~t”prtuVqfy!vjvpr,|Vlnrtw yZ’”jl:0y ~ty!@(:w^uVqfqjrtvpyZmnll –
yrt!,Qs^Nqps^w@lnquVy!~vpjqso
vjyy
s uVrty!vp~unz6z,lns vœ˜,y!w^srtzœw ”j/˜,yš@s ‘LyVrtuV”†~tì¢¤j‘6~t˜Ÿuy
‘SrtyyZw sqz{vjr:~t|Vyljmjjqfs^z{w^rrtqq“s^vjo&vj˜Ÿps yvjq|~o!qqrtv†uy
~trty!y
y!w ¬ps^~o
z&vjs ry LyVsrt vj|p”js y – €
½Ž”pq~l ¹ uV~Q½ŽyZqVzŽ’ ¹ ¡@rt”pqfrq~tyŸqVztzŽs |VvjyZlQrtu-uVvjyŸu‘@q&vNmjš@y!~
u‘1vNmjy!~ts^o!qw#j~ts uV~zŸj~tyZlny
¬pvjyZlJšN’pzŽ’no”juVy
rt~ts^o
s^qvpz!
Á¶mjy7w rtlns^lnyZszto
~ty!s š@vpyzŽs uVrtvp”jqs^z:wbo!zŽqVy
zŽrtyZmjzd†š@y!‘LuVw uf~˜irt€Z”jrty”jy!uVvvjyzŽ”jlnuf˜¶s ”jy!ufvp˜¶zŽs uVrtvp”jyŸqwztqqvpl y
sqvpjlnjy!~t@uby!qVvpoln”y!o!vbqr&vuVšpqw^zŽzŽy!uœ~tfš@qfyrts mpuVvpzŽyZz!lJ rtu:~ty!w^qfŒ:rt”jyqVztzŽmjnrts uVvu‘
d4 ñ õ¤=SaS=pI<X!A/ò/MN[f?/I<?#ôVMXZU ;>=SA/MN9<U œILXZó†Y/?/ILajhn[fI<hnXZM
Á£o!qv”jy!š@v)y&WOqvNøtù’i  uVvjufrt÷SuVøtvjù s^oC
b€Ÿ‘Lmjrtvp”jo›y7rts uVjv~tu už ‘dyZo›÷Srtøts uVù #v‘L»mjztvpzŽo›mjrts uVs v vj|-@rt”p` qf5 r¡
rtmp”jzŽyyGq&w y!wVs vjy!w^yZzGqu~/‘6‘Lmj÷Svpøto›ù Jrts uVqv~tyiuV~tvuVrtmj”j|VyG”jws ’œvplnyZy
ãbŒdmp€ q@w ’J zŽ
pqVo
yZlJ¤¡ ˜Ÿyio
uVmj7w^* l
vj uGœxGqfrŽ”jrts^y!z,~&”junufln˜—y!wOœ|Vqs vNVyZ’:zGz{mprqfz rtž yZmpzGz{r&u‘6r{˜Ÿ÷Søtuœù :pquV~~ qøty
ù rtÂy!~rtzC”jrty!u~tyiy!wqs^~to
yVs r 
xGzŽ@”jyZyo
s s¬@vbortmjrtsurts uVzŽuVv7w Ns^szvjrt|J”px/qf_r qVzŽ­] d• øtù 춝is^zxGrt”j”jyy‘Lz{mjrtmpvplno›rty!s vbuVrZv þ z-@j~t` u5 ¬@¡o
s^s zy!vprt”jo
’y
j~q~tu ž y
yZrto›y!rt~s uVv7 u‘,s^zi÷S~tøty!ù w^qfuVrtyZvblrtuJrturt”prtqf”jryzŽq\pVqVy!o
~yVq|VyxG”jlnyœs áo
o
uVmjvpw z{r{r’7qvburi‘Ÿrtp”jqfy –
s˜,rty!”js^o”«€Nq~tvpyZlzŽ@rtuV”jvpy&zŽzŽyw uVj@~ty uVšp—qšjlns w y!s rt@s y!yZvpzljlnzs^ztuVo
v~ts rt”jsyvpzŽqfy!rtvpy:zŽqs rts NuVs r{vj’|˜,w y!s rtb” –
y!jw^~tzuVšpuq‘-šj÷Ss wøts ùrtVs ¿†yZzQrt‘L”puVqf~rw y!s^z!V€1y!w^rtz”jyu‘ln÷Ss #øtùy!“~ty!qvpvpo
l“y:s”jv«y!vprto
”jyœyrto
”juVy:vpln˜Ÿs y!rtss uV|Vvp”brqz w
u‘1y!Ns^lny!vpo
y-‘LuV~Grt”jyQrqVzŽ•#
x/q“qršjqVw zŽy •·¨ ˜,s|Vrts ”£VyZrtz¶”j~to
y!uVyvplnuVs ~rtlns uVy!vp~tyZql·w~t@yZubzŽzt@zŽuVs šjvpw zŽyyuVjmn~truVo
špuVqšjyZs wz!s €&rts yZqzvpl£‘LuVq ~
szŽqrts vpy!vjl |Vw y¶@pzŽq•N~ s
qw Qfy
qrty!~t§~s^q¡zšjmpw y7zŽyZ˜,l)¨s rtY‘L”™uVJ6~“rt”jí/!n~ts y!|Vy¶mj~tuVxGy ~”pln¨ qfy!r)~tqyZ~tl£s^yz!€“z{qrqf|brt”jrtqyZys z!vë z{mprxGqfzŽyZrt”jyZldyz €
qvp
l d* û¨ ~t yZ"zŽ!#@OyZû%o›$&rts V'
y!$ w ’V
: q~tyœqj@yZl¶rtu­fqw mjyZziu‘Ÿ– ¨ €Vcj€
d4 aSI<A/MN?/ôVM;>=SA/MN9<U œILXZó†;¶Y/9LXZILajhn[fI<hnXZM
õ¤=S=pX!ò/[fI<?#XZU
‚&z{rtuf~tmp˜)o›r,zŽmjrtj”j@yiubjzŽ~tyQu rtž ”pyZo›qfrtrQs uVWOvøtù‘L mjvp o›rtfs uV÷Svøtù qV
z(Zû!ü!ü!ü!û÷Søtù ) bÁ¶yo
uVvn–
\Z ¤WOøtù i¡ *@ $+2ù úf §÷Søtù (
¡›û!ü!ü!ü!,û +2ù -# §÷Søtù )N'¡ &ü
rtœê&mjy!q~t~tyi~tyœ|V‘Ls mjyZvpqVvpqoo›wN.” rts svuV+21p2v mjy!@ù /bvp §o
÷S y,­øt] ùøtuù ‘d0!¡zŽù •Nú\ sû!w ü!pü!­÷S] ü!øtøt%û ù ù­]øt0Ÿù /œù uVs^ùvz-j¡,x/qqVlnjzŽyZ~t•0ztu o
¶ž~tyZs š@o›1rtyZxGs z,uV”jv“”jy&ufuz{˜)rt‘G~trtrtmp”j”jo›yy –
rtpzŽ”j•Nqsyœ~Žw rt^z:zŽs^o
•Nmjss vbw w^/qrty!w~Oy!~rVqVqVy!o›zŽw^r:•#zQ/rtqu·»~tyz/j~t~ts vuVunmjlnrt|Vmp”j”jo
yŸwy7’mjvjjyZs ~tãbfumpq¬@~tqo
s^w qfs y!’rtvpyGzŽo
o!p’·qVqVzŽo
s yVv)yZ€\ls zŽ‘@uV˜Ÿ˜Ÿw yNyGs o!vjqVq|>ztv7zŽmjrtln”jy
s^yz–
zto
~tùs /iš@yqvprtl”pqf rG~tùy!/w^ qfrts uVvpzŽ”js ˜,s rt”:r{˜Ÿupq~qy
rty!~z6@y!~,zŽ•Ns w "?
