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A"7]SA$H:A%Y-3 A'O4A('A*΁CA,zp%!A.JnSSA0qUA1su׫A19A2=A3 !2A4IA56A6sEѰA7bRA9IA:'-A;˺A< Y8DA=lA>HVA?& ҳA@ ^EMA@~WAA7)ڲAAA/-AB Y2AB2l]AC' uJACFhAtAD-lKnPAD1GAE3ftAEFAF9ӇAF}D?3AG?^!HAG3`9XAHD&AHDŽ{HhAIJDߖAI^,AJN)ҲAJ6E{AKRApqAKԪ7̒ALVrALHAMYҒAMAN\afANݑFAO^s]AOߔCvAP04l*APp3HQAP,APAQ1? yAQqZ.AQfn`‡AQbebAR1NxlzARq*зOARܩAR#AS0[IFASoHjASse*ASBAT.>QkATmsOAT<AT*AU*BAUiiAUrZ3AU95AV&X 0$AVeHAVxjAV >AW 1TAW^dAW#ɏAWSXAXoxb1AXWvJAXiI$AXG[j]AYjAYNŦFdAYe}bAYI;bAZbAZD AZ5{WAZ-AZ99NA[97A[u A[ A[#HA\+~2A\h*s\A\P3A\NA]qsVA]XsA]jwcZA]-"A^ C%#A^GcA^փ=AA^._hA^kfwA_4A_oRA_R!:A_SMA`"ڡ;A`-S:FYA`Jr1A`g(vlA`NA`CmA`!}A`q6A`-%_AaDAa1gZAaMHwAajN~@AaAa Aa 6Aa"j8Aa#FAb,Ab.2FAbJ};AbfXPэAbCċAbw Ab$aAbBh AbHAc XAc%5Ac@တ4Ac[ɳEAcv[Ac8}JAAc]Ac%9QavAcjڂ:AcJAd+Ad.x1AdH<Ada&sAd{c!vAdŷ%8IAdAd)˓Ad+9gAd ZP~Ae'ȾAe*m1&nAeBwAe[MAesMAeKAeJ'GAe_lAeI0Ae疥7Afe`LAfcFAf0ioAfGߜ@AAf^ Afu*W AfL5{AfcpAfDQAf\TAfԠAf#`AgD:KfAg%ƍAg;2ŀAgPD;cAgeJKAgz)X-Ag*AgrKVAgۍapAgYAg8:²Ag+TBAccumulates pods (curls) as they develop from pollinated flowers.# $%&s@Lah?@Lah@Ԍrڙ@Lah@Lah@Lah/?????+female_offspring0 !"?--#?)%@g@ _ЄB@j@nŜ@#!@@'&v@-6ϠA@1iT»@4c㣅@7K`@:Q @>I/O~@@Kl @B׹|f@D2a@F_NO@H*ejF@J@@M2Q;@OxG@P5@Rzy@SWIc+x@T-<`{@U$I{J.@W;&@X4P@Y@[Xx关@\WzDM@^(t@_H@`viaF@a9O(@aʞub@b1E7nx@cej@dYr@dz/nO:@e@fQc}h|@g (RÐ@g /g@h?ç@iA +@iL@jc;@ku@l1lMP@l@m<5@ndF@o [1]K@o?p@pKNFc@p% 4@qn3@qeY@q¦sT*@r &`@r}O@rt@s80Y@s_x>@syݽ@tOAi@tnj@u I>bW@uf ,@u¼ᷫ@vUP@v{" @vF@ƥ@w4@qs@w @w@xI /F@x^j8{@y$@y\ @ybh@z.o@zo@z,1O@{&'D@{p@{{%@|7Ɨ@|ޡ6E@|5#@}Hh,U@}Y{@}W@~W屐L@~,CS@ W"B@k@fe4C@V2@ /@9@fF@~Qʔ@.V@Kl}@d8@EW?@r^^@@@hZ@#IQ0@OˈL@{wAZ@ҽ@ݛֲ@1OsM@+'<@WJW_@|H@ =@ 1ز@}W@0W@\$+{u@Zxk@~6B@ݎg~@\K@3uTv@^KK@ @/@[aM@I9@3[l@]>@\{<@K@q‹R@׶@0vB@ZQs}@)@2r@;XG@V+@)`E@S#r@|5F@*{ @wf@uve@XJ'@Gx]@p8ru@{Zf@N4@.m@[@8_@`"s@@@6\@iD?@%{@$sa@KBߐ@r@3jsy@@׍@ ;v<@2;s@X+@}JkE@-Mu@x @G!@d@7Df@[֤/@:4H@pH@wW@Pe@n A@3w۰@V@yї@`y @@@/!&@@&"@H>@jm*@Ln@z@87@ۓ`@XOD@5@(Bf@@83@Hϙ@Xl@hbu'@xj@uu@l e@6L@dlz2;@vg@lJ@FR@-8~@@+ U@@]?@*T; @9HC@G'wn@U X-@b|6@pb.@~e@8Ri@aS>@OJ@6D @;ze@]@>D@ɫQ> @|YB@@ @(r@&;< Y@2gk@>y< @Jo@VK_@b s@m@y> @@5@?@`AV@ci/r@Gnm@ 2@Ѯ@/S7@ԉ7@ɖ4@B@@Yl1@V z@!|@+F@44v@=v O@F@Ow$g@X)@`x@i"w]R@qi6@yt@Us@e@8@Lah0Accumulates female offspring for yield results.# $%&f Ah-A`Q?Ah-A`QAh-@OK{Ah-A`QA`~uMA`Q ????Ah-,buds10^(7.1-.0000000126*pods), ( @ff ffff - >K Zp^    !"Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-AhqAg'oZAgEb³AgC'AgdWAgQƛ8Ag1쵠MAg&&AgyNAgήKҽAgǜ\8AgEjFAgԃAgͽkAgDAgOfqAg/AgҥAg/EAg|\5AgrJw AghXBAg^䗵+AgTM AgJvAg?V$Ag4]LAg)+uUPAgTAg!Agz?Af97.VAfzAf7AfexAf1Af}GAfT)`Af4 \Af$XeAf(AfQFNAfݢAftَ,Afi Af^twAfSMAAfH-C[Af=Af1Af&EAf$>AfBAf(Ae`AeZJAe- AeP MAezj [AeĭtAe7Ae*WO>fAethAe;-Ae^ZAeAey'AeoZ˂iAed)rpAeZS0`AdnBAd`]YAdY Ad[f|Add2Adu/AwAdBAdokAdz JκAdqBlAdg?;A,Ad]~ڹAdSl[MsAdJIAd@liAd6kAd-1VjAd#AWAdMgLAdʗAd_KjAc6,qhAc7-:UAcұ}AAcuAc