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Flowers take 15 time units to travel through the conveyor (mature into pods).# $%&sA(L7?A(L7ABZA(L7A(L7A(L7A?????,pods0 !"A(-A@!?XAL`UAU,?^A\U?%~AaASͿAeEAjky>AnrM<ľAq{K1As90Av=1e]Ax`uA{N3A}W)XAVp ASA(i?3AAAXd^A1~Ƕ7A)7_Ad\~-kA/A̓OAA-Ag۩;A@^AêA˭[AŻM(AAnAA_]AHuAAAAPJًA}y@XAQwA`z AҭM@AʴAtIjA* NwA}YAshA?yAf A&TAaQdaA+7A!Ae A;6U͔AB\6AyM!*A@Ab\Aº2:A"˥FxAQ{xA=aA<A8dA쾤sA?E>N2A|>rVAO/A#IԱAga6IrApAY0AAQpkAAA;lTAA'AH޼Ag~I80AI(AkA3~A3^A?UA?mA2îBA{wA`@{xA)S[_A4zrw"A>h[AGcxAO2AV۰>bVA]E2@Ac,6GvAhAm ;ArW-AvaAz BeA}[zA^qA[UAxAN0A>9A|Az&/QANϲAq->AiA礅zALjhAAˤBALAeTAnSA\xA@ZAX\z:A<Aq ADAkVBA XA8iAVUIA)A#{HAA=AF`Ay 5A[}Ak A!A)AP\Au^A@ȏ11A@Ȑܿi@Ȓ-zU@ȓC:IQ@Ȕ@(N*@ȕ&Ry@ȕ @ȖOP`@ȗfI@Ș@p@Șz@ș/'@șH @Ț;@Ți/u@Ț?@ț;@ți"n(@ț x@țn̴@Ȝ0/@Ȝi̩@ȜƵ@Ȝ2qQ@Ȝsoz@ȝ)U@ȝRv@ȝyne@ȝ^:@ȝz @ȝ:78@ȞD[@@Ȟ U@Ȟ>)@ȞZrX@Ȟv6@Ȟ@ȞO@Ȟ~( 7@Ȟ\Yx@Ȟ:@ȟ @ȟ%%_@ȟ@ȧ@ȧ @ȧ6-@ȧ_`@Ȩ.@Ȩ&`a@Ȩ:;9@ȨN@Ȩa@Ȩu!@Ȩ90Accumulates female offspring for yield results.# $%&f Ah-@OK{?Ah-@OK{Ah-@ڲrAh-@OK{@r/@OK{ ????Ah-,buds10^(7.1-.0000000126*pods), ( @ff ffff - >K Zp^    !"Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Ah-Agx\b=aAf(mAe JAdpuVAc[`t2XAbE%Aa3o4A`$&A^8\ؒA\7o|40AZGB:OAXizsAV׬ATqAB8RAAprA>u}A;  A91$A6B16A4ulA2sUnA0>-A.#Qg A+( A("!A&18W^A$rA"+ًJA s¿fqAP:iASA|Sc8A7,t1A0~;A]§A.AwgA QA Q)grA6'Ak(A7.A$hA$@3@Dx@Rw?s@2'@BoqY@}c(@cU@·@)V@Kt@zCצ@8@m~A@1jwq{@[q@+R%@h@@bJ@#fC@֍%@^U@Rqr䞛@dP>K@Ґ5r@Ӱ7@+ʺ@ЖE@w s@V/d@3Sa g@_Cb@͢ bHQ@z>@aƟR@yOf@aD{@[X:@ʕ"/@? H@S@ɭ1@oеXM2@8t᯽@83@3rL@Ȳ!¡4@Ȏ@mYY@PtU@6 Ο@`@Z@.?@.@"w@ŽH@Ǹ%N@Ǭ8}@Ǣiwt@ǘE&/@Ǐ^@LJE i@|@y/߅@sǿK@mUak@hl&@c˯1gt@_I@[s]l@X9xq@U@R@Oq$@MRw @J@H|@Fܱ9@E"Zg@CT@B9@@_@?i/@>86pB@=o@< FW@; $@:x0:@95DN5@8ZW-@7.d4@6㌧*@5 0@5Br@4!@3vj@32,@2 g@1`@1GX @0u@0,j6@/x*@.K@.NSQ@-pTo@-+T=@,AZ@, K~@+J@*Q85@*i @)H6,%@)Uu@(̱,L@(DPVl@'w/@'5!F7@&*@&'^@%s$,@%m@$ 3@$y@#9@#(Q@"E3@!+u @!yQf@ |j@ qe @@ig?@gD@bDZ>@߃W2@\3@i@@U.@ҹ@OF4@̼9@Id/@DY@D(@eV@>ZN@l@9\e@l @41N@@/*@3@*C@J@%zg@!<@ f@M@@|@{z@̸ a@|Z@r/@OK{!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.