Знакомство с эволюционной генетикой (Гаевский)
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QZklhlu khhl\_lkl\mxsbo Zee_e_c \ km[ihimeypbyo jh^bl_e_c |
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pa( f ) = paa + 0.5pAa |
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p (1) |
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(58) |
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+ yW1 + zW2 )(gW3 + jW4 ) |
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pAa(1) = p A( f ) • pa(m) + pa( f ) • pA(m) = |
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(59) |
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(xW0 + yW1 + zW2 )(gW3 + jW4 ) |
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p (1) |
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(60) |
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p (1) |
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xW0 + 0.5yW1 |
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(61) |
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p (1) |
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zW2 + 0.5W1 |
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(62) |
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42 |
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GZijbf_j baf_g_gb_ qZklhlu Zee_ey Z ^ey jZkkfhlj_ggh]h \ur_ kemqZy fh`gh hij_^_eblv ba \ujZ`_gbc
^ey kZfhd ∆ pa( f ) = paa(1) + 0.5pAa(1) − (z + 0.5y) |
(63) |
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^ey kZfph\ ∆ pa( m) = paY(1) − j |
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(64) |
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∆ pa( f + m) = |
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(65) |
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== p2 s0 + 2 pqs1 + q 2 s2
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hl[hj |
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IH ∑3 |
(pi2 s0 + 2 pi qi s1 + qi2 s2 ) |
(68) |
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∆ q = pq{q[f(2pq)-f(q2)]+p[f(p2)-f(2pq)]}/Ws,, |
(69) |
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]^_ Ws = 1 - [p2•f(p2)+2pq•f(2rq)+q2•f(q2)] |
(70) |
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45
ba\_^_gb_f qZklhlu ]Zf_lu gZ \_ebqbgm hlghkbl_evghc Z^ZilZpbhgghc p_gghklb Z1)
p•1 Z2) q•(1 - s)
H[sbc nhg^ ]Zf_l hij_^_ey_lky dZd kmffZ
p + q( 1 - s ) = p + q - qs = 1 - qs
Hlghkbl_evgu_ ^heb qZklhlu ]Zf_l ihke_ hl[hjZ jZ\gu khhl\_lkl\_ggh
^ey Z1 p/(1 - TV^ey Z2
J_amevlZl hl[hjZ ij_^klZ\ey_l kh[hc baf_g_gb_ qZklhl jZkkfZljb\Z_fuo ]Zf_l Baf_g_gb_ qZklhlu ]Zf_lu Z2 aZ h^bg wlZi hl[hjZ fh`gh hij_^_eblv ke_^mxsbf h[jZ- ahf
q1 - qo = q(1- s)/(1- qs) - q = - sq(1- q)/(1- qs) (71)
bebT1 - qo = - pqs/(1 - qs) |
(72) |
Ihkdhevdm qZklhlu ]Zf_l \ kmff_ ^Zxl _^bgbpm baf_g_gb_ qZklhlu ]Zf_luD2 \ i_j\hf ihdhe_gbb [m^_l lZdbf `_ dZd ^ey ]Zf_lu Z1 lhevdh k ijhlb\hiheh`guf agZ- dhf
Kh\f_klgh_ ^_ckl\b_ w\hexpbhgguo nZdlhjh\
JZkkfhlj_ggu_ \ur_ ijhp_kku kihkh[gu_ baf_gblv ]_g_lbq_kdbc khklZ\ ihim- eypbb b \ua\Zlv w\hexpbhggu_ baf_g_gby \ _kl_kl\_gguo mkeh\byo qj_a\uqZcgh j_^- dh ^_ckl\mxl \ qbklhf \b^_ GZ ijhly`_gbb h^gh]h ihdhe_gby ihimeypby ih^\_j]Z_lky ^_ckl\bx fmlZpbhggh]h ijhp_kkZ ^j_cnZ ]_gh\ _kl_kl\_ggh]h hl[hjZ b fb]jZpbb >bnn_j_gpbjh\Zlv baf_g_gby ih ijbjh^_ \uau\Zxsbo bo ijhp_kkh\ ljm^gZy b qZklh g_jZaj_rbfZy aZ^ZqZ H^bg ba ih^oh^h\ d j_r_gbx wlhc ijh[e_fu aZdexqZ_lky \ hi- j_^_e_gbb mkeh\bc ijb dhlhjuo j_rZxsbf hdZau\Z_lky h^bg beb \ djZcg_f kemqZ_ ^\Z w\hexpbhgguo nZdlhjZ
< jZ[hlZo :cZeZ> @ =jZglZ> @ ijb\_^_gu khhlghr_gby iha\heyxsb_ hp_gblv kh\f_klgh_ ^_ckl\b_ ^j_cnZ ]_gh\ b lZdbo nZdlhjh\ dZd fmlZpbb hl[hj b fb]jZpbb Bgl_gkb\ghklv dZ`^h]h ba gbo fh`gh \ujZablv ihkj_^kl\hf dhwnnbpb_glh\ u, s, m.