MAcYAcŋ0AcLfDyAc#AcAcwAcd}Ac̸mAcAc|{Z;yAcs~45 Acj*Aca7FgAcXR;AcOt@!AcG|Ac>8yAc5s=(Ac,09cAc$AcTDAcNRZAc $Ac{AH*lAby2Abf!AbdImAbpٹ`AbejAbΙuAb9E 7yAb⬏AbAbR] AbFAbMAbAb-,Ab>EAb|e^AbtrٓAbl_3AbdAb\Z,vAbTn(AbM~AbE>? Ab=}NAb5NAb. #BAb&q1hPAb/Ab?fAb;Ab22[Ab_nAaGlnhAa0tSAarAa+s;Aa"pU8AaԨx\cAawƴ( AaS&c[Aa:(R$Aa,Aa*hAa4wAaIAaj x-Aa٘LAaUAaQmRcAa\*AazgcAatuEAam_uAagPaAa`2~A`wA`>RA`ЮA`n ]A`-9YA`͌tA`ŽizA`[O $A`30bA`~uMA`Q!Buds start to open at a high rate when there are no pods. If none are pollinated, 3.5e+8 will bloom by the end of the season (70 time units; 35 days). As flowers are pollinated and pods develop, blooming shuts down at an exponentially declining rate, because limited resources are going into pods rather than flower production. The buds go to 0 when accumulated pods yield the maximum kg of seed that have been obtained by Northwest Growers. An exponentially declining rate of bloom is based on data obtained from commercial alfalfa fields.# $%&UfAAgpu?Agpu?aںAgpuAamx)AagP???,wilting(DELAY(buds,10)*DELAY(unvisited,10)*DELAY(unvisited,9)*DELAY(unvisited,8)*DELAY(unvisited,7)*DELAY(unvisited,6)*DELAY(unvisited,5)*DELAY(unvisited,4)*DELAY(unvisited,3)*DELAY(unvisited,2)*DELAY(unvisited,1))AA                                                    !"Af(1Af@)Ag%'=AgʹAg"y$'Ag,Þ8Ag507SAgAg7AfUAfڥHAf<aAf(Af0YAfQ- Afw1Af1AfJqAfNAfawAfAfyt#AfncEr[AfcPǼAfX= &AfM'RAfBxAf6yAf+gYAf oAf Af %sAeEHAenAe򓜧Ae$fAeAezAe0Ae^^AeI Ae֜TAekAeg}aAe}HAesAeh}1W&Ae]H͸AeS`S\AeHtAe>d Ae3~Ae):Ae+ Aeѵw@Ae B\AeAd0mdÃAbtJAb01-$Ab4Y!Ab󒝞AbؗAbu6cAbZgLAbHBAb?H_AbEAbTNL3AblAb|sAb&)Ab<{AbyGF{AbqXMSAbi Aba"AbZPs!IAbRXAbK#NAbC]Ab<u^(Ab4]OLAb-9Ab%~Abz;Ab)'/AbZAbAbnmAaE%MAa%9AaXAa9cVAaqVAa JAa9HAa;ijAac%AaAa'\Aa=.)Aac%9ueAa|ZAa*lBAa,tIAa)0AanAaWkAaz AasFkAamx)AagPDelay functions keep track of how many buds opened 10 time units ago (about 5 days), and what proportion of unvisited flowers were left each time unit. If flowers are visited randomly (a useful first approximation, though possibly not true), then multiplying the original numbers of buds by the proportions of unvisited flowers in the previous 10 time periods should be the remaining unvisited flowers. Any unvisited flowers after 10 time periods flow out of the system when they wilt.# $%&mAoI?AoIAkn:$AoIAs~A5????,pod_development15 !"@ݻK@*`-@'&ʮ5@|&5E)@@A>E AAݰEA2LA[rSAM*AοkA~[^A3[DAGgAVWA?!A q1A '0¦A q[ZA u)A DN;A "8A rTA\*A ?A;Q/A>Aꎟ2SAG> A? A! ]*A,SA7SAAx?HAKc'ATt|A^ 3xAfև~UAoIAnAlXAk@ibAj7mAh'G:%Ag{ݩAf\YMAd:AcGxX)"AaLUA`npaWA^( >A]$ A\bAZ AVAS4v(;AOy2YAK6|AGJ_ADAYA@WA<Ы0A8HϽA52 vmA1g;IA-0ZA)黀A%| hA"AF//Ai(ۻAŷ A yA/A It9 A{ALtAcVA tq A%jnA $A#6ApؓBAA0NAWo 'A+A1AJfAzSAPA|7~ArAhЫJA^ATAJfA@)ƣA6e A,uJA"FV5AIA hAt>?AQ$FA"Ao~AjiAAż^A^RpAtAE4RA4k8A"LAuc'Ag,AZIAMVjA?6,\A2@#A$;eAa1ĘwA MA &tA mqA U͠aA 4A z{A Y!EA ԂA (ƩA CA \_AA vH5A h A [{ύA NkHA 98ncA $[sEdA 0wA ?A ;A fA )/׸A X}$A ܭEA }KA hjȘA T*`\A ?d !;gA *nA ݝ!A  A _wC#A ףA 7A 28TQA |A *) A pt9tA [hPQ A FR5^A 2<6A g>,'A ZPA 2a)A Ǩr?A !FA uA fCA E0 A %'ȱm A ?A ? kyA ϲA c7A ~A bY\A B3A !A yVBA!e݃Ax?A{e]A-E4gA_t!