# $%&UfA?aں??aں@(A?aں???,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                                                    !"?aں??2Delay 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.# $%&mAkn:$?Akn:$Aj`&X)Akn:$@06@0%????,pod_development15 !"AH-AUMgAXɹ,AZ؝7A\#ĂA^MUlA_PxPhA`ەAa_ Ab$ͱAboyAcZYagAcx!DAdbAe+R]0Aep*:AfMr.2 Aji!Ak c( Akn:$AkJedw/Ak&[f_AkiAjx(AjAjQAj{꠪Aj\H:Aj=!b!Aj 7Aj@wAi4pAi_ϩ'AiIjAi.Fh5AhzQ>Ahbc6AhOAha+AhJí@Ah8XDMVAh+;fAh! ]rAhw3bAhXAhAh x@Ah 4R|AhmnXAhDMhAhdtAhX{}AhȍAh\_6Ag\@8WAgI:+Ag AfcuzAebAdʨ!Ac5 Ab^Pv0Aa?sAa6A` U>A^.}M`A\K>3&AZs|AX8դAV6(AUIAS AR4KAP2AN?5ALVyAI!MAG5ߎbAE_ACLjAAPPA@M"ԴA=Xj:A:-:GA8AJ6%A5-]A3jƌA1Q02mA0>rK0A-b1&~:A*$?>A( TKA%bڕ9A#vܞA!տA 'L3AGֱHA OA `VA+@A5BJA"W=AqI#rA TA @p{AҊ4A$$A>AʁA"02*@?u@ .@o@ C@yO@-j@d,@r97@ N2Q@yM@'N`@gzn@2<@ LDB@;i@Tx_@;Wń@h@{q@WIս@ڸ_]W@ֈ@Z]\@O3ӎx@`.Ȝ@Ҍ8N@5r@( ѳ@ВVtP@ ٍF@+ő@W]Pu@͙*06@CLz7@Z%@*{@[@]:@@ʏh@9 'P@/c @ɨpV@j`@3@+@ս~x@ȭ֯ҳ@ȉ1Hs@i@L6&F@2 XM@:=@*@c@T{z@CYy@f@Ƕnp@Ǫe0@ǟM0@ǖ]@Ǎ\ACP@Dže W@~&4@w>@q D@l\@g#+Z@b!A@^|@Z@WKЉ;@T*_@QOpAf@N,w@LN`@J~!8@Hap@F?,l@DT]@BT@A~@@!S @>ܸ$'a@=hD@@@պà@4O@čRr_@obg@#@%45@O[@2B@J׬@V& @SGwl@]Lo@Q<@ @Bp մ@d@Aas@uM/m,@{԰@~?@~?4@|@@{j2 @yR)@xUYq@v/@u[Iz@s8ę@r7V@q=#[@o(Kk@mC@kC,Gc@irp @gqM@e*tKՍ@caE:@a*T@`*Oz@]we]J@Z@Xb@V&?@TI ]@R=Vii@P"(@M~˭R@K)=Ă@H@FJ7@D1L+@BJ#"@@@j9@> U#@;@J?x?zr,?} t?#hMs? 9x?4=?svq?S?S|?o?ޕ}?܆$?Vm?yLN?x[h?듢X?DŽJ(?yl+?o2V8?1x@?\9?oa+?V?hp?&:eE?a?L|Jh?Hrc1? yX?طLbH?i?~n?XUz?6PM)??xDX?wⱁ?C ? 9?[Y?䖀he?䇬S-5?zDמ?n#νt?c(UQ9?Y5?P0þ?HXJ?@p6?9C9J?3b^?.%1?)d&x?$zGK? I20?x'FU?Nk?һSO??Jщ? (Ӱ? ? y?lh?&c?2u? X Y?{J?uBm?K2'?5?1‡?=8H3?V"H?}X?s=?Ί?.CS?z? #"?'֌]?Gf}d?eS?T@?^?2Ss?Hgz?北?r?db_?9?7q4?+I?Ir?L9u?/3M?N?' C?쮺-?77c]?b-?J,?ԃ?_Z0W?#?vW+?i\?L9?;+?Mf?5?.?P&?ްA-?l"?p[?3BpN?O?7"P?4V?ë:"*?RH?}?p,$?@w,@wY̾@vk@v(L q@u߆h@tDV@tR9@sۣ@s` a@rwQ@q:M@qBIW@p豈@pC@o Xaڏ@m&@ltn@kpx@jSI@iw[@h@g*Q@f*@f ‰@e4a@dc17Y@cV*@b{@bk @ai{@`,.pF@`$%C@^\@]sU@\PV$@[ctu@ZM@Y@kR@X=B!@WDOߜF&@VT"&k@Ul@TۥI@S @R%@R(@Qo1t@P,hp@P(^@OXE<@MAVY@LA,@Kr@J!v@J5@ISPa )@H_=p@Gd\@G[\e@FΧl@FN1@w@EL@Em~I@E @DD@Dd >@DS/@Ct @C<@Cgg@C7[;@C wle@B3@B9;@BXמ@B' Y@BiS@BQ@B<}Z,@B)t @BO @B۱< @Ah@A_n@A XoM@AѨS@Aϕ{v@A=+Rq@A:H@Aɪ@AT@Ag$@A]@Ab֊L@A3:@Af@A@Aͪ@AIFO@AX^@A@AbZ @Ao~@AI@Ar64p@A jw@Am@A_<&o@A>k@A6@A~E:@A}i/@A|v@A{C@A{9N@Az2~@Az .