Ih :cZeZ ^j_cn ]_gh\ [m^_l hkgh\guf nZdlhjhf dh]^Z ijhba\_^_gb_ •N•xi ]^_ xi h^bg ba mihfygmluo dhwnnbpb_glh\ 1 wnn_dlb\guc jZaf_j ihimeypbb Dh]^Z \_ebqbgZ \ujZ`_gby [ebadZ beb [hevr_ _^bgbpu fmlZpbb hl[hj beb fb]jZpby klZgh-
\ylky j_rZxsbfb =jZgl [6] hij_^_ebe mkeh\by ^ey ij_bfms_kl\_ggh]h ^_ckl\by ^j_cnZ ]_gh\ ijb \_ebqbgZo \ujZ`_gby •N•xi≤ Z ^ey bo kh\f_klgh]h ^_ckl\by bg- l_j\Ze \ dhlhjhf \_ebqbgZ wnn_dlb\ghc qbke_gghklb ihimeypbb[i≤ N ≤ 0.5 xi.
46
>jm]bf ih^oh^hf fh`_l [ulv ihkljh_gb_ g_keh`guo h^ghehdmkguo fZl_fZlb- q_kdbo fh^_e_c oZjZdl_jbamxsbo baf_g_gb_ qZklhlu dhgljhebjm_fh]h Zee_ey aZ h^gh ihdhe_gb_ Ijb wlhf lj_[m_lky ^hims_gb_ qlh ^_ckl\b_ w\hexpbhgguo nZdlhjh\ Z^-
^blb\gh GZijbf_j ijb khq_lZgbb hl[hjZ b fmlZpbhggh]h ijhp_kkZ h[s__ baf_g_gb_ qZklhlu Zee_ey jZ\gh kmff_ baf_g_gbc qZklhl \ dZ`^hf hl^_evghf ijhp_kk_
∆ qh[s = ∆ qhl[ + ∆ qfml |
(73) |
∆ qh[s.= pq[q(W2-W1) + p(W1- Wo)]/Ws + pu - qv, |
(74) |
]^_XbYkdhjhklb ijyfh]h b h[jZlgh]h fmlbjh\Zgby
Ihkljh_gb_ ]jZnbq_kdbo aZ\bkbfhkl_c ∆ qh[s hl T iha\hey_l \ jy^_ kemqZ_\ \u- y\blv ^hihegbl_evgu_ lhqdb jZ\gh\_kby beb gZclb baf_g_gby iheh`_gby ^ey m`_ km- s_kl\mxsbo
=_g_lbq_kdZy ^bnn_j_gpbZpby \ ijhp_kk_ \b^hh[jZah\Zgby
H^gbf ba ijhy\e_gbc ijhp_kkZ w\hexpbb y\ey_lky \gmljb b f_`\b^h\Zy baf_g- qb\hklv JZaebqby \ n_ghlbibq_kdbo ijbagZdZo hkgh\Zgu gZ kms_kl\mxsbo ]_ghlbib- q_kdbo jZaebqbyo Ihke_^gb_ h[gZjm`b\Zxl k_[y dh]^Z m^Z_lky ihemqblv \lhjh_ ihdh- e_gb_ ihlhfdh\ ijb kdj_sb\Zgbb [ebadhjh^kl\_gguo \b^h\ H^gZdh \ jZfdZo f_g^_- e_\kdhc ]_g_lbdb g_\hafh`gh hl\_lblv gZ \hijhk dZdh\Z kl_i_gv ]_g_lbq_kdbo jZaeb- qbc f_`^m ihimeypbyfb h^gh]h \b^Z beb f_`^m jZaebqgufb \b^Zfb K ^jm]hc klhjh- gu hl\_lb\ gZ wlhl \hijhk \ jZfdZo fhghnbe_lbq_kdhc dhgp_ipbb hj]Zgbaf_gghc w\hexpbb fh`gh g_ lhevdh mklZgh\blv kl_i_gv jh^kl\Z gh b kjZ\gblv w\hexpbhggu_ jZkklhygby hl^_eyxsb_ ij_^klZ\bl_e_c ^\mo jZaebqguo \b^h\ ^jm] hl ^jm]Z b hl bo
h[s_]h ij_^dZ
< gZklhys__ \j_fy kms_kl\m_l g_kdhevdh f_lh^h\ ^ey hp_gdb ]_g_lbq_kdhc ^bn- n_j_gpbZpbb ^\mo ihimeypbc Fh`gh mihfygmlv f_lh^ hp_gdb lh`^_kl\_gghklb ]_gh- fh\ b [he__ ih^jh[gh hklZgh\blvky gZ f_lh^_ ZgZebaZ we_dljhnhj_lbq_kdbo k\hckl\ [_edh\ IheZ]Zxl qlh dZ`^hfm Zee_ex \ ehdmk_ khhl\_lkl\m_l k\hy bahnhjfZ [_edZ hlebqZxsZyky hl ^jm]hc bahnhjfu k\h_c ih^\b`ghklvx \ lhdhijh\h^ys_f ]_e_