@A? AVyAہ~A$A.oAf[GA~2`MTAVb8A/)'Au[AmAa;YAGqAi\^ AA["WAh qA/A˃RMtA}A|{'AUI|A-uAA4<AߊqA,cAiA=AAr AX#As~A5# $%&f% @7۶?@7۶@,zWN@7۶@KN<@V6????+female_production_rate&cells_produced*sex_ratio*survivorship      !"?--#@ @3nX @4>;GP5@4s4@5@*I]@5Q@5{ō@68b< @6mK'@6H{@6V@6wXq@65p4@7TQ2N@7(S"@7@6J.2?@6Vb@67k@6l@6 w@6!@6\ @6b@6E@6l@6|_!P@6u2vM@6m!@6fHre@6_@6X@8!@6P4`@6I"f<@6BUc#@6:W@63_qu@6,F@6$媡Lq@6Ğ@6 @6 ?3@6sHK@57@5ʼ`*@5{L@5@5ԥ^1 @5'Gz|@5fMb@5h% @56@5c^@5P~e@5&&@5[@5~z@5tMö@5k=H @5a\@5X-@5NbZg@5Dās@5;'!@51L:@5'?@5RBX@5`\1@5mKٸ@4m @4xm.@4ʕV)@4̏iT@4ÒŤ@4,O,@4Ph @47"@4TEg@4z1H@4k"?@4\.@4N+a@4?U~w@40}4U@4!x@48@4|@3-~!@3= @3f(o?@3ȏ^@3 )x@3[&@3Hh@3@@3|M@3ib *@3VgG@3Af1@3,*@3O}HG@3%u@2$ @2@2C[N@2[h@2^ @2wS@2`<)@2I@21ڶ@2+^@2H@1R_@1^,Q@16G@12 @1br.@1xp@1a?@1J7r@13haB@1LԐT@1߻Hu@0v3ZքU%@/r?@.͗.}I@.2~ۂ@.\\&i@.$l jh@- /`@-xYN@-{XtW@-Cژ@- q@,lD@,',@,al@,)6U#@+x}@+@+@+Mƪ<0@+ @*7l^@*ס@*s~j@*=V@*\^@)ѷw@)I@)e 3@)0Ru@(2@(e_9{@(a:(@(XQ@(#"@'m^@'˼|@'QA)@'LqZl@'ԙ L@&9lB@&V{@&vix @&@3*@&N8F@%Ȉ@%I@$w'z#@$0O@#]v@#ːhUE@#[f"(]@#r8#@"".6L@"Z @"<ӳb@!@!C}@!d|e@!)3@ ɜ$@ ~X@ E6ν@*U@j\֎@Qp@KN<@V7Calculates how many of the cells produced are females.# $%&c @@@@?@@@@@@@@@@@@@@????@@?, introduced_bees500 !This parameter is varied between 500 and 35,000 females per hectare in order to create a graph of seed and bee yields as introduced bees increase.# $%&c @W3E?@W3E@g_t?G@W3E@ѫBKg@ѫBKgi?????, flowers_per_bee1/(handling_time+search_time)       !"@v;Ddj@zW{ 4'@}̷mT@{ @Y}'@=ψt@@@*O[]@L,@)q,@%u"@gȀ@ӂ @8 g@ 2{i@:D*@d0I@Ukh@0@XL@c٨@u@0aF@L/&У@f]:@~G)@g>N @rа@Vj@[@EA@uw/N@­@!@1ߒ8O@B_@Q!w@`kKi4@oa^)@}} eC@%+Z@z@Ѐm@;3@x-z@0B@@Xnm@.!'@P$~@pI@pC3@t U@@@2@n@/)W@>@㝇@-9`7@:VN8@F#k@O8&@T(@W3E@U`@Pc{@Gz@9@'ߗЀ@r` @꬈~@׉ݪ@d 1@W@\N@)@X@ @r@+*]@O@HG.7@2#@Կ1Ť@p@m&@8[@);@ 5@߿j@Yw .@2>@j`x@Y@&eV@z|@/Y@,@Mj@CN@Y@^=(@ ya@~/I@}NLP@@|iO;@{@z @yCh@x$6@w興s@v3t@uȶ9@t<4{@s_Ǘ)@=O`@n@`@h@57j@}k'@Dr @ ۍD@ W&@ ߤe@ wD[@ RӃ@g-5@g@;@ɝ'@K@=@ iY@(G^@t#FD@%OM@.@8'@CKޚ@Nt:@Z8@f}N]@s8K@TJ@(@Ko@xk@,@@U@@H @_ @14@G\@^S@uS*@V@ꧢ>n@͢@[>@ϝ@ @31;@S3.@s!@HI@ⷚZ1@Y h@C@&Yd@Mg@vr@ݟԮX@%0h@ @$plP@S1W@ك;]@شb@5(_@(@Piϫ@Նȶ@ԾM>S@@@2@nn?v@ѫBKgjThis calculates how many flowers a bee can visit in a time step., based on the search and handling rates.# $%&c  ?;nCy?;nCy??;nCy?;nCy?;nCy?;nCy?;nCy?;nCy?;nCy?;nCy9?????;nCy?, handling_time.00042    ?;n Cy!:For a time step of 4 hours, this is 6 seconds per flower.# $%&c  ?OU??OU?Vi?OU?P|sM?P|sMi?????,  search_time3/SQRT(open_flowers)+.0007 $      + ?F  !"?cZSâ?_2>?[s0?Y[\bS?W)!