xGzŽ•N”js wy¸^zz{s rtvb~trtmpy!o›~rtqVmjo›~trZy ‘L}NmjuVvpo›rty·s uVo
3v uV@uV` 5v`¡'oln”jyZuVzts^o
o
~tyZs zš@yZqz'~tKy ”j[ufZ˜ 4prtå ”j
y 5
!çfæ 687 <zŽmj¡§¿—zŽ•Ns w ^z™o
uV@y!vpztqfrtyë‘LuV~—yZqVo” urt”jy!~Z€ ¿
rto![”jqZy,v«
:98j;š@~t
y:uV
šjmp"æ wzŽy!fyZåbl¶ L€¿—rtu¶s v@qvp¡§zŽ¿—uVl w VqZyw <98rtzŽ”j; •Ny:
s w j^"æ z~tfuVqåbšj~t LwyJœy!vjqfŒpyZo
¡§¿—yZÁ¶ztztqy:qvN~t”p’’7q\uV‘L‘@uVy~œrt”jqzŽw^yuVzŽuwzŽN•Nsy
s vjwŒN^| z–
tr@˜,s y!uV”j~tvps^s oz!” y!uVvbÀ vjrt‘6y,yZlpzŽq•N˜,~Žs wrtsjs^rto
”“mjmpw^zŽquVz{~r6sš@vbyyrtqVy!qfzŽ~tr6’NyZq-z{r-rts^”jz~ty
yZrtrt~tzŽ”js^”jy ouVw^o
l
uV=%f?q>šjwEsmjæ vpy,qf6š@rtsy
uV‘LvunuV~tln‘LyGy!mjw1rtvp”jso›v y –
rtuw^qurt~t”jzŽw y!’mj~|VzŽ|VuizŽ•NyZ˜,z{s wr1^”jzQrty!”jvœjyGw^rtq\‘L”j’7mjy!vp’qJo›rt”p~ts uVuVq\wVvpyœy&qqfwjo
r‘LuVuVvpq~tz{w`rt§~tmpuk‘o›rtŒn@yZ@ly!` ~Žr5 r¡›qVzi¼VzŽ•nrtq”jz6~ts^ylnz6y!s^uwz‘Es rtš@py!y!qv“~~Žqfrtqrts^o
šjy!mnww ’y –
rtrtu¶s uVv y!Vð uV •VcyJjo
~tufy!~ŽNrs^qlns yZv·zCy
zŽ•NŒjsqw ^zjs wv†yZzŸo
uy!~Ž‘Orrtq”js v·yQœo
uVqfrt”jšjy!s œvpqfqfrtrts s^uVo!vpqz!wdz{rt}N~tmpyZo›o›––
rtjmj~t~tu yZž z6yZo›‘LrZuV ~GzŽuVy@ `5 ¡‘Lmjvpo›rts uVvpzŸ˜ŸympzŽyZlœs vrt”jy-¾Ÿs uVœqVztz
dA4 @ HJMbòCMN?/A/MN?#X aSI<A/MN?/ôVM
lunÀ ‘Gy!vjvprty-o
”jywy:s s^z{zrts rmpo
qfuVlnrtvpy!s uVzŽvbs^vJrZlny!u~t‘SxGyZrtlJ”j”js^syQzvp¢{qVln¥1zty!zŽx—@mjy!vplnnuny!rtlnvbs uVy!r-wdv“|Vs^zCsšjV~trty!yZ”pvqqf•nr&rtz”jqylnw #ufju˜,~t‘Ouv“rt¬@”jo
s yQv“s y!y!vprtN”jo
s’y –
jfqf~tyZrtszŽuVy!vpvpz!o
€,yi‘LuuV‘~:o
y
uVŒjqjw y
jŒ:w yVr€qVq>zŽ•nz,~tyZ˜,qVln”jss^vjo”|>’Nps qVy!ztw^lztq|Vymjw ‘LrtuVs wjufw y˜ŸuVyZšpl†zŽy!šN~Ž’ –
@˜ŸzŽy!y!uVVvjmjy!yZw^~l™lqwdlnrtãbuu£mjš@yZš@y
z{y“rtrŽsrtuV‘<y!qvp~,z!qV1so
w¢µ~ts^vJqub~ztrtz6”j˜,qs^z,ws rt@y
”)uŒj‘Sqrtrt”j”jy“y-jw rtãbyVuVmj€jjyZz{s^rtz{o“rtmps lnuVuy!vp‘vbzŸrtrqf”jz,r,y«˜,q”jpvNuœqV’zt”pztjqq~t|Vnuy––
¬@o
s y!vpo
’w y!Vy!w§
¢µvjvJurtrts ”juVyv7¾GšN’q\’Vs yZvbzŽrts^~tqunv:lnvjmpy
o
r{s ˜Ÿvj|:uV~ts •œvbrtu:unrtln”jy!yw§€jy!˜ŸNs^ylny!o!vpqo
vJy‘LuV~tunœlnqy!w ws â!qy-v7rt”js vns^z–
s^lnqy!~tun@s lnr{y!’Jy!vpw/ln˜,rty!”js vbrty”r ~t[rtyZZ”jzŽ
py@æµuVCårtBVvpuVæSjzŽyZzŽs^oz&•Ns ‘LuVw uVN~-~Qfo
qx/uV~tqVvbs^qzŽrtšjd•y
ŒNw Ey¶r-D8uF€ ·‘CD8x/ìrtqVuzŽs^~t•Izy!jrt¶~t~tyZyZqfzŽy!rtÁ£vbyZlrO”j‘<y!qVqvz-˜Ÿqs wv y –
y
qŒNšprtzŽ~uVq:~tšjps vjq~t|:y!vbqriw 1uy!‘CNs^rtln”jy!yvpuVo
yšpzŽ‘Ly!~t~tuVfºqfrtsx/uVqVvpzŽz•d‘L~t uV rt”jx/s^z-qVzŽf• q~t¶s^qšjœw y»,‘Eo!rtqy!v ~
š@y
ŒjyQqlns^ztjo!w qyQ~slnvyZl}NyZ˜,o›srtrts ”œuVv rt”jð y- ¨ ~tyZs wz{rCmpz{urt‘d~rtqf”jrty-yZzŸy!rtN”js^lnyy!mpvpzŽo
yQyu‘unqlno
y!uVw§vbrtxGy
”jŒNyr
fo
mpq~tzts^z,qqšjw zŽyVs , §s }Nw^qy!~,yi¾Ÿ~unqVlnlny!w w#uf‘L˜i~tuV€NÁ“qqsvJvjy!q~Zw rt€jy!q~tvpvplJqfrtÁ“s Vqy-vj@|py!€ ~zލZ@©VyZ©Vo›© rt€Ns VlnyVs^z{ ¡–
G „ ° ³ WXP ‰p´Ž‹#IŠ H P&J Š WXS H P
@S4 ñ K ó/M LI<=@;>hjUZNU MQ[fP= OZMNôX
s¾ŸzŽvjyZs |ztuVzŽœ}Ny!qVy!~tztvbNzSrQs^˜Go
˜GyqVqVzOs zQv q,ln!jy!c@~tVuc@y!žcjw yZuVQo›@r/»yZo!lqo
~tuV‘L~tuVs ~yZjlQzŽmnyZuVrto
mny!uVr1~Žvp–¤qfšpljr1qqVkC~tzŽ’byZlnl–µmpztoo!j”jqf~tuNrtusuVrtuVuwSvpr{šjq’NswV@uVxOyw uVyZqV|Vz{rŽz{’V–– €
˜,~tyZs qVrtzŽ”£uVvjqs v·vj|y!s vjrt”p”jqVyzŽs^o
zœuVuVvbv·rty
ŒNs vprãbumj‘s ~t’s^o
zŽ~t•NuNs wy!^VzœuVqw mnvprtl·s uVvunqlnvpy!lJw –¤rtšp~qVqzŽvpyZz{l –
j~ts^uztrtzŽus uVr{v’N@|VyQy!vjo
uVy
rtvps^zŽo!s^z!z{1rtyZxGlœ”juy‘Oz{¬jrtmp‘Ertlny!y!y!vbvJrCfq~tuns^lnqy!šjwdw yZWz!/s v¢¤r,rt”js^zGyz޾Ÿ”jufs uV˜,œvJqVqVztzz
í/ztãbs |Vmpmjq~t~tdyyZz!n~t¶y!jxG~t”jyZzŽy:y!vbufrfqjw^z~tuV~tšpy!jqšj~tyZs wzŽs y!r{vb’)rlnrts^”jz{yrt~ts }nšjä2mnrts fuVqvp~tz!s^€qšjqw vpyZz!l)€/rtrt”j”jyy
yZflnq~t|Vs^yZqzœšjw ~tyZy!z!j ~tyZzŽíjy!uVvbmjrœ~7rt”jy7mjwlnrty!s^z{@ry!qvp|Vlnyy!vps vNo
VyyZz{~trty!s w^|bqfqfrtsrtuVs Vvpy“zŽ”jrs qVpzŽz•nzq˜ŸuVy!vj~t|y
lnlny!y!Vvpy!o
wyuV@yZunldln€Gy!˜,w^z&”jrts^uJo”†œ~tqyZvpãbqmj|Vs ~tyyZl†s vpo
q¶uVrtus rvjq|:w&s uvn‘Q‘LuV‘L~tuVœ~Žr{qf’brt–¤sy!uVs v7|V”bqrœš@y!uVNmns r–
š‘L@z{~trty
uVmpr{ ln˜Ÿy!y!vbuVy!rvjvz!yœþduVvjjrtuy,~tuq‘L¬@uVvpo
mjls ~y!rtvpy!z{o
rtvs mpyZuVlnz!špy!vbzŽ»&y!rŽ~t–¤v¶fqy!unšjNlnw s^yŸy!lnwŸfy!qvpf~tqo
s^y~tqs^šjqšjw yZunw z yZlnziy!wCs v>o
€VuVs qrvbzivprql‘LsuNvj”puyZqVrŽl z–
j~ts vbrZ
­] ø Eú D ED 6~Z cj ïjc ¡ 6~Z "cj!# ðVjî ¡ 6~Z< $&cj'
 ¨$n! ¡
–

c@c cj ï c cj ¨ !