@Ayv:@Ay*@AxXk*@Ax!9D@Aw@AwX<3@AvtE@Avd@AvSJ@AvHe;@AuK @AupAx@Au* @AtzW@Atvd@Ate|WI@At' @AsGFw@AsFvt@Asvz@@As=ʝu@As䞶@Ar7@Ar@Arcu@Ar.|\@AqNR$@Aq~@Aq b@Aq`&|@Aq-c\@Ap;b @Ap7@Apv@Apeʹ@Ap4-@Ap~L?@AoҊ"@Ao.s@Aoq@[@Ao@@Ao6@AnXs@An@AnoVL@AnO_@Anb@Amt@Am@AmwW@Am`p@Am0J^@Am@Al`!@Al[@AlqDz@AlB;1a@Almt#@Ak5?@Ak@AkGqX@AkTH@Ak%l@Ajn@AjƢ.@AjCGC@Ajg^#@Aj8@Aj 9Q@AiY{@Ai\3@Ai{H@AiK@AiJ@Ahoo@Ah+v@Ah}@Ah_Z]@Ah0l#!@Ah0]0@Ag&jThis 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  ?Vi??Vi?UգI&n?Vi?_G\?_G\i?????,  search_time3/SQRT(open_flowers)+.0007 $      + ?F  !"?cZSâ?`4?]#v1?\ 8j?Zޞd?Yʠ?YNkag?Xo?XP.?Wd^?W9`.g?YCI8?YF9-'?YI=r?YK(?YMe?YNOM ?YOnrD?YPO^{?YPҒú?YQ4ߙ)R?YQ~WF?YQ;?YQpA>?YQ?Y\!qR?Yu"0[?Y?YФq^?Zqd,_?Z[ }J%?Z4R?nM}?J"-?T"cv? *i?@ID?/#A?g߉#?_XEL?:?}C#T"??vd?g!G?LD_$?Ԩ? ?]5w? u??6.?t2?nC+?M?/j[?:(Ї?aOs>?$wD?Sn-?VХ?w?L? )^%?d?1I ?B,?P,B?^~{ ?jԸ?uڂ%'?L?Y?tlI}?/?gͯ\?3>ǧ??k\?#!?(z#l?;6?B9~?o?pW?ʢT dY?Y?_5f?o\dB?Q3^E? ?֝q%?%O9?ay?ڙU ?۸&?\?ݵCQ?ޘ=_e?k_&?0X?^?kߌ?8?&(?e?2n?tUL?+?mګ?85?T^#?¶^?-?v;?_=?^Ь?? `?!,?|f{P?ؾG?30?ꍻE}?桫?>u?ȑG?7vWK?AI?-[ ?7N?@?Ɵ?&U[?:-;?u?Tӓ?1?x$?96v?&`?x0r?o9P?Do?k)?g:? ,[$?]ڃ?s-?`V.?Ol#? ]?%=?@n,?1? P?1W?%GC?=#?!MN?qW tv a   !"@DZ@@3 '^[@@4[@Hl`@PWyp|@T뿱@YMTt@^@aJְ@d)Sn@fg*Q@iT:@l宲F@oWP@qFu4@r׾:@ts\~@v i]} @wȉrpe@y*'?@{CӒVZ@}@~H@_G@Q> @GWj@AqR@>A@:hx@49@.-Mh@&+Ta@ @|~0Y@蕓@@7K@@~#g@;/@2lc@Uء@z[ @?=+@@2@#F[@@pTE@uӵ@@IU@T @ެf@3E:@\bw@_r@T@>j`r@^ @t @;ҁmuc@O @v΁L@E#@s$!@cjW@cwHy^@4z@|@i/v@T2ct@@@De@M7yH@FI@z@+L@[0_@1M@Z@s@'p}s@Q|@xLZ@w@v@ډV|@V@t~@%@1zT@&۟@/#/@6>5@=׾ڱ^@D,@@Io@Oǽ)@S@W@[k@_Lz@bo@eFՠ@g@@j-X,;!@lI7PW@n3 @oC,@q͡@r@t@xJF@uop@v@w@xdی@y5M5I@yC1@z?@{?@{-0@|R# @|ʢa@}8@ @}@}@~J"@~ZXB@~WHt@2@TW @@ fU@\@~W@8H@[$@}e@E*@ >@~ @@e@M%@5ii_@JZ&@_[Ap@s%CA@B܈@@k3@?af@QG@Y@\o@h1/@/@C@- &G@<*8A_@K)@Y b@hg#@w@C/@c"@@<@Q9@Tʩ9@IDƖ@0# @ ?@9W@"@\ @-C@: @Hb@VZ@cH@q2X@~yq@Or@l@]P@_@^P@#@UV@^@Cl{@P@*FO`@ ^@. @;y.@H4@VS &@cI˿@q($O@~. @C@bh@:@0R'@H@$D@a@sb@)Z@@|.