`?Vg9S?Ul?ULE?Tz?TD ?S۶KX?Sn?S0Jp?R)k ?Rj\Ϋ?Rn?5.?R9Jo_?R[ 4?Q7#?Q$?Qɣ?Qi3d?QGf"?Q(Ԃ,n?Q ?P N?P O?Pvʔj?P)c?PhK?Pz3?Pf]?PS}^;?PAoՂz?P/?*0?P =?Pao?O6?OW܃?OĶ#?O! J?O.;.?O~Nk?O]?Ou>?O #w?Oه?OU7K?O?O+?O?OG?Oq?OJ?O?Op?Od?OB?O#]/?O.-?OǶ?O-?O|l?O]?OU?O?Og?O?Ox, ?O?O=?׭?Os~$?OZ5?Ol(?OMĝ?Oh)?O ?Op,?Ozp?O?O;#?ONj?OSN?OV?O\?O8?ObcI?OEl\?O5%fq?O1.?O<?OSqt?OxNvl~?Ow?OP?O8<?Oh?Og?OsŸ#%?Oʤ!?Ot ?O-%?O7(?Ov;?OMSU?O$?OsJI?OȻf=?Oʚ?Ó i?On?Oaz^w%?O[ N?OZ_*?O_- p?Oi"\?OwPs?O܋M^?OޢP?Ok[?Oݎ?OP"2?O%s_|?OMդ?OxhЗ?Oˮ?O>?OƓ?O3 ?OeC;a?O?O?OyoY?O2?Pĝ?Pc?P6s?P6RA?P]X?P:8 ?PV {7?Pqn?P w!?P *j?P }Ȏ?P ~a?P Ge?PHI?P0uQ?PK"?Pf?P/?P?PY?PXT?P?Px?P"KQj?P<+e?PW%jo?Pqm?P?P"B?P  ?P!ٚH ?P"fz\?P$ !?P%&?P&@*?P'YhN?P(ri"?P)+ا?P*O2}A7?P?F.uOp?P@Y-?PAlE?PB?PC;K?PD" ?PE%?PFP]?PGW1?PH2 ?PI?PK З?PL1v?PM)| ?PN8YYr?POGvt?PPUP!?PQcgM?PRpm?PS}h?PT;?PUQFd/?PV'?PW):?PXi ?PY0H?PZ1?P[ZIX?P\8"Wq?P]?P^}6?P_?>3?P`Nu?Pb'"NM?Pc ?PdlA?PeL^?Pfj?Pg}?Ph?Pi!lf?Pj#G?Pk%IX1S?Pl&Bĝ?Pm&Jc?Pn&P7?Po%\Q?Pp# ?Pq!i6?Pr_g?Ps&?PtAr"?Puʃ?Pv A?Pw!S^?Pw=`?Pxǵk,?Py~_j?Pz]?P{bgZ?P|ɉL?P}ԓ?P~[?P ?Pճ?PW-?Plƅe(?PYh?PD#z?P/.O?PK3?P4[?Pp?PS?P9΀?Po?Pu/>?PU_a?P4^?P Y5?P_q%?P]fm?P-?P{T&?PRI@?P'C?P\?Pl?P|sMjAs flower density increases, the distance between flowers decreases, so the search time decreases. Density (area) is the square of distance; thus the square root function for search time. The 3 is arbitrary, because it gives reasonable values, but this is pure conjecture. Little information on search times as a function of flower populations is available.# $%&g+???????? Bee Offspring Production!# $%&c @[ 7?@[ 7@|@[ 7@[ 7@[ 7K?????, seed_yield.0000088*pods  >tv a   !"?t7?/)?_Kug?P?GFA?\? 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K?/J?⏃'?.eoW?Năެ?E? ɏ?m?Y?Hu(?+scX?劈q?4gc?Ho~ʫ?AՐ?m@?d $?0ba?!Kg?Z?R?<fE AAݰEA2LA[rSAM*AοkA~[^A3[DAGgAVWA?!A q1A '0¦A q[ZA u)A DN;A "8A rTA\*A ?A;Q/A>Aꎟ2SAG> A? A! ]*A,SA7SAAx?HAKc'ATt|A^ 3xAfև~UAoIAnAlXAk@ibAj7mAh'G:%Ag{ݩAf\YMAd:AcGxX)"AaLUA`npaWA^( >A]$ A\bAZ AVAS4v(;AOy2YAK6|AGJ_ADAYA@WA<Ы0A8HϽA52 vmA1g;IA-0ZA)黀A%| hA"AF//Ai(ۻAŷ A yA/A It9 A{ALtAcVA tq A%jnA $A#6ApؓBAA0NAWo 'A+A1AJfAzSAPA|7~ArAhЫJA^ATAJfA@)ƣA6e A,uJA"FV5AIA hAt>?AQ$FA"Ao~AjiAAż^A^RpAtAE4RA4k8A"LAuc'Ag,AZIAMVjA?6,\A2@#A$;eAa1ĘwA MA &tA mqA U͠aA 4A z{A Y!EA ԂA (ƩA CA \_AA vH5A h A [{ύA NkHA 98ncA $[sEdA 0wA ?A ;A fA )/׸A X}$A ܭEA }KA hjȘA T*`\A ?d !;gA *nA ݝ!A  A _wC#A ףA 7A 28TQA |A *) A pt9tA [hPQ A FR5^A 2<6A g>,'A ZPA 2a)A Ǩr?A !FA uA fCA E0 A %'ȱm A ?A ? kyA ϲA c7A ~A bY\A B3A !A yVBA!e݃Ax?A{e]A-E4gA_t!@A? AVyAہ~A$A.oAf[GA~2`MTAVb8A/)'Au[AmAa;YAGqAi\^ AA["WAh qA/A˃RMtA}A|{'AUI|A-uAA4<AߊqA,cAiA=AAr AX#As~A5A?PA}?,AVǴA/h110A nA AbM$AAs83s'AM}W{JA')|ALƝAܹ3A*~(AtAlPNAF.