¨
$&
'
$"!# * cj¨  c@c@cc cjcj îVðî cjcj !ï c cjcj !¨ !
cj ª
cj !
cj ðVî
cj ï c
x/qšjw y ¨ ?»Âmjvjs fq~ts^qfrtyQunlny!wd‘LuV~&qrqVzŽ•˜,s rt”Jrt”j~ty!yiuV~lny!~tyZl~tyZzŽ@uVvpzŽyio!qfrty!|VuV~ts yZz!
÷S
ø DKMendel
DK
WK
Context
DKTrnGen
DKMechEv
IK
WKModExp
WKInqiry
DKMendel
DKNatSel
IKModEvd
í/s |Vmj~ty ! ?xG”jyiz{rtmplny!vbr&unlny!w#‘LuV~Ÿrt”jyi¾Ÿs uVœqVztzŸj~tu ž yZo›rZ
rtíjz{”jrtuV~ty~mpo›yZy
rtqVŒnmjo@~t”«y!y6~Žuy!rN‘nzs^rtln”j˜,y!y6”jvp~tu™o
y!y:w^lnqfrty!sVuVuny!vplnw uVzŽy!”j@w§€6s yZl)˜Ÿqy:rt”jy!uVy«w s^vjo
|rs rtqVz{yZzŽrtl«•nmpz7lnrt”jy!qVvby:zrOuVrtjuuns vjln <s qby!uVwb¡vppzrtq”ju~Žy –‘
rty!mpsvbzŽVmpryVzCq€nw§‘Ls €QuVvj~Ÿ”jyZyZqVs šjqVzŽssorty!”s ~uVuVvSrtšp”p¼OzŽq Ly!š@v)~t¡Ÿfqmp˜,šjzŽ”jmpw y›y
q¿£rtw§”j€is§y!uV~GyV~J rt€N”jr{o
yQ’NuVjrs^qVo!@zŽq•y!wvp˜Gzts vëqfqVrtzŸuVln”p~ts ’Váq€N~o
lno
mjuVy!w v~Ÿr{ž’—rtmj”pvp‘LquVo›v ~–
rt˜,”js y&rt”js svbv†rty!qvpvlnyZy!lNs^@lnuVy!jvpmjo
w^yJqfrts uVunvœlnuy!‘dw,z{zŽrt”jmpuVlnmjy!w^vbl>rz!š@¼#y <oZo
¡1uV˜,vpzŽ”js^y
lnrty!”j~ty!yZ~l>ro
qVuVzŽ•nvnz–
ulnz{rt‘Gs mprtzŽs lnuV•Ny!vps vbw q^rŽz!w –¤€#’J‘LuVunln~ilny!@y!uVwdy!špvppzŽy!lnq~t~ty!fy!vbqvbrZšjrZ¼dw qyxGvpfl“”jqy-~t <s^lp‘LquV¡Gšjw wrtufyZ”jz-˜,ys˜,vj~ty!s|rtw^”¶qfzŽrtyZso›VrtyiuVs uV~ts yvpzGrt@”pjuVq~t~ŽyZv¶rzŽqy!uVvpvbvjo
rZyy €
‘LztuVqf~Ÿrts zŽuVy!vpw yZzio›qrtyZvpll7uVrtšp”jzŽyy!~t~tfyZqzŽšjmjww rtyZsz!vj€f|rt”jo
yuVvpuVmnlnrs rto
s uVuVvpqyZwz6ju~t‘#uVrtšp”jqyZšjzŽys w s o
r{uV’7vNVœy!qf~Ž––
rt~ts^o
yZz!
@S4 8:e@=@YOXZI ñ =@?/A/ILXZI<=@?/hj9ŸHJMbòCMN?/A/MN?/ôVM
sí/zŽv•Ns |Vs rtw mj^”jz~tyyq»&vpð l|VuVzŽ•N”jmnvjufrtuf˜&sS˜,ziw yZuVrtln”jmp|Vy:zŽy,yy!qztNš@o
s^y!uVlnvpmny!qvpr1~to
rts y:~upq€nvp˜,zŽun”jlns^s^y!oztwC”zŽs‘LuVo
uVuVv~vp|Vrto
”jy!y!vjy~tvpy
¬prtzGs^~o!s z{vpz!r1ãbrmjxGqVs ”j~tzŽ’•y
y
Œjunqlnyœs vjuy!‘,y:s vj”jmpy!~tz{rs rqšjvpmjo
s yw^l‘LuVq~‘L”puVq~tœs ~qo
wŸuV~tw uVy!~ij~ts yZv«zŽy!qvbr@qfuVrtjs uVmjv“w^qf‘LrtuVs uV~v“rt”juy ‘
o
uVs^w o
unyVãb€Smj˜Ÿs^uVq~twj•Nlns yZvjzt|o
~t‘Ls ~tnuVrt's uVvrt”juy‘dq~tyZ¬@zŽo›mjrtw srrtz-s uVump‘Ÿz6zŽz{uVrtmplnyy!o
vb~trZubþ zztzŽ”NyZ’Nz-@quvprtl7”jy
q –
mpzŽo
s^uVqfz!~trt6~tyZyZ}Nldo›y!€rtV~tvjy!y yZv1pztyZz&‘Lo›yZs rtqfv7s rtvjmjmp|-~tzŽyZss rvjz6z1|:uqV‘#rto!rt”jo
”jmjyy~~tqVy
y!o
Œjj’Vq~t€\yZs zŽvbsy!rtvjvby!y!r~tyVqfvpþ rtzCqs wnuVzŽvpuVo
uVwqmnvpw/rtzŽo
s s^uVuVz{vrtvNy!Vqvpy!~to
vby&’Vrt€y!s uVqfvpvpqz!wl – 
u <íjrt”juVy!~~šjz,~tqy!~tNyQs r{zŽ’Vs €1uVs w^vjqw ~Z’7 ¡ ‘LuVmj~q~tyzŽ”juf˜,v«s v«rt”jyœ¬p|Vmj~tyVxG”jy
š@xGQyZ”jvjqy—uf~i˜,y
uVw Œnv«yZln@q|Vy!~ŽyzŽrsz>uvj‘Q|Vs vbw rtyœrt”jy!y7z{vprtmplìälny!y!‘LuVvpvb~·lnrŽ–¤y!qw s^w qun:v—lnuy!‘äw6frtunq”jln~tyZy!s^zŽqw y—¿)šjw uVyVšpV€ izŽy!ä~ts^ztfy!o
qvps šjjlnww y!yZs vpwz¶q‘L~trtuV’u ~