@RNY@,mb@:#@Gwu3B@Tc@b8@o"l@|LAssumes an average of 4 seeds per pod, 2.2 mg per seed. (.0000088 kg/pod)# $%&c ?ffffff?ffffff??ffffff?ffffff?ffffff?ffffff?ffffff?ffffff?ffffff?ffffffL?????ffffff?+ sex_ratio.35   ?ff ffff!MThis is the average proportion of female offspring (Baird and Bitner, 1991).# $%&s@d}xq?@d}xq@| $y@d}xq@exҜ@exҜ1????@exҜ?+cells_produced0 !"@xb@H{@=;%@@N4mt@<<.@(@(cN>@C{̶@18I@|q7@Q ?@~@ؓ:k@—,@;W:$F@8QV@"7 @kh@W@Fɯ9@h@\G]@ೣ{@`] G4@o6@Q"E^ @6nh@FV@>|@YLJY@d}xq@c$d@ZI@Kmg@8M[@!?Ił@ >wr@Yx@ԳZ@! @ӕ@c8@)4@r@@f9@^M@:s3<@_8@׭@l@۶@@ͭFЂ@W)@;Oì@u%@#@x@](@ ߵ@r@;D@:M@vJVu@>@< `s@yJE/@푭/,p@IC-_@L@Ș r@%X@@*%ϸ@>2M/#@Q@!V@<1@-EMs@m|z@B?a@6L @`,-@$,@\R@:,f@'I {@x @3()S@j@B@?wUͶ@dl@ߤ@">f@^W@_Oc@4@G@&[@+@[@}Kڂ7@z@x wSe@uЋI[@si@qʘ;2@p6=@mh3F!;@;S~@9OT73@7A@5iV@3$r4p_@2F h@0@/K@-k@+A$@)_UQ@(X:@'@69@%b8c @$5@#։@"iV@"6Ӯ9@!?`l@ j@ j)o@TXH@@GJH@-?@\B@wl7=G@є(@ (G%@-7@g>@k@@֌Ji@ȥÊ@ɮCB@0 @i @A4kɓ@@ ,@:!@ØA @x@8T @h +@p{f@`@R[cZI@EH(@9pY~@.8/@$@]@\@ ͩ@,)@%R@r@y&6@!STyf@Q+@7Іw@ƵR@6f@f}@"@ڹTG@؃Dd@z_@Ԛf@@Eѝ@99@f @2@@@k=@ɰ@ȭ:$@ǷM"b@Lo@@ Eq@Jk@Äv2@Ş$@ zW@Xɫ@x@e@X><@-x@K@v:~k@ߕ@Aa&@p|_@2@8Bg@ip\@]F@ܦ%@=!@r>@!@@;@ .Y@}@=l@hPA<@L@TU@m0@B+1@(@1@a]@!|B@rJ@I<@a @ň:@|@@oM?@Zt&@aƯ@JePN@T@Β.@HSA>@%<@<^d@a@/ @J @$"G@Hj @y-r@@ 1>@L*x@Pr@|w@r<&@pSo@`{ȕ@exҜ2Accumulates offspring cells as they are produced.# $%&c@@@@?@@@@@@@@@@@@@@@@M????@@?+flowers_per_cell2000 !NGerber and Klostermeyer (1972) estimate that one bee can produce 0.5 lbs of seed per cell. At 2.2 mg per seed, this is 6,400 seeds per cell. If pods average 4 seeds, this translates to 1,610 flowers per cell. Stark [1983) estimates 2500 flowers per bee. 2000 is a compromise. Waters (CIS 106, 1969) estimates 3000 flowers/cell)# $%&#c )?333333?333333??333333?333333?333333?333333?333333?333333?333333?333333?????333333?+ survivorship*MAX(0.3,(0.8-(.8/35000)*introduced_bees)) H ( ?33 3333 ( ?陙 ( ?陙 / @      !This survivorship is high for the Northwest U.Sl., and a bit high for Canada (Strickler et al., 1995, Canadian Cocoon Testing Centre, unpublished data). Maximum is 80% survivorship; minimum is 30%.