@;M@iJ0Υ@qն@ K5̏0@ɸ2Y@DQ16@R@{z f@@h@N{@;@7`p@ \@!0[:@I@Y|W@bݯOm@QE^@-GuDFaMultiply the calculated number of flowers that can be visited per bee in this time period by the number of bees foraging to get the number of flowers pollinated. If bees could pollinate more flowers than are in bloom, then all flowers will be pollinated in this time period. (and bees will gather fewer resources than they are capable of gathering).# $%&f*@`CP?@`CP@TD@`CP@D @Cr"????+cell_production_ratevisits/flowers_per_cell     !"@AE[\@E!I@H!s@K91]u@Mi١@Ogs@P@QCa>@R^tkp@S2a j@Tg@TʿuV@Uӵ@VU@W1[@W!.@X@YQ @Z ^L@Z^@[z @\:L?f@\m;|$@]@^`$)L@_xՇV@_͓7@`Aw@`PB@`^*D(@`kjm@`x+N@`$YA@`m@`a5@`XQ!@`L@`@?q#@`œIT@`˜0"@`CP@`@`ƪ{;@`o@`h$@`ͭ6@`D̩@`n8@`i8_w@`C@`ƃf%@` ,@`Ô@`6Pm@`eQJY@`"K@`R @`'&@`N@`1@`)A@`2@`[|$@`r@`e.@`Ʋ@`e@`1l@`|mc@`-\7@`?lE@`N @`}Y@z$@`ya @`uen jN@`qfQ/K@`mc/U@`i]B@`eS@ݦ@`aE?s_@`]3@`Yw^@`Ui@`Pva@`Ln@`G=%@`B%RA.z@`=1S@`88Gh@`3<@`.:~@`)4e@`$*%$$@`!d@`y@`vxx@`Ek@` kVe@`:@`a\V@_d@_ @_Ᏼ"@_y`@_̢5Ǿ-@_#ip@_@_]Rw@_@_m@_eWo@_-@_use@_gj@_Y5[w@_K=@_>Bd@_0iD@_"i@_ ѫ@_Jx'@^o+@^ǨF@^[@^BR@^€w@^F/@^Qʙ@^9/~@^x@^}9C@^o@^b;i/@^T~@^FU@^9g@^+LIR"@^%@^!g@^$En@] Vi@]g@] 7@]&N@]\@]"3@]lpz@]Wdڹ}@]BbAC@],@]-۾@]7 @\a@\׭ܚo@\l&>@\,H6@\*vO@\zpj@\mza@\XC/nt@\C @\-T! @\P@\}p@[Q9Yw@[''!@[:!@[s@[k@[l1 x@[J?@[)6R@[O6@Z u@Zʇ4@Z ~@ZRᵻ@Zb\+@Z@%f@Z[D@YB\@Ydf(@Y>qu@YE@Yynt<@YX 9(@Y7"*@Yf@XN@XԖtž;@X\@X@Xqcy@XPu.@X/m@X%,^@WY@WvL@W{]@Wlt9 .@WCRG;@WI(@Vs @Vʠ-1@V5J7@VyΉ@VQke@V) 9s@V*@U\'a@U @UC|@U_p/@U7*X@U9o&@T-)4@To@T9l3@Tn.@TEjFm@T3@SrX@Sf,x@SG0R@S~A/@SX@S1VS@S vz@Ru@Rk@Ro. @Rp]!e@RJxAU@R$q@Q4&@Q"g,@Q@QQp/||@Qcv @Q=m]&@Q4nO@P܍n@Pʈ~@P8@P}@PWMf@P1_S@P T)@Or{@O}OuO]@O0Zc@N3x@N}_ x@Nqf@MhD @MG@LJ"@Lx@3@L|[@KX@KC?R+1@J/ZlX@Ju(;T@J*ո`@I6|@I@K} n@Hi@HrB@H ddo@GlX@G>=/@F׈s@Fp܋\@F 9c:J@E@E= !6@Dփ‹@DpK@D @Cr"The number of tripped flowers is divided by the number of flowers required to make an offspring to determine how many offspring were produced during each dt.# $%&f%/@[L{?@[L{@V\@[L{@AQc@AEtRm????+ overflow&cells_produced-female_production_rate     !"@=QLW@,,34@4"_@:DN"@@(z@BVI,@D,&@F<@@H@Jr}Ѡx@Ll)@MSK2@O |3W[@PGwΰ@Pz_j@QS@@RM@RUԴ@S6@T6@T;Fک@UrX&@V)f@V@WB@WۡK0@Xs2@Y 0J@YmVY@Y?@Z0+H@Zo@@Z[m@ZψN8@Zqz@[h(@[25ָ}@[KXi@[bA@[wN@[*Ex@[5@[w\@[S@[;'@[֪9@[M:@[L{@[' @[sEg@[SB@[ex@[/I@[N#$@[In@[(@[[\@[ ܧ@[ @[([@[3-p)@[1&@[E@[o5@[z_:_@[t x@[n_ߋ@[hdn.@[bN"@[[@[UaGn@[NnU@[Hu@[Bu%@[;{@[5Y@[. R@['3}@@[!\qB@[I@[~Z@[ pS@[F%@[ ek@Zm@Zr@Z Zj\@Zo$@Zڞ.@ZҲ@Zʱw@Zž@Z{I@ZJc@Z]u@Z'[A@Zuaf@ZHIV@Zc=@ZK@Zw f@ZoZa@Zf9@Z^K2.;@ZUTq@ZM"Ͳ@ZD(ǝ@Z;A!@Z3>{yi@Z*`X@Z!GT;@Z3?@Zѩ@Z.֙{@YZ@YU>@Yw @Y^A@YQQ@Y¨}@YT`^@YnK@Y3Hl@YC@Yd:U@Y\E@Yw *-@YkW@Y`e @YUA0@YI8@Y>d*ž@Y3 ~@Y'l@Ya$@Y *@YBvd@Xbi@Xp@X㼩r>@X#[ @X:e,@Xb@X)\@X /w@Xs]@Xxh@XgPT@XVz@XEtz@X4#QU@X"̿@XW!J@W㛭@Wj @WU @Wnh!@W&@Wm @WF%@Wm cT@Ws @WboA@WPƼ@W?vVLN@W-Yl@Q+; @P$Ir@P2@PXQ@P7!i@PwSWk@PW/C@P6s$B@P @O$fU@O7 t@Ol@O-*y,@NO @NQ@Nn<2@N.v%m-N@M\ ؊@Mv@Mp2E@M0_-@L:@f@LD@Lrl,@L3A~@KK@K@Kuz@K6SF@J(Sȼ@JSQ@JxN~@J9*@I&&T@IX@I`m@I0@H7gƤ @HpҎ@HaB@GŴ p@GxL:}@G$o17@FJU@F{)@F'qmQ@Es@E~,y"@E)u|@DԸ! @DmӒ@D+60@Cvb+@Cz=@C-X;@BLbV&@B@B.R@AQc@AEtRnThis flow and the stock that follow (males_and_dead_cells) keep track of all of the males and dead offspring.