zŽ”juV~ŽrZ1¾ŸyZo!qmpzŽy&qw pu‘drt”jyZzŽy&uVšpzŽy!~tfqšjw y,fq~ts^qšjw yZz6q~ty&qVz{–
DKSexCyc
DKDrift
IKSysOrg
WKModUse
WKModRev
+
MendModRep(1)
+
MendModRep(2)
+
MendModGen(1)
+
MendModGen(2)
/ío
uVs |Vvpmjln~ts rty s uVð vp?q»&w vJ’:lny!Ny!s^@lny!y!vpvplno
y!yQvbr&uVunšplnzŽy!y!wS~t˜,fqfs rtrt”s uVvpzŽy!z!V y!v“ E‘LuVmj~&zŽ”juf˜,v@¡
@yZuno›lnrzJy!w yZul`‘irtqV”jz¶y¶o
ztuVqvplny7s rts juV~tvpuVqšjw w ’Ây! lny!zŽ@uVy!w mnvprtlns y!uVvbvSrZ€,€rt”j”jy!y!vp’£o
y>q~trty”jrty†uqVš@lNy –
lnxGs ”jrtsy!uV’vpqs vpw lns^bCo!qfuVrtvbyZrtly
ŒNrtrZ”pþOqfpr-qrt~t”jy!yvbr¬pu~z{‘Gr-rtu”j‘y:rtuV”jšpyzŽy!zŽy!~tfVqy!šjvSw€#yztq\f’q~ts^qOšjwúyZù ú\z!€
˜Gy!w^qVzŸzrt”pyZqfqVr,zŽs y!~qf~&rtrtyQ”pqqv:vy
r{Œj’Nqjs^o!qs vjw§y!yV þ zGOzŽúuVù w úimnrt”ps qVuVz&vJrtqV”jzC~ty!rtuyrtuV”j~lnyiy!o~t”jyZ~tluVw y!bu––
szŽo
¬@uVuVo!vpqflnyrts s rtuVr{s ’NvpuV@vpz!€Cyqwd˜Ÿ”jjyy~tuV”po
šp~tqVyZqz-qfšjrts s vpyZw sl>lnr{’œs^o!rtqf”jrrtqyyZšjld‘Lw uVy-w ‘LíjufuV~t˜,~ uVs 'vj|“Ortú”jz{ù ú\rtyZ~t zŽmpyo›rtVmjy!~t~tyJšpq‘Lw1uV~zŽ@rtyZ”jo›y –
xGq~t”jy^yQr{ ˜Ÿiuœäpqy!vp~ty!lnvby!rw™zGuq‘ vpl ObCúù uVúZvb€@rtlny
y!ŒNvjrZu rtyZlxG÷S”jøtù y!Os Cú~ (-q~qvpvjl|V÷SyZzøtù Oqú ~ty €
rt”jO
yúùdú ¬pû ~z{
r¨ uV"qšp!#vpzŽOl y!%û ~t$& fOq'
šjú$ùw ú y
QBqs^zœvpJ l yZ¨qV¼NzŽ
s rty!”p~dqfrtr&%û $&”ps^qz!v†'
€ $ r{
b’Njks^o!Œnq@w§y!€,~ŽzŽru«z6rt˜ŸuVyw^lzŽmpy
rz
+ Oúù úf §÷Søtù OCú (
¡ ­] øtù Oúù ú ¨ J ¨ ü
xGcj€ ”N¨mp€pz qvp
_l d!nû€j˜,
”j s^"o!#”O˜,%û $&s w O'
w $yZqV
l:qrt~tuyœ”jœs |Vq”jjy!@~&yZl“j~trtuVu špq­] šjsfw qs rtw smjyZyZzGz‘LuVu~‘
”jqvps |Vl ”jy! ~-Owúy!ù Vy! w/~tJ yZzލ @ü ï uV€jvpzŽzŽu yZz!-íjuV~0bCuVvbrty
ŒNrZ€#˜ŸyzŽy
r Oúù ¨
+ Oúù §÷Søtù Oú !¡ ­] øtù Oúù * J ¨ ü ï ü
xG*”N ï mpJz ¢µv«
uVd~ln%û $&y!~Q'
rt$ u
y q#~tyZyo›rœo
quVjvp@lnyZs l“rts uVrtvpu qwŸ­] lnfy!q@w mjy!vpyZzlny!uvp‘,o
–y ï ˜,qs rtvp”nl –
uV˜GmnqrvbrSqZ#rtuyZo›o
rty!s vbvjrt|y!~drt”jrt”jyiyCœjq~t~ts uV|V~Os vplnqs^w#z{rts ~tvs 1pšjmjmny!rtvps uVo
viyiuu;‘ ‘HbC uVivbrtäy
ŒNy!r/vpqln~ty!uVw§€nmj˜Ÿvply
â!qVy!o!~to
upuVxGjw”js^zŽy”jrt~t”juVs^@z!ubzŽSyZuNluV•NzŽ@s vjyZ|io
s ¬@q”jo!qfyZrtqVs luVvprtufz˜G‘LuVq~~l O~ty
ú¬pù vjsqvjvp|l ln s^z{Ortú~tùs –
rtrtšju:”jmny,rt~ts y!s uVvpNvplns^zQzŽy
y Œ‘L~tifuVq˜,w mj”jljyZs w z1qfyruqj•V‘y!€ObCy!˜ŸjuVyœsvbvjrt˜,|œy
ŒNs rtw r66”jqy|V~ty!lny vjs^y!z{rt~¨ ~tqû[s w !šj’
bmn€\rt˜G˜Ÿs uVqy&v7vbo!rQo
qy!rtvvburtå.y!š@›~tæ"yyZœldq&šjçfæµw¢¤yå‘
Qqvp_l !å
æ J ¨ ü ï f
»o
uVz/lnšjyZsztvjo
yZ~tzs š@rtyZ”jlQy-s svv1p}NyZmjo›y!rtvps uVo
yv u!n‘d ð rt€Z”jrtyZ”jzŽyŸy&z{r{rt˜Ÿ~tuimpo›‘<rtqVmjo›~trtyuV~‘Lmjzvps^zŸo›rto
s uVuVv@rt”py!vnqfr–
ztqfrtuV~t’V€NuV~&zŽmjœqfrts VyV¼Nrt”pqfr&s^z!€
­] øtù Oú /ú Oúù j÷ Oú * Oúù -ü
x/qšjw 0y !zŽ”juf˜&zŸrt”jyi~tyZzŽmjw rts vj|œo
uVvplns rts uVvpqwdj~tuVšpqšjs w s rts yZz!