FZkZlhrb G_c [1] ij_^eh`be ^bnn_j_gpbjh\Zlv ^\_ ihimeypbb gZ hkgh\_ we_d- ljhnhj_lbq_kdh]h ZgZebaZ [_edh\ < dZq_kl\_ oZjZdl_jbklbd ]_g_lbq_kdhc ^bnn_j_g- pbZpbb ij_^eh`_gh ^\Z iZjZf_ljZ ]_g_lbq_kdh_ koh^kl\h , dZd ^hey kljmdlmjguo ]_- gh\ dhlhju_ b^_glbqgu \ h[_bo ihimeypbyo b ]_g_lbq_kdh_ jZkklhygb_'dZd kj_^g__ qbkeh aZf_g Zee_e_c \ dZ`^hf ehdmk_
47
JZkkfhljbf ijbf_j hp_gdb ]_g_lbq_kdhc ^bnn_j_gpbZpbb q_luj_o \b^h\ ijbfZ- lh\ lZ[e gZ hkgh\_ ZgZebaZ ehdmkh\ dh^bjmxsbo [_edb djh\b < klhe[pZo ^ey dZ`^h]h \b^Z ijb\_^_gu pbnjh\u_ bg^_dku Zee_e_c b l ^ < kemqZyo dh]^Z ehdmk ihebfhjn_g \ kdh[dZo mdZaZgu khhl\_lkl\mxsb_ qZklhlu Zee_e_c
LZ[ebpZ
|
Ehdmk |
RbfiZga_ |
=hjbeeZ |
=b[[hg |
;Z[mbg |
|
|
|
1 |
2 |
3 |
4 |
5 |
1. |
Ak |
96 |
98 (0.20) |
92 |
96 |
|
|
|
|
|
100 (0.80) |
|
|
2. |
Alb |
100 |
100 |
100 |
99 |
|
3. |
Aph |
100 |
100 |
100 |
100 |
|
4. |
Cer |
100 |
98 |
98 |
102 |
|
5. |
Dia |
100 |
85 (0.67) |
100 (0.67) |
95 (0.88) |
|
|
|
|
|
95 (0.33) |
108 (0.33) |
100 (0.12) |
6. |
Est-A |
100 |
101 |
102 |
96 |
|
7. |
Est-B |
100 |
100 |
102 |
95 (0.17) |
|
|
|
|
|
|
|
96 (0.08) |
|
|
|
|
|
|
103 (0.75) |
8. |
G6pd |
100 |
100 |
102 |
102 |
|
9. |
Got |
100 |
100 |
96 |
96 (0.14) |
|
|
|
|
|
|
|
100 (0.86) |
10. |
Hb |
100 |
100 |
100 |
100 (0.92) |
|
|
|
|
|
|
|
102 (0.08) |
11. |
Hpt |
105 |
107 |
107 |
107 |
|
12. |
Icd |
96 |
100 |
100 |
100 (0.94) |
|
|
|
|
|
|
|
107 (0.06) |
13. |
Lap |
100 |
100 |
100 |
100 |
|
14. |
Ldh-A |
96 |
96 |
96 |
96 |
|
15. |
Ldh-B |
100 |
100 |
100 |
100 |
|
16. |
Mdh |
100 |
100 |
93 (0.62) |
106 |
|
|
|
|
|
|
100 (0.38) |
|
17. |
6-Pgd |
97 |
97 (0.15) |
94 |
94 |
|
|
|
|
|
105 (0.85) |
|
|
18. |
Pgm- |
96 (0.12) |
100 |
100 |
94 |
|
1 |
|
|
100 (0.88) |
|
|
|
19. |
Pgm- |
100 |
96 |
100 |
102 |
|
2 |
|
|
|
|
|
|
>ey jZkq_lZ ]_g_lbq_kdh]h koh^kl\Z ^\mo ihimeypbc ih h^ghfm ehdmkm bkihevamxl ke_-
^mxs__ \ujZ`_gb_
I k |
= |
∑ |
ai bi |
, |
(75) |
|
∑ |
ai2 ∑ |
|||||
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|
bi2 |
|
]^_ ai b bi qZklhlu Zee_e_c i - ehdmkZ \ ihimeypbyo : b <
48
< dZq_kl\_ ijbf_jZ jZkkfhljbf ihimeypbb rbfiZga_ b ]hjbeeu Ehdmk Alb (2) fhghfhjn_g b ij_^klZ\e_g h^bgZdh\uf Zee_e_f k bg^_dkhf QZklhlu wlh]h Zee_ey
a100 b b100 jZ\gu _^bgbp_ b ihdZaZl_ev ]_g_lbq_kdh]h koh^kl\Z jZ\_g
I |
2 = |
1 |
•1 |
= 1 |
|
|
12 |
|
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||||
|
|
+12 |
|
|||
Ehdmk&HU\ dZ`^hc ihimeypbb fhghfhjn_g gh ij_^klZ\e_g jZaebqgufb Zee_eyfb |
||||||