# $%&s1@ ?@ @7Q@ @ @ ?????+males_and_dead_cells0 !"?=QLW@hEl@%)0fA@1OA@9cx@AXE N@F a@LA HB@Q7h"@THw1@X%K 6@[o@_:y@a:7N@cSF@f,?.@hvre)@j'/?q@mG@oλI.Ȩ@q4Y!@r轳@s'e @uWG~d@vqjs>@xI,"K@yjQNL@{a$_Q@|[F@~ǯpK@G>@Cz@ݦXa@Y8@t2@Ly(@&AA.@4@۳=@p66@xb@p,G @M`+@*A@aL(@@ÀW|r@9{@~@.##_@6@ ̚@zaU$9@@W@\X@4Mn@tt%@s$@D[=@QZ@\~@T8@8-ƀ?@Ci@;nE@XZ@W߫@]@ac@8GH)@.xZ@U$(@P@@Yp0@*ED)@2@OVS*@ yq@x It@@Y@P[s@[ @(?q@_t@ɸ@5P-@kQ$ @"@֌U۽@ ?@A%Ґ@v@?:TS@ȣ @y?@K @ZxcM@@ٟܕ@Thv@Tܫ@BA @ @PXm@'\@[%|>@o@D0I@@,p@`ڲ@qL@^@ *A@0Sw}@dE~@v;@s 7@Ht@2G%:@e@pJL@@|cʡ@1ϕ@d Ρ@gf3@l@km@/"3 @aOQÈ@׾i.a@r@2(@*>@\2΃@e@f@c@#u@T)bW@|j@zZ@&@:Tʲ@I&S@z;>@ $4@ۈjח@ cf@;7@keo@;@ˇ@\G@*|ԕ@Ytޑ@)@cH@>\o@@Dj@rȰ=@D@}^v@g@+@,M(c@ClBq@ZL @pu3@5SHF@@]#@@([@"u|@ p8c@!ę@7lB@L;_@bkV <@w*P@]E@D6@!/k2@ 3@=q@܇@ #}k@֠@3@GFlm@[p8r@o~_@nby @?Sm,@̮\@RB@k@D/J@t1@ @p@1=l"@C@Vt ӈ@h[_@{%s&0@LQBM@Q$N@6[F@@ԛ}j<@<@{Ǖ>@!LC@LwM@*L0@;#F\$@Lgܴv@]d@mx#)6@}R$@!LI@["@&t@鐏.@͠9@6= @0ꫦ@5 @ ;@R@R:@)IrW@8!t@Fw;e<@Uq@cb3@rCRUr@| @9I@77@j@%Y3~@V@<@*@ԋQ@r S@~P@1%A@!rh /@-+@:\=}@Ff@Rqt@^TNq@jFz@uزw@@s@~>[T@N@{@; B@@:"@z@֏@za@;@QT @>w7I@F6@I'@ # $%&c %3@mg?@mg@ZX@mg@mg@mg?????+ Total_cells&males_and_dead_cells+female_offspring     !"@E[\@AZ6*@)Jܚ@481K0@>f%@E֡D;@KT:H ^@Q0@T_@Xߝyٰ@] ,"@`Wj|@c+{@eu8@h4¿u@j4-@m1B8@pC{@qڹ@sF$y@t*@vz|@x&Lג@y(ς@{DEZ>@}oG1j@J3ְ @?g@^JB;@d:{@VZ7`@2V@&R@t@`D@]Ա@D@j*@ٽb:@Q@ehTq0@t-/R@׺c@wh@RUN@w^@ -C=@/9Y6@|م@ƈ<@# h`@H{/E@/}J@{@;A#B@K; @Gm@~(.@S +@ىZ*@_6}@Ɂ@j@'@']c@tx+@}@~?<@-@sS@ D4X@g@2gcU@zμ@@Q~|@QV+@Kzu@0  @_@XY,~@@%>@l@_?TFJ@$@z@#hR@d *@Ծ# {@|؉@'U@h*W@Ǹs@꓍=J@+K|@k>@~#@G]T@-bS@m @Ƕ_@hv@.4gh@n50@"+@s@-k@mj`:@Th@QF@+KLծ@kP94@)@DuOe@(ٞH@gm@wI$I@u6@u-mm@u$mn@uI$I$@um@u $I$@uI$I@t@tI$I@t$I$@t6m@tI$I$@t[mn@tmm@t@tI$I@t|I$@tnm@t`$I$@tRmm@tDm@t7@t)I$I@t$I$@t 6m@sI$I$@s[mn@smm@sՀ@sǒI$I@sI$@sm@s$I%@smn@sm@st@s]@sG@s0@s@s@r@rր@r@r@r@r|@re@rO@r9@r"@r @q@q@qȀ@q@q@q@qn@qX@qA@q+@q@p@p$I$@pI$I%@pmm@pI$I@prm@pVmm@p;@p$I$@pI$I$@omn@o$I$@o_mm@o'm@n@nI$I%@nI$I@nHmm@n$I$@mmm@mm@mi@m2I$I$@lI$I@lmm@l$I$@lSmm@lm@k@kmm@kxmn@kCI$I%@k m@j$I$@jI$I@jm@j7mm@jmn@iI$I%@im@ia$I$@i+I$I@h@hmm@hmn@hUI$I%@hm@g$I$@gI$I@g@gImm@gmm@fI$I$@fm@fs$I$@f=I$I@f@e$I$@evI$I$@e-mm@dI$I@dm@dRmm@d @c$I$@cxI$I$@c/mm@bI$I@bm@bTmn@b @a$I$@azI$I$@a1mm@`I$I@`m@`Vmm@`@_I$I$@^I$I@^fmn@]$I$@]Cmm@\m@\ ]This is the number of bees that are actually foraging for pollen during a given time period.# $%&c<?????????????????,foraging__fraction.75   ? !No bee spends all its time tripping flowers. This is the proportion of the population that is foraging at a given time. It is speculative, but changing it does not change the shape of the curves of bee and seed yield vs. introduced bees.