@SA4 @ 8:e@=@YOXZI 8:? ?/ó/ILK1ILXZI<=@?†3:MN9<hnXZI<=@?/UZó/ILò
r@í/qVubs zŽ|VzŽ•JmjyZl~ts yvq¶rt”N”jzŽ’Ny”j@»&ufu˜&rt|V”jziuVyZmnrtzŽrt”js^sOzGyJ‘LuVy!uVN~&mps^rtlnzŽ”jyy!yvpzto
o
y:y!unvplnqy~tuns lnupuy!&‘wŸs»,vj‘LuV‘E”jrt~y!y!~t~-q7s r”pqzŽq\mjvpNšpo
s yizŽvjyZ|œuãb‘1mjjrty!~t”jvbuyr–
rtuVuVvìs^w^o
l£yV”j€6y!mp~«rtz:”jmjrty”pvpãbqflnr:mjy!yZ~rtz{z{”jrtrsqy¶uVvpvy
lnŒjs s^vjqz|˜,s uvj”p‘Jy!qfyVrrtþ zJ”jrty†u“qvplns vpzŽu¶˜Ÿãbmjvjy!~:s y
~tŒN’lnrZy! j@~ty!À unvpo
mjljyZ~zJztzµy
œ¿£Œn@qs sy!r“vj~Žwrs^’ zz
rt”Ns ’N@yurtrt”juyZzŽo
s^~tzµub¿£ztzšjmnzŽuVrJrtyœ”jy“y
s^o
ŒjyVq€/rtsuvjy!jy7~tuf”pNqVs^lnzyrtu·ljqf•NrvjqJufrt˜ urtqfyZrJz{rw yZrtqV”jz{yr
y!jvj~tuVuVšjmjw|Vy!”q1š@xGuV”jmnrCs^zrt”jyQyZqävpz1y!vprtln”jy!y,w s^~tqy!vw^qfrts uVunvplnzŽy!”jwps rtuš@mjy
vpr{˜Ÿlny!y!~y!z{vrqs vpvpãblmjrts ”j~t’y
uVzŽuf•NšpVs zŽwy!y!~6~t LfrtÁ q”jšjyQQw ”Ny:¢µmjvps^~zãbln~tvjw ’jyVuf¡þb˜ uq‘Ovps vj”p-l ”jq\Ns šjs vjis rt| säuV vSy!ivp¼Glnrtäy!”jw&yy!vp˜,y
lnŒjs y!rtq”·wdqf~trGs yZvjwzŽy!yZ@yJqVyZz{o›rIrmprt
z{u¶r "rt|V!#”jy
yr
š@y
‘LuV~tyQÁ Q¢µvpãb~t’:o!qvo
uVyis vbrtujw^q\’V
@S4 CFJH I MbVòChn[fMNA?/A/ñ MN?/HJôVM I<UOZY/?/ôXZI<=@? =@?/A/ILXZI<=@?/hj9
L‘í/lnuV~ts ~i|VyZztmj}NzŽ~ty!yZy |Vzï ˜,zŽy!”j”jvby
ufr rt˜&”j¨ zOy!s~rtv”jq¶yGrt”jy!z{y¶rtNmps^ln½Žlnw y!y!s âZvpvbqo
r~yGlo!qztv uno
y!lnž vpy!mpwjqln~t¾G|Vs upq\yJ’V ¹ rtyZ”jzOxGyvj”jy
z{s^r1rtz~t‘Ly!~rvjqqV|V|zŽ•rt”qVy!vblNur–‘
ssqvjvjv£|J|·qrts ~t”pv)|VqfmjrqzŽjy!@~tvbyZuVro
šjs ¬@‘Lw uVy!o~lno
yZs^ztuVoo
vb”puVrtqvny
vj¬pŒNs^rZ~tzŽœ sz-vjxGu|p”j‘C€Gy7y!zŽVmjrtuV”jjw ~t@mny!uVrty¶s~ŽuVrtvjv¶s vjun|pqln~t€ŸyZyzJuVuV~uV@v—jy!~t~rtufqf”jbrŽy ––
~tJøs |Vt”bù @rú\~t y!j~tyZuVzŽœy!vbqrs v£uVšpy
ŒnzŽy!@~ty!f~Žqršjz:w yJlnyZfzŽqs |V~ts^vjqyZšjl·w yZrtzµ¿†”jyZrzŽy¶q•Vãby!mjv«yZrtz{uVrts|VuVy
vprtz”jy!rt~Zu €
y!uw‘,s^o
äs r£s^o
y!~tNuNs^y!lnVy!uVvpw mno
y™rts uV‘Lv†~tuV % irt”jäyëyZoz{”prtk6mplnjy!¡Qvbqr—vpl¶qš@¢µuVvpmnãbr mjs ~tQ’·vjuf LÁ ˜,w QyZln¢µ|Vvny–
rãbqV~t
zŽ’j•¡›dJû ”p»&q\
Vw y"rt!#rt”j”jOy:~t%û y!$&z{yrtmp'
uVln$ ~y!
blnvby!rŽ~t–¤yZl·unflnqy!ww^mjzyZqz!vp€Gl¶˜,uV”jšps^ozŽ”£y!~t˜ŸfqyšjwqyZ|bzQqss v“v†rto!”jqs^w z
+
MEFactors(1)
WKInqry
+
MEFactors(2)
+
MEFactors(3)
WKInqry
EffMeth
DKMendel
sí/vjs ”j|Vsmjšj~ts y rts uV2v?Q»&~ty!v“w^qfrty!s NuVs^vplnzŽy!”jvps o
Sy unlny!w˜,s rt”¶r{˜ŸuJpq~ty!vbrz-s v“qv
wrtxGy!”j”j yyœs^y
z-Œnqr{@~t’N|Vy!js~Žvps^ro!qz,qw1s w§vpj€/ln~tzŽus^uo!ž qfyZ˜Ÿrto›yZyœrtlJs uVzŽy
vrtNr”p‘Lqfmjr&vprt!o›”jùrtú syuV v7lns á‘L¨ uVo
~iqmjvpÁ w lr{’JQ u¢µ‘1vp!ãbrtù ú ”j~t’Vs^z&jxG!:~t”puV‘LuVšnqfr~–
s^z!€ + !ù úf §÷Søtù (
¡ ­] øtù !ù ú * J!Gû
q¨ vpÂl íjuV
I~ d û i
ä y!"vp!#lnOy!%û w§$&€,˜Ÿ'
$ y
&y!œqjpw z1uf’VrtyZ_u l†­Q] q>fqlnw mjs #yZy!z~tuy!‘@vb–r:¨ •N€ scjvp€Vl†qvpul ‘
œq~t|Vs vpqw@‘Lmjvpo›rts uVv ?
+ !ù §÷Søtù Z¡ ­] øtù !ù c¨ ss ‘‘ ) c ¨ [û ! ü
¢µs vv¶
1p umj"rty!!#”jvpJy!o
~QyuV˜Ÿ_v uuV‘ ~ ljiz!iä€däs y!rivpy!s^vplnz lny!c:w§y!€#wCs q‘Ÿs^vpzirtl ”jrt”jy¨ y!y
v«s ‘6ŒjqzŽy”j#yyZs o›vjs^rtz!y!yZ,yl“xGs^zQšN”j’vjyiurts rvj”j”jy:qfsrQšjz{rtsw rtyZ~tsmpqVvjz{o›| r–
rtmj~qw#‘Lmjvpo›rts uVv
2$ ­] øtù !ù ú\û ­] øtù !ù & $ ¨ JB­] øtù !ù &2$ !ù ú $J ¨ &#* !ù ú &#* ­] øtù !ù ­] øtù !ù ú\ü
x/qšjw y ð |Vs VyZzŸrt”jyi~tyZzŽmjw rts vj|œo
uVvplns rts uVvpqwdj~tuVšpqšjs w s rts yZz!
DKMechEv
Context
pfí/qqs |V~t~ts^mjy!qvb~tšjyrw zyZï z!q?C vp»&lvo
uVy!vpNlns^lns rty!s vpuVo
vpyiqwjlnuny!ln@y!y!wOvp˜,lny!s vprt”o
yr{˜ŸquœuVz{vjrtmp|-lnuVy!špvbzŽry!~tfunqšjlny!w y w
š@xGzŽy!y
”j~tr{fyG˜Ÿqlny!šjuVy!w vœœyZz!rtq€6”js ˜GvyZzŽqVy
y-zŒnzŽ@Z•Ny!s ~Ž<w 98r^z!zO; €n
s o
vp
uVln"æ vps^fo!o
åVqfy!¼rt~tyZvj Llis š@vjrt¡|i”p~tqfrtyZ”jr,zŽy!@ <s qb~ŸuV¡dvpyrtzŽ#”jyJyZyŸo›jrŸ~t~ty!uVuVw^qfvœšprtqsrtšjuV”jvps y-w szŽrtuV”js šnyZs  z–
˜Ÿqvpy!l£~ty <oZ¡-uV~trty-”jyzŽy!uVvpšpzŽzŽs rty!s ~tVfy&qšjrtuw yZÁzzŽQ”juV¢µvpmjãbw^l¶~t’š@rty”pqv:unuVlnIv y!w yZ l«iqVäzyZo
ouV”pvpk6ln#s – ¼
rty!sfuVqvpw mpqwqfrt’s uVlnvpy!z@y!uvp‘Qlnrty!”jvbyrZ€#ztš@qyZo!yqmpzŽzŽy
yrquw ‘OuqV‘o›rtrts ”juVyvpzuVšps v—zŽy!~tq«fqo
šjuVwyZz&quV~tv y
juVšp~tuVzŽšjy!~tw y!fqšjwzŽyVy
€@rŽrtvps qvj|pGy!w Á¶’V€dyiÁ rt”NQmp¢µz&vp”pãbq\~t’VV€yQ rt”ji~täy!yyZpo”pq~tk6y!#vb€drzGqvp‘LuVl ~&bCyZqVuVovn” –
rtlny
s ŒN#rZy!“~ty!vb <‚&r&ufrtqyœ~ts^rtq”pšjqfw yr rtbC”puVqvbv4rty
bCŒNuVrivb‘LrtuVy
~ ŒNrGS‘Ls uVâZ~&q~»&Ol |V uVmn¨ rts^s z¨ qV ¡ o›rtmpqw ’7q
r¢µjv)qf~trtu s qVž uVyZo!vpo›o
z!rtuV€6s ~uVlj˜ŸvpqyJz!vpJzŽo
y
yíjruV˜,~rt”js Árty:”—Q‘LuVrt¢µ”jw vpy¶ufãb˜,~ty
’VsŒnvj€ @|7+ y!~Ž@frúqz!ù w úfþŸmj §yZV÷Szy!øt~tù ‘L@špuVúCq~(›w-¡rtj”j ~tys uV­œ] ~:øtùq@y
~tŒnú|V@ù súvpyZo›q – w
¨¨ üü cï #HJTJ !nð J»&íjuVvpY~l¶ ‘LuVi~ äbCyZuVovb”prtk6y
ŒN#rZ€ I€ + + @@úúù ù § §÷S÷Søtøtù ù@@ú ú !Z¡ ¡ ­­]] øtøtùù @@úúùù +uY‘ J ­] øt¨ ù ü@ï úù úxGq”jvpy:Kl z{­rt] øt~tùmp@o›úrtù mj€d~q‘LuVw6w ‘Lufmj˜Ÿvpo›yZrtls uVšNv“’rqJq•Vo
yZuVzQrt@”jy!yvpœztqfqfrtŒnuVs~t’mj~ty
–
w^qfrts uVvpzŽ”js J˜,s rt)” ­] øtù @úù ?