k bg^_dkZfb b IhdZaZl_ev ]_g_lbq_kdh]h koh^kl\Z jZ\_g |
||||||
I 4 = |
(1•0) + (0 |
•1) |
= 0 |
|||
(12 + 02 )(02 +12 ) |
||||||
|
|
Ehdmk3JG\ ihimeypbb rbfiZga_ fhghfhjn_g b ij_^klZ\e_g Zee_e_f k bg^_d- khf \ ihimeypbb ]hjbeeu ihebfhjn_g Zee_eb k bg^_dkZfb b < wlhf kem- qZ_ ihdZaZl_ev ]_g_lbq_kdh]h koh^kl\Z jZ\_g
I17 = |
|
(1•0.15) + (0 •0.85) |
= 0.15 = 0.174 |
|
||||||||||||||
|
|
(12 + 02 )(0.152 + 0.852 ) |
|
|
0.863 |
|
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|||||||||
Kl_i_gv ]_g_lbq_kdhc ^bnn_j_gpbZpbb ^\mo ihimeypbc hp_gb\Zxl ih g_kdhevdbf eh- |
||||||||||||||||||
dmkZf >ey wlh]h fh`gh \hkihevah\Zlvky nhjfmehc dhlhjmx ij_^eh`be F G_c [1]: |
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I = |
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I ab |
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(76) |
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Ia Ib |
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]^_ Iab kj_^gyy kmffZ ijhba\_^_gbc qZklhl h^ghbf_gguo Zee_e_c |
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N |
Q |
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∑∑ |
DL EL |
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, D |
= |
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, |
(77) |
||||||
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N |
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Ia kj_^gyy kmffZ d\Z^jZlh\ qZklhl \ i_j\hc ihimeypbb |
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∑k |
∑n |
(ai2 ) |
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Ia |
= |
1 |
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1 |
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, |
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(78) |
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k |
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Ib lh`_ ^ey \lhjhc ihimeypbb |
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∑k |
∑n |
(bi2 ) |
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||||
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Ib |
= |
1 |
1 |
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. |
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(79) |
||||
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k |
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< jZkkfhlj_gghf ijbf_j_ |