# $%& d {A   _A'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''a P+{>@()Bee Offspring Production*Foraging bees create provision masses at a rate that depends on the number of flowers that are being pollinated. Some of the offspring produced die, but surviving females will be pollinators in the next generation.+, 'P(,(u? }@()Flower Pollination*Flowers bloom and are pollinated or wilt, depending on how many bees are foraging relative to the number of flowers. Pollinated flowers develop curls, containing an average number of seeds. Each flower is assumed to be visited only once.+, 'C?,> N -@@ '.%()*+, drmd  9H?,    H'cG:d()*+, 'f*W"FxluD( pN*N*)*( V\V\+, 'lbn()*+, 'sC b)()*+, 'sw H w['5()*+, 'fF=A (dk)(FF)*( [[+, 'f eZ .9G(b)*(qN+, 'mP {()*(v+, ' t@@ 8&()*Model of the alfalfa seed - leafcutting bee pollination system created in the program Stella II version 3.06 for windows (High Performance Systems). The model consists of two components, a plant component and a bee component. In the plant component buds open, are pollinated, and develop pods from which seeds are harvested. If not pollinated within 5 days, the flowers wilt without producing seed. The number of flowers pollinated depend on how many foraging bees are present and how fast they forage, which depends on flower density. Buds open at an exponentially declining rate relative to the number of pods accumulating until a maximum number of pods have developed. In the bee component, offspring are produced with the pollen and nectar collected in flower visits. 2000 flowers are needed to make an offspring. 50% of the offspring die. 35% of remaining offspring are live females. +, 'f/V3 }k3 !0(c)*(+, 'c:(\  -XS&8()*+, 'c  ()*+, 'c z ()*+, 'c} k jA()*+, ' t), )R (!Z()*(Exponential Decline in bud opening rate+, 'c} ()*+, 'cb  UoA()*+, 's d!2()*+, 'cUZ 5v-()*+, 'cJ   ()*+, 'at,]A ff??wI|w()*+, 'a , ()*+, 'a , }()*+, 'a ,  ()*+, 'as+  6yfy()*+, 'cc\(` V7()*+, 'sN^dAG()*+, 'a,# ##LL&H()*+, 'aJ,3 EEZ.EZ()*+, 'axb,K KKxbF]}xb()*+, 'dG, >"P[()*+, 'a,:5T a::55TT()*+, 'a+ }G C}} 33()*+, 'a+ h. z !00()*+, 'dC*+cg ":L()*+, 'D/o, #"_M()*Table 1+r, 'cliBF $_%'()*+, 'a&@+$ R%p()*+, 'c\ +vz &%()*+, 'a+$IQ II'QQZ}()*+, 'D. , (!L2()*Graph 1+, 'a5 ,pv pptt)6G46()*+, 'fu *C"-.(K)*(k+, 'gP' >P'9&U @+3A.()Bee Offspring Production*+, 'g?1:1 ,9B()Flower Pollination*+, 'a+*7M @@-11Ns()*+, 'a@@,*D] F FFYY.:y:()*+, 'f.V2 / u .02( m)*( +, 'a  +/7 cg055 E ()*+, 's+ 1P 4()*+, 'a+/e 2{{/ /()*+, 'c; 345()*+, 'a1+3 =4()*+, 'a(S+30 005(S(S()*+, 'c& $ 6X89=7()*+, 'aW,62 227W-\W()*+, 'aF( ,6& _Wc&&8F(A!-F(()*+, 'a6,  9#()*+, '''cNSTW <?=()*+, 'aF<,6- >:B--=F(KF()*+, ''''a, 4 A44Kx()*+, '''d*, D!3\()*+, '''a,d ddG_()*+, drmd10 +66py#>s###$>s##B#l -bb9").)?(d6#+rAlfalfa Pollination Summary./0".!.!|0.`B.!z0.A.!D0..G.!1 -+9"0'. Z'?(Qd6r#+rFlower parameters./r$ 0.!.!0.V:.!80. Z@. !0.C.!0.9.!