@ú $ ­] øtù @úù úZ%û ­] øtù @úù %û ­] øtù @úù & œqfŒ $ ­] øtù @úù úZ%û ­] øtù @úù & * ­] øtù @úù ü
šjxGw ”jy yp~t yZzŽmjw rts vj|7o
uVvplns rts uVvpqw6j~tuVšpqšjs w s rts yZzqj@yZq~s vx/qf–
6~Z cj ðVjî ¡ 6~Z "cj!# p¡ 6~Z <$&cj'
 ¨Z$jî ¡
cj ðVî
cj ¨Zî
cj
cj ðVî
cj ðVî
cj ¨Zî
cj
cj ðVî
cj ª !
cj c î
cj ð c
cj ª !
cj ª !
cj c î
cj ð c
cj ª !
cj © cj î !
cj c ð
cj ¨\ï
cj î !
px/qq~tšjy!w vbyIr&! q? vpl:bCuVuVvpvjlnyis rto
s uVuVvbvprtqy
w6ŒNjr&~tpuVqšp~tqy!šjvbsrGw s sr{v’“qœlns^o
z{uVrt~ts šj@mny!rtvps ztuVqfvprtziuV~t‘L’œuV~~ty!qw^qfrtrt”js uV~ty!vpy
zŽ–¤”jfs qSw mjyZl“uVšpzŽy!~tfqšjw yfq~ts^qšjw yV€/˜,s rt”>uVvjy:z{rtmplny!vbrŽ–¤unlny!w
iäy!vpljqw
"!#
$&
'
$"!#
$&'
$
­V] ú bCuVvbrty
ŒNr
cj c@c
cj c@c
¨¨  c@c@cc
n!n!  c@c@cc
$& '
$ – cjcj­ ] ïï – cjcj ïï ­cc ]
$&
'
$ –– cjcjcj ïïï cj¨¨  ïïï ccc
$&'
$ cj ï !n ï c
Eú D
cj ª !
cj î !
cj î !
cj © !
cj © !
ED
cj ¨Zî
Á
Q ¢µvpãb~t’ – ¨ V­ ] c@ú c i äy!vplny!w cj­ ] c@c – ¨  c@­ ] c cjE  ïú D c cjE  ¨ D ! 6~Z cjj ï ¡ c 6~Z "!#cjp ðV¡ î 6~\ <$&cj'
$n ¨ ¡ !
cj ðVî
cj ¨ !
–– ¨¨  c@c@cc $&
'
$"!# ¨¨  c@c@cc –– ¨¨  c@c@cc cjcj ïï cc cjcj ¨¨ !! cjcj ïï cc
cj ðVî
cj ¨ !
""!#!# cjcj c@c@cc "!# cj¨  c@c@cc – cj¨  c@c@cc cjcj ï cð cjcj !¨ ! cjcj ï! c
cj ðVî
cj ¨ !
cj ª
cj !
$&
'
$"!# cj¨  c@c@cc $&
'
$ cj¨  c@c@cc – cj¨  c@c@cc cjcj ï ðc cjcj !¨ ! cjcj !ï c
cj ª
cj !
cj ðVî
cj ¨ !
$&$&'
'
$$ ¨¨  c@c@cc $&
'
$"!# ¨¨  c@c@cc ¨¨  c@c@cc cjcj îVîVîî cjcj ïï cc cjcj ¨¨ !!
cj ðVî
cj ï c
cj ðVî
cj ï c
~tx/y!qw^qfšjrtw ys uVvpð zŽ?0”jbCs SuV vplns rts uVvpqwj~tuVšpqšjs w s r{’lns^z{rt~ts šjmnrts uVvpz-‘LuV~iq:rt”j~ty!y
–¤fqw mjyZluVšpzŽy!~tfqšjw yfq~ts^qšjw yV€ds w mpz{rt~qfrts vj|qv7s vj”js šjs rts uVv
Á
Q ¢µvpãb~t’ – ¨ V­ ] ï ú c i äyZo”pk6 – ¨ ­ ] c@c bC
uV vbrty
ŒNr – cj­ ] ï c – ¨  ï ­ ] c cjE ðVú D î cjE c D î 6~Z cjp ª ¡ ! 6~Z cj
N ð ¡ c 6~Z <$&'
cj$j c ¡ î
–– ¨¨  ïï cc "!# – cj¨  c@c@cc $&
'
$ – cjcj ïï cc –– cjcj ïï cc cjcj ªª !! cjcj ¨Z¨Zîî cjcj ðVðVîî cjcj cjcj ¨Z¨Zîî
–– ¨¨  ïï cc $&
'
$"!# cj¨  c@c@cc $&
'
$ – cjcj ïï cc cjcj ïï cc cjcj îî !! cjcj ðVðVîî cjcj ¨Z¨Zîî cjcj cjcj ðVðVîî
""!#!# – cjcj¨  c@c@ï ccc $&
'
$ –– ¨¨¨  c@c@c@ccc $&$&
'
'
$$ – cjcjcj ïïï ccc – cjcj¨  ïïï ccc cjcjcj ©ªî !!! cjcjcj ªðV¨Zîî! cjcjcj cðV¨Zîîî cjcjcj ð c cjcjcj ªðV¨Zîî!
""!#!# cjcj c@c@cc ""!#!# cjcj c@c@cc $&
'
$ – cjcj ïï cc – cjcj ïï cc cjcj ªî !! cjcj ðV¨Zîî cjcj ðV¨Zîî cjcj cjcj ðV¨Zîî
""!#!# cjcj c@c@cc $&$&'
'
$$
¨¨  c@c@cc $&
'
$ – cjcj ïï cc cj¨  ïï cc cjcj î© !! cjcj ðVª î! cjcj c¨Zîî cjcj ð c cjcj ðVª î!