# $%&c $?d %??d %? :E?d %?d %?d %S?????+females_per_bee!female_offspring/introduced_bees      !"?3VKN8?PVDq?a?nk?v=?W'?CT~?2'?wJ?p?2[ ?JS?)xnF?o:i?[Gg?X?|?e?-OC?R(?H&?5T?Z4?G?1uͣ?q;_?Ee?kp?R}?RW?䆭'?Ub??6?/֣?oZ?~?1c̈́T?|N?ÄMѡh?-q?J?}/X섮?#5?Нxi?)C?8z?хn?Ȭ?Ѳz/}?\d?f?Ү?K ?8*Ypi?z=Q>H?Ӹl%?芈?.~7?d[@a?ԗsRk? #?V? oP4u?Hm@?miO?ՐԔ?հF?γZyl?\RX3?㨗/2?ed~?1&n?Dт?V̤6?g?vb~?քz?֑`m?֜r?֦ф ?ְ;`?ָт1?s?džŨT?u?ӥsF{?ʭw?ݖy?jA?|i?CEĢ?sJ?W(?aC?Xyk?~?ys"?B?^C?\B?G=?- ? h?OC??E?O]?K?wf*?k? }3?ͥ"l?.^H?aʮ?{? `tR? f? )Q? Ix? 1? k+? ~? @1Y? \rH? + ? TQg ? z;? Ij? [? ? ? ? ;dp? V qs? q#? v75? ? q? N? ? ת? :? /=D i? D[N? ZHA? oc? ?V#? E\? YUA? Q? +? 齚? ?Y?$?87?La?_nM?rnJ? j?CWi?oM?]?Ҧ<2G?? ?!? g?9?1Q~?D9?Whp3?jHߢ'?}$[?;?`m?D)?o/?:g-?%]q?ɡr? V?&PBA?9[R?KЊ^?^@z0?qJ(?A|??xq?0B???R8??O?,l??&G?QЩ=?d/?w1???$k??/d?7 ?Ԛ?G{?2v? 19?K??1g?DLo?WKe?i ?|8-?FR?=~?M?>}?u7P??2x?$?$} (?7!ѻ%?I5?\j,ȫ?o Н?2?SN,?AA??9 ?'i?z}U???)Z?; iv?N?a5Z?sf]?pt? ? j?Fr?~l?|?1?.?L,#?-K?@~uQ?S̋?e?xG҉??v-? Q?£?9x??d %TFor record keeping, number of female offspring produced on average by a mother bee.# $%&g,????????Flower Pollination!# $%&f*Akn:$?Akn:$Aj`&X)Akn:$@kQ @-`????,visits+Min(open_flowers,foragers*flowers_per_bee)       !"AH-AUMgAXɹ,AZ؝7A\#ĂA^MUlA_PxPhA`ەAa_ Ab$ͱAboyAcZYagAcx!DAdbAe+R]0Aep*:AfMr.2 Aji!Ak c( Akn:$AkJedw/Ak&[f_AkiAjx(AjAjQAj{꠪Aj\H:Aj=!b!Aj 7Aj@wAi4pAi_ϩ'AiIjAi.Fh5AhzQ>Ahbc6AhOAha+AhJí@Ah8XDMVAh+;fAh! ]rAhw3bAhXAhAh x@Ah 4R|AhmnXAhDMhAhdtAhX{}AhȍAh\_6Ag\@8WAgI:+Ag AfcuzAebAdʨ!Ac5 Ab^Pv0Aa?sAa6A` U>A^.}M`A\K>3&AZs|AX8դAV6(AUIAS AR4KAP2AN?5ALVyAI!MAG5ߎbAE_ACLjAAPPA@M"ԴA=Xj:A:-:GA8AJ6%A5-]A3jƌA1Q02mA0>rK0A-b1&~:A*$?>A( TKA%bڕ9A#vܞA!տA 'L3AGֱHA OA `VA+@A5BJA"W=AqI#rA TA @p{AҊ4A$$A>AʁA"02*@?u@ .@o@ C@yO@-j@d,@r97@ N2Q@yM@'N`@gzn@2<@ LDB@;i@Tx_@;Wń@h@{q@WIս@ڸ_]W@ֈ@Z]\@O3ӎx@`.Ȝ@Ҍ8N@5r@( ѳ@ВVtP@ ٍF@+ő@W]Pu@͙*06@CLz7@Z%@*{@[@]:@@ʏh@9 'P@/c @ɨpV@j`@3@+@ս~x@ȭ֯ҳ@ȉ1Hs@i@L6&F@2 XM@:=@*@c@T{z@CYy@f@Ƕnp@Ǫe0@ǟM0@ǖ]@Ǎ\ACP@Dže W@~&4@w>@q D@l\@g#+Z@b!A@^|@Z@WKЉ;@T*_@QOpAf@N,w@LN`@J~!8@Hap@F?,l@DT]@BT@A~@@!S @>ܸ$'a@=hD@@$_k@#Rn9@#R,Y@";@!7@!z<8@ pz@ r6@"@jf@4@c`@/ .