+0.>!.!0.ș!.!d0.ʜ!.!0.b!.!p1 -'9"`).)?(\d6>#+rBee parameters./ 0.!.!|0.E.!0.F.!0.B.![0.dD.!0.!.!0. E.!0. VA. !21 ## p+n#r|#(%%r|#%B( 2bb#$ &6&&@Q6@Q+Pollination Model3r4J.D&?x 3@.24.R&? '/@.24. `&?=^AT.24.n&?Y?6vAS.2  !"#$%&&'()*++,-./0012344567889:;<<=>??@ABBCDEEFGHHIJJKLMMNOOPQQRSSTUUVWWXYYZ[[\]]^__``abbcddeeffghhiijkkllmmnnoopp4. |&>ГXXA˨.2wk_SF:." xk_SG;."   !!"#$%&''()*+,,-./0012345567889:;<<=>??@ABBCDEEFGHHIJJKLMMNOOPQQRSTTUVVWXXYZZ[[\]]^__`aabbcddeefgghhijjkkllmnnooppqqrrssttuuvvwwxxyyzz{2WXZ[]^_abdefhiklnoprsuvwyz|}~    "#$&')*+-.0134578:;<>?ABCEFHIJLMOPQSTVWYZ[]^`abdeghiklnoprsuvwyz|}2$>$&%@Q6@Q+Dynamics of pollination34.&?M.2~~}}}||{{{zzyyyxxwwwvvvuuuttsssrrrqqqpppoooonnnmmmllllkkkjjjjiiiihhhhhggggfffff4.(&?p =q.2~~}}|||{{zzzyyxxxwwvvvuu4. &?Fr2LfQ.2}yuplhd`\XTPLHD@<84433211100//.........///////////000000111111222222333334444455555666667777888889999::::;;;<<<<===>>>????@@@AAAABBCCCDDEEFFGGHHHIIJJKKLLMMMNNOPPQRRSTTUVWWXYYZ[\\]^^_`aabcddefghijjklmnopqqrstuvwwxyz{||}~4.&>Y?6v.2lkkjjjiiiiiiiiiiihhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhiiiiiiijjjjjkkkkkllllmmmmmnnnnoooopppppqqqqrrrrssssstttttuuuuvvvvvwwwwwxxxxyyyyyzzzzz{{{{{||||||}}}}}~~~~~4. &>=2.2}zwtqnjgdddddddddcccccccccccccccccccccccccccdddddddddddddeeeeeeeffffffggggghhhhhiiiijjjjkkkkkllllmmmmnnnnnoooopppppqqqqrrrrrsssstttttuuuuuvvvvvwwwwwxxxxxyyyyyzzzzz{{{{{{|||||}}}}}}~~~~~2WXZ[]^_abdefhiklnoprsuvwyz|}~    "#$&')*+-.0134578:;<>?ABCEFHIJLMOPQSTVWYZ[]^`abdeghiklnoprsuvwyz|}2k$v'+''@Q6@Q+,Standing Crop over time; by introduced bees3f4.'>Z&jjA.2|wrmhd_ZUQLGB>94/*&!!  !!!!"""###$$%%&&''(())*++,,-../0012233456678899:;;<==>??@AABCCDDEFFGGHIIJJKLLMMNNOPPQQRRSSTUUVVWWXXYYZZ[[\\]]^^__``aaabbccddeeeffgghhhiijjkkklllmmnnnoopppqqqrrrsssttuuuvvvvwwwxxxyyyzzzz{{{||||}}}}~~4.'>Z&jjA.2|xsokfb^YUQLHC?;62.-,,++***)))))(((((('''''''''(((()))**++,,-../0123456789;<=?@ACDFGIJLNOQRTVWYZ\^_abdeghjkmnpqstuwxy{|}4. 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V(>Z&jjA.2|ywtromjgecb`_^]\\[ZYYXWWVVUUTTSSSSSSTTUUVWXYZ\]_abdfikmpruwz}4. d(>Z&jjA.2~|zxvusrqponmllkjjihhgffeeedddddeefggijkmnprtvxz}4.r(>Z&jjA.24.(>Z&jjA.24.(>Z&jjA.2zuqlgb]XSNJE@;61,'# !!!!"""###$$$%%%&&&'''((())***+++,,,---...//0001112223334445556667778889999:::;;;<<<====>>>???@@@@AAABBBBCCCDDDDEEEEFFFGGGGHHHHIIIIJJJJKKKKLLLLMMMMNNNNNOOOOPPPPPQQQQQRRRRRSSSSSTTTTTU2WXZ[]^_abdefhiklnoprsuvwyz|}~    "#$&')*+-.0134578:;<>?ABCEFHIJLMOPQSTVWYZ[]^`abdeghiklnoprsuvwyz|}2$ ))@Q6@Q+Untitled Graph32#( p56 HG F0"r4  >   !  drmd P 7   7 !  drmd      % !  drmd  8I!1T9bb(4'2>444F L(:; h' @@@@p@p@@p@L@j@?ttt  ,Arial (# Setup #1(#6/5/95 3:37 PM(=Input Variables(RRun #(R}introduced bees(g1(g}1000(v2(v}3000(3(}6000(4(}9000(5(}12000(6(}7714(7(}8857(8(}100000 ))  @x2ABCArialCArial@D  E PEPF F d+rFF `+