$&$&'
'
$$ ¨¨  ïï cc –– ¨¨  c@c@cc $&
'
$ – cjcj ïï cc !n¨  c@c@cc cjcj îV©bîï cjcj ï cð cjcj c¨ !ï cjcj ðV!@î! cjcj ï cð
$&$&'
'
$$ ¨¨  ïï cc ""!#!# cjcj c@c@cc $&
'
$ – cjcj ïï cc !n¨  c@c@cc cjcj îV©bîï cjcj ï cð cjcj c¨ !ï cjcj ðV!@î! cjcj ï cð
$&$&'
'
$$ ¨¨  ïï cc $&$&'
'
$$
¨¨  c@c@cc $&
'
$ – cjcj ïï cc !n¨  c@c@cc cjcj îV©bîï cjcj ï cð cjcj c¨ !ï cjcj ðV!@î! cjcj ï cð
~tx/y!qw^qfšjrtw ys uV2vp?+zŽ”jbCs JuVvpuflnVs y!rt~Ÿs uVr{vp˜Ÿquwjjz{~trtuVmpšplnqy!šjvbrŽs w–¤s r{’unlnlns^y!z{wSrt~tfs qšj~tmns^qrtsšjuVw vpyZzzG‘LquVvp~Clq-o
rtuV”jvp~tlny!sy
rt–¤s fuVqvpw qmjwSyZllny!uV@špy!zŽvpy!ln~tfy!qvpšjo
yiw yG˜,fqs rt~t”Js^qršjqVw zŽyV•n€zŸs w ‘Lmp~tuVz{rt ~qfrtrt”js vjy|ztqqvyiqizŽlny!s^|Vz ž mjvpy!vbo›rtrZs  Vy
&J ˆ·‡Vˆ PS ‡
P
Vu¾Ÿ}NšnyZs uVo›rrtqœs s uVv`qVv ztzs vjð y!s rtNzŽs^s^”jqlnwufy!˜ŸvpfyZo
ql—yw mjyZ”jzufun˜ ln‘LuVy!~“˜Ÿw^z!y“£o
uVmpvpxGzŽln”jyZs yl™rts uVvjy
vpy
ŒnqŒN@wr:y!~Žjz{r rt~ty!uVž ·špmpqln˜,šj|Vssww s&rty!s š@vbyZryzrtrts vuu
|bw ufqf˜,rt”js vjy!|7~Oy!䏐s^jzŽws y!~ts^No!’—qwNå
ljæqfrçfq,è é£rtu ¨Z~t©Vy
¬p©V©vj¡Qy6rt˜Ÿ”jyJyZzŽqyŸ~tyj~tjuVw^špqqvjšjvjs sw vjs rt|s yZz!rtu7OíjmpuVzŽw y –
äzŽs šjqw ~t’•Vufmp zŽs vjbC|”pq¾ s vœ iä}¶uVvb §rt}Ny jbŸs y!q|V~ty!w w u”pqrtuQw rty!¬j~r6å
rtæG”jy,çfè pé € q~¨Zq©V©bï y
¡›rt y!~z!€@ubz{–
Á¶¢µv¶y-rt”jq~tyœy¬py
~Œnz{jrZw€OuV˜Ÿ~ts yvj|Q˜ŸrtuV”jmj~tw^y!l¶y-mpqzŽjyj~trtub”jqVyœouV”jmnyZz1rtj‘LuVmn~Crrtu”j‘Ÿs^zCrt”jw^qfy rŽrt¹ y!j~G~tuz{rtž y!yZSo›– 
rtw y
s uVrv·j~tjs wuVmp~zzQ|V‘LuV~~iqVlnrtyZ”jl«y:~to
yZuVzŽvp@lnuVs vprts zŽuVy vp¹ qw6jun~tlnuVy!špwGqrtšju“s w s jr{’~tunrlnqmpšjo
w dy yZz!€/srt~”joy!”nv –
mjzŽy!#~tljfqfqfrtrtys uVvpyZqVz!o¼O”rt”po
qfuVrvplns^z!s rt€Os ˜,uVvps rtq”jw/uVjmn~truVšp‘Lmjq~Žšjrts ”jw s y!r{~’o
lnuVs vp~tyZz{o›rtrt~wq’Js vb‘Lr~tuVuV'v¶rtuV”jšny –
wus ‘Ÿ•Vy!rtw”js ”jyuNy!unvblQrt~t‘LsmjyZvpzio›˜,rts uVs w vpCz!š@1y:ê&ãbufmj˜Ÿs rty!yVy!zŽ~Zp€fqqV~zOzŽyV˜Ÿ€SyCrty
”jŒns^z@yZ˜,o›r1s w 6rt”pjqf~tr1uVšpœqqšjvNw ’’
vjuuVrœvjwuyZrtqVuVl«vjs^rto
u“s r{’·|VuN~tuny!l>w^qfrt~ts yZuVzŽvpmjzŽw ”jrzs pz LyV¡›ì |p €C» mjvpzŽyZz{o
ruVqvpšjwl†yV€C@uVub~ztzŽNs šjs uVs w w^s qfr{rt’†s vjs^| z
rt‘LmjuJvp‘Lo›uVrtw s uVufvi˜rtuGärts^s zŽyŸw y!zŽNs ’s å
w^qæ-~Sçfy!è w éy! ¨Zy!©Vvb©Vr©zS¡&u‘bqrtvp”jl7yŸmpo
uVzŽyvplnrt”js rtys uVz{vprtq~twmpjo›rt~tmjuVšn~ty –
mrtpq”jšjzyJs wrts u¶zŽr{•N’ws yZw œ^qz~tqfvsrtv>~tss ŒJvnyZqV‘LrtuVouV~t”«|Vœy
rqfrtqV”jrtzŽs y!•#uV~Zv&Á¶ê&qš@ufyJuV˜Ÿmny
y!rŒnV@y!rt~ZyZ”j€jo›yrrt”j~trty!s^”jz-w^qfy:lnrtsuNVyZyJubz&z{ztrvjo!uqjrQw ~ts uVvjqw|7ufs^uz{˜ –‘
suVvjv|rtq”jjy&jV~ty!ub~tqVšpoq”w s^’bz1–¤rtfuqw qVmjztyZzŽls |VqVvztzŽjyZ~tzts zŽuV~z/y!rtvbNu rz1u‘#ù /&uVmjq~6vply
Œn @y!~Žù /&rz!šp€bqVqzŽvpyZll
rtrt”j”jy!y v w yZpqq~t~v™qrt”jy
rtyZy!zŽ~y«zp‘LuVqI~~qbCuVy
vbrtrty!y
~ŒNzrœlnfs ~tqyZ~to›s^rtqw šj’ìw yZ Lz~tyZqo!~tqyJw vjs vju|·rœrtyZ”pz{rtqfs r–
œ~ts y!qfvprto
yZylp¡›˜,:s rt»&”¶|b¢{q¥1s v¶x˜Ÿyuno!lnqy!v“w^z-lnrt~uq\˜j~tuVuVv¶@ubrtzŽ”jy s ~Žr{~t’yZqV’VzŽyZuVqvp~qz-šjuw yV‘Gþ@y
jŒn~t@s uVy
~–
lnlns^y!z{vbrtri~ts šjvjmnuV~trtœs uVvpqw/z!1j»~ts uVz~z{zrquV~Žv rts vj |zQ@quVvpsl7vbrZw €VuV˜Ÿ|VvjyŸuV˜,~tœs w nq@wOubjzŽ~ts sruVs~vpzlnuVy!v @y!