@\MB@يP@VVe@6@P&_@'.@J6zx@Tln@DMI@<@>u"@Gm@9@@4n,6@P@/aj@א@*vk{@ ͕6@%W|@PZ@ "@/@kQ @-aMultiply 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).# $%&f*@TD?@TD@3;S@TD@lo@P 9????+cell_production_ratevisits/flowers_per_cell     !"@b@v@n_h@};D@U"T}@^5@O-B@ @a@| @)hgp@@yW@t1$l@ӛ4 @cQm@D]# @ًrz@e @̉@xw`@V@{DX@mJp@m1z@YJ@Ll]@@TD@S"|@*ݘw*@p @5_'@bA8?@@ ;@oEj@ :@W.@A@!@[ l@hs@/3@R"@|eVWJ@B-@4PQ@@Svs@&@[ˊ@L&@>gh@@IS@Tr@(o@l@ )@vK7@T@Zs@$8@t Xi@^p@v@.L>@&v@Jf.4@^'@i,h@m0Z@n~@o]o5@ݑi@@@AZI\@~+m @67@.m@3Կ@/z@;@^@ "@Os @/ݑIQ@6@bF5@³@GSh@n.O@P$@y @Uk?CZ@d]=G@@~i?@{8vI@x1t@vIsHa@t+3@rCSڦ@pT,@m@k/:#"@hcu@fg0.V@d[YZb@b/s~@`O&@^$u>@[=T @Yk O;@W(@UY@@S=yi@Qt&9@O@M/8@Jhx@HI@F(&u@D7[Ql@BsShD@@@>F<@<"zt'8@9(?ѝ@7G/@5nՌ@3G@2uc@1^J5@/pg@-A~^@+W@)LCP@(mHv@'\@%3"Yv!@$o@#a@"ы+@"=?X@!?@ '`@ ovS:@,Ҁ@KD @O<\ZT@mi@W@~u@TW})@Tɰ@3K+@]W\@z(@F,a @Yy@΃ <@Ҙt@nS1@Ew|.@ j@٦@L!@-/[@TH@6[>@!f4@swu@cV@U @GI@;x@0@' G@"g@@}'o@@~:@Yum@취@I_@{ſh@6@q@A@Cy@&&]@s[@4@$e@?Kw7@Pt@U@a\@~@ͮ e@w3y0@R @?E@;?{@DM @Yd@y3@ţZi@ՆID@JP@Oy@–i4&@_.@3$;@1.@+U@=Z@@X.@c>ɪ@-@2@Sq1@Ϋ(@v "1@B @Te\@q@6v:@*H@V@-&R@@yRY\@<7@dI@F>@Ql1@M@@A@R\c@/C@p@Ը@h{@@@K5@{r@Φ@n:|@睓@aS5@ڪX@TP@ OF@GՆ-@BZL@;eݪ@Th@/,@8@#k@rw8@16Y@q2@ @w@j@{DŽ@;&@pH@-@e@>@Z@lo@P 9The 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.# $%&f%/@i#~?@i#~@,pb@i#~@%l@%PDtm????+ overflow&cells_produced-female_production_rate     !"@v@0yu@/~!@"@GF@лCH@9%@Nc@0@KO@Df@\&@3t @AåW@,bu@)@ E@@vc@ ٸ@RWzo@xb]@SjMB@ͳ-@C#\@>)`@$djj@O1H@N!@7{ @b*vV@y@i#~@md@{uݰn6@n]@\@H@2GhX@VI@},@ZK?'@U@837@j@61@{J @S@@PjD:@xίZ@a Ԋ@NU@?A@2%@(Вb@ Y^o@$h@%`@xgu@ ?@ P@DE@fuv(@ZX@俲@gfa8J@P-@Cu@(r@M`_Y@1@9yA@*@Aw\x@Zܙ@6?>4@fc@8n@R?N@°@=[fW@OQQ@^kV@a.@{9eM@ 3߹@}z@=&@ɠ @$@$@9]o'@eO Ն@mp@H@z&@lP%@ogy@Fd@q L@|BK@z8^r@wa*Z@u@s}u@q!@pM\@m5g@jQ@$@gy2 @e@cu@a(s @`BX23@]60@Z栝`g@X{'b3;@VIT/:Ƣ@TKxj{@R|f @P݇^@N<@K}@IÝ9@GB{d@E6t;A@CZ|@AxR@@ 6g@=zq@:: *@8h_@6_ o6@4н}!@3*NV@1 K@0[~*@.Wx@,9ꮳL@*TY a@(b@'""<@%B]@$Ƒ@#:%r@"R@!~@ Jn@ MV,i@gV)$[@Uą$@a@c@m4@gҺ@,N@?5m@z>K @ e @A˻#@R*KJ@k@Ȣ%@&k@Fz@K@P( V@\@\@y]@\=M@AX@)ప@uB@׉\~@z@Q@уA)l@Ė@=@I@^$@O@ L@ݼlp@V>&@h@{l*@v4 @qR@mNk@i{g^@f}{f&m@ch@`5@^M@[ @Y:@W@UT@T 5/@R~2d@Q`.