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Iab |
= |
1 + 0 + 0.15 |
= 0.383 |
Ia |
= |
1 + 1 + 1 + |
= 1 |
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3 |
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3 |
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Ib = |
1 + 1 + 0.863 |
= 0.954 |
I = |
0.383 |
|
|
= 0.392 |
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||||||||||
|
1 × |
0.954 |
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3 |
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49 |
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Hl ihdZaZl_ey ]_g_lbq_kdh]h koh^kl\Z fh`gh i_j_clb d ihdZaZl_ex ]_g_lbq_- kdh]h jZkklhygby'jZ\gh]h D = − ln I < gZr_f ijbf_j_' OQ Wlh ha- gZqZ_l qlh aZ \j_fy jZa^_evghc w\hexpbb \ lj_o jZkkfhlj_gguo ehdmkZo \ kj_^g_f ijhbahreh aZf_gu beb
J_amevlZlu hij_^_e_gby ]_g_lbq_kdh]h koh^kl\Z,b ]_g_lbq_kdh]h jZkklhygby' f_`^m ij_^klZ\e_ggufb \ur_ ijbfZlZfb ^Zgu \ lZ[e <_ebqbgu,b'ihdZaZgu gZ^ b ih^ ^bZ]hgZevx khhl\_lkl\_ggh
LZ[ebpZ
|
RbfiZga_ |
=hjbeeZ |
=b[[hg |
;Z[mbg |
RbfiZga_ |
|
0.60000 |
0.4844 |
0.3764 |
=hjbeeZ |
0.5108 |
|
0.5756 |
0.4466 |
=b[[hg |
0.7248 |
0.5523 |
|
0.5050 |
;Z[mbg |
0.9771 |
0.8061 |
0.6833 |
|
J_amevlZlu ZgZebaZ fh`gh ij_^klZ\blv ]jZnbq_kdb jZkiheh`b\ \b^u ijbfZlh\ \ m]eZo ibjZfb^u ^ebgu j_[_j dhlhjhc jZ\gu ]_g_lbq_kdhfm jZkklhygbx jbk
=b[[hg |
=hjbeeZ |
|
;Z[mbg |
RbfiZga_
Jbk JZkij_^_e_gb_ \ \hh[jZ`Z_fhf ijhkljZgkl\_ \b^h\ \ khhl\_lkl\bb k f_`\b^h\ufb ]_g_lbq_kdbfb jZkklhygbyfb
H^gZdh dh]^Z qbkeh kjZ\gb\Z_fuo ihimeypbhgguo kbkl_f klZgh\blky [hevr_
]jZnbq_kdh_ j_r_gb_ l_jy_l kfuke lZd dZd ^ey1\b^h\ lj_[m_lky©N-1»-f_jgh_ ijh- kljZgkl\h
R bfiZga_
=hjbeeZ
=b[[hg
;Z[mbg
Jbk =bihl_lbq_kdh_ nbeh]_g_lbq_kdh_ ^j_\h g_dhlhjuo ijbfZlh\
50
Dh]^Z bamqZ_fu_ \b^u w\hexpbhggh k\yaZgu bo jh^hkeh\gmx hij_^_eyxl ke_^mxsbf h[jZahf W\hexpbhggh ijh^\bgmluc \b^ \ gZr_f ijbf_j_ wlh rbfiZga_ ihf_sZxl gZ \_jrbgm Gb`_ jZkiheZ]Zxl \b^ ]_g_lbq_kdb gZb[he__ ijb[eb`_gguc d i_j\hfm ]hjbeeZ AZl_f hij_^_eyxl kj_^g__ jZkklhygb_ f_`^m wlbfb ^\mfy \b^Zfb b ]b[[hghf b f_`^m l_fb `_ ^\mfy \b^Zfb b [Z[mbghf
(0.9771+0.8061)/2=0.8916. KjZ\g_gb_ kj_^gbo \_ebqbg ihdZau\Z_l qlh ]b[[hg, ih \b^bfhfm, [eb`_ d rbfiZga_ b ]hjbee_ q_f [Z[mbg Ke_^h\Zl_evgh gZb[he__ ijZ\^hih^h[gZ ko_fZ nbeh]_gbb ihdZaZggZy gZ jbk
Kibkhd ebl_jZlmju
1.:cZeZ N <\_^_gb_ \ ihimeypbhggmx b w\hexpbhggmx ]_g_lbdm F Fbj
230 k