vnz!– €
˜,j~ts srtuV”:~zŸqyZvpqlJvpzŸz{rzŽqy
vprGljqfqrŸ~rtl”jlnyy!vNNmjs^qfrty!s uV~tvps^o!zŸquwp‘ rt~¨ q,vp zŽÀw^qfmjrts~GuVjvp~tz6y!uw s‘SVsy!vp~tqšp~tq’ w
˜Ÿs vpuVln~ty
•ŒnyZ”jzy!q~tyœ~tuVzŽmj”jvpufl ˜&cjz-¼rts§”p yVqf r€rts uQrmps^zizŽy ”jJy!w ¶¨ >û rtcju£û ¨ ½ts o
vpy!z{vbrtrtyZy!qV~ l¹ urt‘ ”j¨yœ[û w^!nqû š@ð y! ¡w
r¢¤zŽ‘ŸqV’nzŽz{˜Ÿ•nrty!yz!œ€@”pzŽqfqVmprtl¶os^o!”7qVqljwqVlnz,’:s ‘Lrt~tuVsy!uV~tw^œvpqfrtqqfyZwr-lJo
quVrtvpuœw ^lqfrtrt”jo
y!uVy!~svbq~-w/rty!lns vbvns ár-‘LuVy!o
~tmjw œy!w r{qf’Vrty!€@s vbuV˜Ÿrv¶z,yqrto
š@”puVqfuVmjr-mnw^lrQ˜Ÿmprty!”j~tzŽyyy
rt”p”pqqfv¶r,qrtvpuœl~tyZÁ£lnmps vjo
y-|Vy!rt~”jzŽyi•N’Vj€ ~ty
¨Zrt©VyZ©Vz{ð r¡›zt-q¢µvjrtw ”jyis^zizŽs â!o!yœqVzŽ <y䘟s^zŽyw y!o
NuV’Vmj€@w^}Nl”jmpy!zŽy
y –
rt,.”jy&,o
»uVw lj^qfqrtœy!~z!q€pwbÁ£s vns ‘Lw^uVzŽ~tuVœvS€#qfrtqs vpuVlvÁ“s vquVvjmj|~1 ¨Zun©Vln© y!wj¡Ÿu”p‘ q\Vyiù /j€ ~tuV@ubù /GzŽyZuVl ~
qqšjw yZunz!€Vln˜,y!w&”jqs^ow ”uVvjo
|uVmjrtw^”jlyZzŽš@yJywqVs vjljyZqznrt‘LyZuVl~rto
uiuVvbrt”jrts y-vNmjz{rtuV~tmpmpzo›rtw^mjqf~trtyZy!lvbrw^qffrtqy!~tvbs r–
o
w^qVztz,zŽs rtmpqfrts uVvJ˜ŸyQ”pq\Vyilns^zto
mpztzŽyZl:”jy!~tyV
± ° &‹ H޳‡N´{± °
|V»o
uV~tzGuf˜&s vbjz!rtw €,y
y!Œ~t•NyZvjz{~trGyZufzŽ˜,s @vJs uVvjsvp|vpzŽo
y”j~tyZufljqV˜'qfzŽrs vjq:rtu·|V”pw ’œqVœz-qqš@•VyZy¶šjo
s uVrtzŽy!s uVvpmpyzŽzGy¶q:qVuš@zt‘izŽuyZrŽrtztrt”jzŽw y“y!vjy!~tyZvbyZozŽrC•#mjrw qVrtÁ¶szŽvj•n|yz
~to!y!qw^vjqfvjrtsuuVrivp~tzŽy!”jw s ’pzuVv¶š@y
jr{˜Ÿmj~ty!y!y!w v“’o
y!uVjjs ~tw y
s^o!Œqw1uVšpzŽy
y!rt~t”jfunqfrtljs z-uVvprtz-uqyZvpz{rlqšjw s^mjzŽw” –
rtmps zŽfyq~ty
s^Œnqf@rtyy!~Žo
r uVžvpmpz{lnrt~t|Vmpo›ry!z!vbrQxGrtuJ”js^zCj~t~tunyZlnzŽyZmpqo
~yo”s vjs sw rtmps^qz{w1rt~fqfqrtw yZmjzŸyZz-qi‘L˜GuVq\~-’rt”jrtuy
w^fo
qfuVqrtvp~ty!s^lnvbqfsr-rtrtyœs o
uVw^|VvpqV~qztqVz&wplnjyZ~tlNuVun–¤špln~tyZqy!zŽw^šjz!@s ,wuVs vpr{¢¤’r-zŽyšjrqmj¢{šj¥1s w^w xìljyZzz&‘LuVuVvun~Clny
ry!qVŒnw^zŽ@zi•ny!rtz6~tus s y!vyZvpqVo
zŽyymj˜,w rtrts”js rtfy:”q~tšjmjs^qfmjvjrt~Žs y––
‘žLln~mpy!qlnv|VuVy!v˜Ÿy!uVvbzŽmj~tr•·z&š ž qVyZuz,o›‘rClj¾Gœqfq\rqfq’VrŽyZrtqVzŽy!o!s^~Cqo
v£mjy
ŒnyZ@mjz{y!rtw^~Žqfs œrrtz!yVqf€N rtqs vpuVlv—s^‘LzŸuVq~~ty!y
vp¬pqvjšjs vjw yG|>rtrtu”jrtyZ”jzŽyy
3:MNõ¤Mb[fMN?/ôVMNU
8: ñ A/
hj
;> UVB“3½txG4<B ”jyœ I<mj9<UZw =@rts^?ClnsB_ y!vp4 zŽ3s uV4<vpBqhjw?/~qA vplnuVºhj?/o
eOuNB y
áo
s 4y! vbrz 4
8;mj6twårtœs vjåuV
pæs^q w#ñ w €uV|V¨s rŸ! ð  unlny!w§ ¹ 4#4#è <[å #87@,=fè çfè 7åç 5
8:[½ -9<;>~q=@j”j?/s^ACo!qB wQ3un4E57lny!4<w^B zqhjvp?/l)Ao
uV_`jI<UZmn9<rtMby!ad~ts cpâ!ByZl)3qVlj4 Rq4nrts V ñy7
rt
yZ
z{rŽ – 
s! vjðV|pî  ¹ 4#4#è <å[#87@,=fè çfè7åç 8;6tåœå
pæ @S€ !@! ð
L ñ[f
hj
A/
9<P= B ½t» 4 K ¾G4<B q\’VyZzŽs^hjqvI<?/Mb~[Nq!B vpln“4uV <Bëyhj#?/yZ"Ao›rz돐hjun?/lneOy!Bw>‘L4uV~
rtyZz{rtw y
rz! ¹ #87@,=Zœå
æ 6. #Vç %$ O€ ¨\ïð #¨ZªVî 
PO7=punçf[flnæ ;>=jy!åw^z7hjœ?6?/çfxG?C"æ ”jBCy!çf8uVè~t4 Zç’:&“
q4 vp.@lJñ æµ
çfq"æ'j j›("æ w s^Jo!çfqf½èrts #uVbCvp8uV7@z!vp, ¹z{=rtf~) èq6.s vjE7æ"yZ lC=+@ w^' qf* rt€ y!î ;vb6.rQ#
#¨Vo
çfw^¨ èVqVpzt- z,
KC_`zŽyZMbztI<[fzŽUZeO9<MbBGy!advbF&cpr 4E?1BnW3Á£4 4 ”jRñy!BN
~t8:y-
9<rt;>”j yi=@vN?/½t¾GmjACq\BN’Vš@3yZy!z4E~57z,‚&o
4<y
BNuVrgiz-hjsyv“?C‘L~tkCBjuVH7lnmp4no!¹ hjqf?/rt¢µs A7v uVvpWd/VqXZ
w/MN»I<å ? z{68–5
6æµZç ~qV
plnæ 7yV€nê
O LyZ6›"ælj 08z! ¡›<Cçfäè 1.uV
p~tæµ|bå
qèEvn b– iå qmnå ‘Lœ2 34q3Ovj€ vSO€ qVzŽð •Vy! ’V€ ª   ¾-#qvpl
_`_ I<4EUZW9<4 Mbad ñcp
B&
3@ 4 R:4<B-½tê&WSufó/˜)MNMNrtó/u:hjyZ?Cãb5Bmpqf&“rty4 _ rtyZ4Gz{rhjz?/˜,6A s rt” w sI<rŽ?/rte@w yMb[fuVU!~Tdvjcpu B
ljîqfr qj ¹ * ;6.
#çfè+-,87;2çfæ"Z
#çfè97åç 8;6tåœå
pæ @:S€ ïVï;
hy!jWdvp?/ò1o
AI<y MNe@5JMNzŽI<9<s 9Ló/vjTSY|hjUV9LB>-XZMbs šj[NB:šp4 z,3H7}n4 4qR 4<ñB j
w Ks vj(ó/|p =@€ «y;>½t!¾hj~zŽUV s B:uViv 8}cj?O4<B ï ¾GcjLq\ ’V¹ MNyZU!äzŽXVs^q=B Q¥ v7b·<“s vn¾Ÿ4E‘L57y!s u~Ž4<–– B
$z{r?@qf?BrtADs^z{CrtE@s^o!E0z PP&DvjF?s HrZ+€GIBbŸJqKšj!D~tFs^I#ln"|VLyVF%MINF !OMEP!P'K4E
mpWSæ 6.zŽhj s #V;>vjç|Q8M 4qOZI<~tZ;>yZ
zŽhd@B1uV6tPQvpçC4zŽ4 yŸ=Q pñP qf
rŽV$rtéy!
~tR vSTFu½t‘@@ kCO|Vz{~€SrtqVs <lnœ‚&yZqfuplrt sztuVpo
vuV€j~tuyZq‘z!~Ž w^¹ r qfrt!V#y!¡›vb8 7@r-,q=šjZs œw s r{å ’ 5