@OKK@N}g@MTv@L?m@K;"Y@JE@I]({@H~@G@F&6V@F(0@EpH|@Dǥ!f@D7@Coy4@B@B1z|@Ay@AD1M@@p{@?D.@?T2m@>}@>?#@=@=27@@9}@9+\@8@81<@7o-@79D@6 +@6B˼0@5)@5MoB3@4%ܪ@4Y8@3F@3ev@24o@2r@1y@1ʐ(@1T@06V@0d@/ d@/%@.9˶@.4&@- l@-DZ@,{= @,Ts@+xiP@+d@*쨲.@*t@) %@)D4@) ٲ@(ܘ9@t/@1L% @K@ꦞ#&e@^A@V@Q&@\:@36@=ID@A$R"@%~@~je^@ į4@/j@F=w@L~@8`p@=_@!6@AM@%@[@GrU7@8@u@C.@@1@0?r@*@rw@Dd0x@Kn@5O@ou!p@Qo@n`Q @ ϩ@8.q@cL@ꨞ*@[uS@fc8@oY@ q^9@(|I@AE-%p@W@ly5k@Yڐ@i7@F+j@G@l[/@Zg0l%@Cd@!@䗊 @d'@@^2@NK w@<.n@ e @Ө@@е@xL@@,@" @$H(,Up@&Ps2@()|@)罂@+_]@,F@.'@/0@0>CsJ@13/@2L@2is#@3@4Ce2@4qJo)@5kn3$@5S@6b@6ΌH@71WHw@7Ĩ@77@8+y@8r-ۥ@8 x1@8O@9),@9]@9 @9`ʝ@9OX@:$|{@:922@:^XH%@:-@:h @:Ze@:@;0@;y@;<@;Wpu@;rb]@;``@;V@;\@;U@;@< ُK:@<"ݬR@<:@ #{@>#<Gp@>8Xs@>NB5@>c@>y3ݼ@>o@>]@>|RV@>nͼ@>Fׯ@>p@?wNG@?$a#R@?9h@?O2_]@?dgn]@?y'@?sZ7@?_n@?<@?@?K}@?N^>@@≀@@$,*w@@9v,ß@@NBB@@d^R@@@yMFxv@@o2k@@@@X@@a@@# @@@A*#'@A#k$@A8@AM0@Ac-E?@AxleS@@A.V<@An?@A'&@AdYQ@A@A2@B !@B"T@B7n@BLԅ5@Bb~t@Bw;o@BtY @B@B@F@By@BR7f@Bz2@C B@C @C6(c1@CK\L%@C`@Cu9_@Cn-@C)`[@C[Z)Z@Cʌ%@C߽@Cr%"@D @DN&@D4}LY@DI@D^.@Dt;H@D5/[@DaH@DP@DȺ-4@D呾@D~gJ@E:9b@Ed?@E2u@EG@E\'@Er7"/@E/ݹ@EW @E}.@EƤ@Ĕ# $%&c %3@Z[?@Z[@Z T@Z[@Z[@Z[?????+ Total_cells&males_and_dead_cells+female_offspring     !"@Xb@uv@E}@k٣ @%YƱ@@M5@S@4da(@b@9*]@G>@ŠkIK@}Pj@W6P>@ޡʔ@z@+L $@iF@bŎH@N`}@TM @U!1@h`X@f-d@ۜ?@A9B@mY@O.@)!j@ꢧ:@ &@(}@@o\}v@I?@"-m9@wbGm@0S@騗ϒ@~eAP@SO7N@&:Ѯb@1@ \1@y$:@a$).@ [&@z(@f^@Cn|5@"A@ &0@mȆ@q@@3(@~ @/&ױ@[C@\&@ )T@[o@XL@G eW@whk@(g9@f {0>@/@@.5w @ /JA@?x@k!\@Rv@Y@t@g`ｨ@KS@7@P'B@h W(@} @`E@,@ύ@d6@͔4^%@ٌ Ϳ@go(%@?}*1L@+@A0z@'l9@ 6s@9a@#3@'"@"1@&Jr]@)̓9@-"io`@0)}1؛@2cM\@5hc=@7D=8@9^@;|@=Uw@>8@@N#@A-s@BI]@Cر1lh@D8@ES6@Fģ@GDe}@Gch@HDSb@Io+.h@I.S@JB@JK>@JSE6@KLZ}@Kvj@K U<@L:%pמ@L}B@L@L,@M. 2@Mb@MN(f@MR@MC@NwHg@N>+@NdQ`s@Np@N8@Nll@N@a@O!@O-*R@OKqc@Oi j@O Ec@O%@Oa5@Ok}@O=s @P@P*@PDڳ]@P^ܲn@Px`F@P="@Ps@P@PP@P|@QV}@Q(@QANF@QY|@QrfG@Qצa@Q8r=@Q͡@QU@Q 8@R8:p@R]1@R4yQ/v@RLi@Rd7~@R|d5j@RY@R3M@RĐJs@R܂@RnT@S X7'@S$=ܲ@S< @STb@Sk݄ @S>O@S@Sg,@X>@XVs@XnM@X<@X@wO@XW2@X@X"@X] iV@Yl0@Y+Gzk@YC]^@Y[j@YrC@YYuil@Yq@Ygl-@YPf@YAo@Ze@ZCA@Z/T;@ZG ;@Z_0m@ZvCR@ZwD@ZO@Zq@Z](V@Z[# $%&c  ???333333???333333??333333??333333?333333?333333!??????,pop_reductionTIMEX@@,@5@<@A@E@H@L@O@QX???zG?Gz?Q? =p?