2.J_cf_jk B N Hkgh\gu_ [bheh]bq_kdb_ ihgylby b l_jfbgu±F Ijhk\_s_gb_
k =jZgl < W\hexpbhgguc ijhp_kk F Fbj k
3.DZc^Zgh\ E A =_g_lbdZ ihimeypbc F <ukrZy rdheZ k
4.DbfmjZ F Fhe_dmeyjgZy w\hexpby l_hjby g_cljZevghklb F Fbj k
5.K_\_jph\ : K Hkgh\u l_hjbb w\hexpbb F Ba \h F=M k
6.=jZgl < W\hexpbhgguc ijhp_kk F Fbj k
51
Ij_^f_lguc mdZaZl_ev |
|
Z^ZilZpbhggZy p_gghklv ]_ghlbiZ...... |
34 |
]Zevlhgh\kdb_ ijbagZdb......................... |
5 |
]_g_lbdh Z\lhfZlbq_kdb_ ijhp_kku.... |
23 |
]_g_lbq_kdZy ^bnn_j_gpbZpby............ |
47 |
=_g_lbq_kdbc ]jma................................. |
43 |
]_g_lbq_kdh_ koh^kl\h.......................... |
48 |
=_ghlbibq_kdh_ jZaghh[jZab_............... |
5 |
]_l_jhab]hlghklv..................................... |
8 |
]_l_jhab]hlghklv fZdkbfZevgZy |
|
h`b^Z_fZy............................................. |
9 |
]_l_jhab]hlghklv ihebfhjnguo ehdmkh\ |
|
............................................................... |
8 |
]_l_jhab]hlghklv l_hj_lbq_kdb |
|
h`b^Z_fZy............................................. |
9 |
]jmiiu djh\b........................................... |
5 |
^bgZfbdZ ]_g_lbq_kdh]h ]jmaZ............. |
44 |
^j_cn ]_gh\............................................ |
23 |
_kl_kl\_gguc hl[hj .............................. |
34 |
bg[jb^bg].......................................... |
7, 25 |
Dhebq_kl\h ]_ghlbih\............................ |
7 |
dhwnnbpb_gl bg[jb^bg]Z .................... |
26 |
dhwnnbpb_gl hl[hjZ............................. |
34 |
djbl_jbc ihebfhjnghklb ...................... |
8 |
fZdkbfZevgZy ]_l_jhab]hlghklv |
|
ihimeypbb........................................... |
13 |
f_g^_e_\kdb_ ijbagZdb .......................... |
5 |
fb]jZpby................................................. |
31 |
fgh`_kl\_ggu_ Zee_eb ........................... |
7 |
FmlZpbb ................................................. |
28 |
hl[hj ]Zf_l............................................. |
45 |
iZgfbdkby .............................................. |
15 |
iZgfbdlbq_kdZy ihimeypby.................. |
14 |
ieZlZ aZ hl[hj .................................. |
43, 44 |
ihebfhjnghklv........................................ |
8 |
ihebnZdlhjbZevgu_ ]_ghlbiu............. |
18 |
ihlhd ]_gh\............................................. |
31 |
ijbagZdb kp_ie_ggu_ k ihehf ............ |
16 |
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53