\(?333333? =p ?zG?333333  !"This is an emergence plus survivorshiip curve. Bees emerge in the first few days, then die off over the season at an increasing rate, until at the end of the season, only 30% of the original population remains. Richards (1984) presents a steeper survivorship curve based on actual data.# $%&c06@٢@?@٢@@@@٢@@@\????@ɢ?, foragers1introduced_bees*foraging__fraction*pop_reduction       !"@ɢ@ʌ@w@@a@L@6`@ @@z@@e @P@O@İ@9@ӯ@$@@ԙp@@Ճ@@n0@`@X@@B@ظ @-P@٢@٠(@ٝ@ٛx@ٙ @ٖ@ٔp@ْ@ُ@ٍh@ً@و@ن`@ل@ف@X@}@z@xP@u@s@qH@n@l@j@@g@e@c8@`@[@U(@OL@Ip@C@=@7@2@,$@&H@ l@@@@@ @D@h@@@@@@@@d@Ȉ@¬@ؼ@ص@خ@ا@ؠ@ؙ@ؒ@؋@؄@}@v@ox@hp@ah@Z`@SX@LP@EH@>@@78@00@)(@" @@@ @@@@@0@@p@@׿@׶P@׬@ף@ך0@א@ׇp@~@t@kP@a@X@O0@E@@()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  ^HA,    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 B B^ :f()*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. Offspring mortality is density dependent and ranges from 30 to 80%.. 35% of surviving offspring are live females. +,  'f/V3 }k3 !0(c)*(+,  'c;(\  .YS&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+ ~H C~~ //()*+,  'a+ h. z !00()*+,  'dC*+cg ":L()*+,  'D/o, #"_M()*Table 1+,  '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()*+,  'aG( ,6& _Wc&&8G(B!-G(()*+,  'a6,  9#()*+,  'a&@+ : ()*+,  ' t//3 ;&';()*&Density dependent offspring mortality+,  'cNSTW <?=()*+,  'aF<,6- >:B--=F(KF()*+,  ''''a, 4 A44Kx()*+,  '''d*, D!3\()*+,  '''a,d ddG_()*+,  drmda` +66pX###11#1斃2#2l -bb2y2.$2?(Od {5+Alfalfa Pollination Summary./0".Tu2.!0.$.!0.$.!V0.$.!1 -+2y2. 2?(Qd}5+Flower parameters./r$ 0.u2.!0.z2.!80. $. !&0.j$.!0.0z2.!+0.v2.!0.w2.!t0.t2.!0.t2.!1 -'2y2. 2?(\d>/+Bee parameters./ 0.Tu2.!0.8$.!0.$.!0.$.!m0.$.!0.w2.! 0.$.!0.  $. !D1 ##  +K#Z\#(К1ޚ1Z\#1–2(2 2bb#1111@Q@Q+Pollination Model3r4J.:1?x 3@.24.d2? 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