AN AGRO-ECOLOGICAL SIMULATION MODEL SYSTEM

Transcription

1 Ldány e l.: An gro-ecologcl smulon model sysem A AO-ECOLOICAL SIULATIO ODEL SYSTE. LADÁYI* L. HOVÁTH. AÁL L. HUAEL *e-ml: mldny@kee.hu Deprmen of hemcs nd Informcs culy of Horculurl Scences Szen Isván Unversy H-8 Budpes Vllány ú 9 33 Hungry (phone: ; fx: ) (eceved 5 h Aprl ; cceped 5 h June 3) Absrc. In hs pper fve dfferen models s fve modules of complex gro-ecosysem re nvesged. The wer nd nuren flow n sol s smuled by he nuren-n-sol model whle he bomss chnge ccordng o he sesonl weher specs he nuren conen of sol nd he boc nercons mongs he oher erms of he food web re smuled by he food web populon dynmcl model h s consruced for pece of homogeneous feld. The food web model s bsed on he nurenn-sol model nd on he cvy funcon evluor model h expresses he effec of emperure. The numbers of ndvduls n ll phenologcl phses of he dfferen populons re gven by he phenology model. The food web model s exended o n nhomogeneous pece of feld by he spl exenson model. nlly s n ddonl module n pplcon of he bove models for mulvre se-plnes s gven. The modules bul no he sysem re closely conneced o ech oher s hey ulze ech oher s oupus neverheless hey work seprely oo. Some cse sudes re nlysed nd summrzed oulook s gven. Keywords: food web populon dynmcl model cvy funcon spo-emporl smulon model mulvre se-plnes Inroducon The need o pply compuer scence nd elecroncs n grculurl producon for rgeed regon hs become ncresngly urgen. By precson nd susnble grculure we men no only new producon mehod bu lso complex sysem h negres bologcl echnologcl nd economc fcors nd jons he nurl crcumsnces flexbly. Ths form of grculure ms o opmze profcency nd envronmenl proecon by ssessng ogeher forecss for rsk dmges nd prof. In order o ge o know beer how he exmned gro-ecosysem s funconng we need correc smulon models of he complex food web sysem s well s connuous monorng of he processes [ ]. Ths smplfed food web model ccouns for sesonl weher specs [74 75] he nuren conen of sol nd boc nercons (g. ). On he frs level K denoes he wer nd nuren conen of sol s he npu of he sysem. The npu comes from smplfed nuren-n-sol model [54] descrbed below. Above he nuren-n-sol erm K re culved plns denoed by nd wo knds of weed denoed by nd respecvely. On he hrd level monophgous consumes he culved pln whle monophgous es one of he weeds. denoes polyphgous pes whch consumes he culved pln s well s weed. Addonlly here s predor denoed by h consumes pess nd. ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

2 Ldány e l.: An gro-ecologcl smulon model sysem K gure. A food web model. The nercons mongs nuren-n-sol (K) culved pln () weeds ( nd ) monophgous ( nd ) nd polyphgous () pess s well s predor (). (The rrows run from he nuren o he consumer.) In hs pper fve dfferen models s fve modules of complex gro-ecosysem re nvesged furhermore n exr module s consruced: The wer nd nuren flow n sol s smuled by he nuren-n-sol model. The bomss chnges ccordng o he sesonl weher specs he nuren conen of sol nd he boc nercons mongs he oher erms of he food web re smuled by he food web populon dynmcl model. The model s consruced speclly for pece of homogeneous feld. The cvy funcon evluor model expresses he effec of he dly verge emperure on he cvy of he ndvduls. The numbers of ndvduls n ll phenologcl phses of he dfferen populons re gven by he phenology model. The food web model s exended for pece of nhomogeneous feld by he spl exenson model. The ls module gves n pplcon of he bove models for mulvre seplnes. Alhough he modules bul no he sysem re workng seprely oo hey re closely conneced o ech oher s hey cn ulze ech oher s oupus: The food web model s bsed on he cvy funcon evluor model nd on he nuren-n-sol model nd cn mmedely be followed by he phenology model. The nuren-n-sol model pples he oupus of he food web model s s own npus. The food web model nd he spl exenson model cn drecly be lnked. The mulvre se-plnes module s bul on he resuls of he food web model compleed wh he phenology model nd on he ones of he spl exenson model. To smule he nercons dscree dfference equon sysem wh dly scle s used. As n he lerure here re pleny of excellen models whch descrbe cern prs of he processes que excly our m ws o cree model h descrbes he whole nercon process n order o be ble o pply lso n cses when deled d re mssng nd o exend n cses when more complex d re vlble. The pern nlyss nd he nvesgon of spo-emporl nhomogeney of grculurl felds re lso of gre sgnfcnce especlly n he precson nd ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

3 Ldány e l.: An gro-ecologcl smulon model sysem susnble grculure. Addonlly s mporn o elbore he mehodology of he nformon nd d hndlng nd he opml decson mkng. Our m s o go hed n hese problems. In former works he gro-ecosysem models (sol pln weher pes sysems) nd pern nlyses were opered seprely. By spl exenson of he gro-ecosysem model spce specfc complex ecologcl model s obned. Some cse sudes re nlysed nd summrzed oulook mongs ohers of possble wys o develop nd pply he models s gven. evew of lerure Afer he frs food web model ws descrbed by Shelford n 93 he mos populr erly monogrphy becme Brd s book from 93 (In Jordán [4]). Snce h me severl heores hve been ppered nvesgng he food web from severl dfferen pons of vew such s from energecl spec [56] from populon dynmcl spec [4] from sbly grph heory or nformon heory specs [ ]. The srucure of food web nd s nercons re chrcerzed by Jordán [4 44] whle s relbly hs been nvesged by Jordán nd olnár 999; Jordán e l 999; Jordán [ ]. In he ps here hve been few ppers publshed on foodweb reserches ppled for Hungry. odels hve been consruced for ecosysems wh food web smulons [65] h neverheless re bsed on clsscl Lok-Volerr nercons gnorng eher boc effecs or phenologcl specs. Crop weed compeon s nvesged e.g. n Kropff nd Lr [5] nd populon phenology smulor s ppled by ols [6 6]. Agrculurl modellng nd emprcl survey del mnly wh sol pln weher sysems wh dfferen ddonl mn pons such s clme chnge mpc sudes [ 58] mnerlson nd he wer nd nre rnsfer [8] sol he nd wer dynmcs [7 79] non-homogeneous cropped sol profle [47 64] mngemen mpc [7 77] envronmenl condons [5 6] wer nd nuren dynmcs n pln [68] ferlzon [4] physologcl nd physcl processes [8] wer run-off nd eroson n sol [49] phenology [48] plnnng nd decson suppor [ 3 8] croppng sysems [77] nd nformcs [9 ]. Invesgons of food web syems re however no nvolved n he bove sudes. Comprsons of croppng sysems cn be found n rncvgl nd rche [7] nd n rdn e l. [5]. A vluble revew of mehodologes o evlue smulon models s gven by rorn nd Bellocch [59]. There hve been publshed some recen ppers on zoocoenologcl explorons of fresh-wer perns [ ]. Invesgons on gro-ecosysems cn be found n Hufngel e l. [3] n erenczy e l. [6] nd n yls e l. [64] for pes populons. ehodologcl quesons of he ecosysem surveys re dscussed e.g. n Hufngel e l. [ ] nd n ál nd Hufngel [ 3 4] whle he ones for grosysem reserches cn be found n Hrnos [8]. esuls Wer nd nuren flow n sol In order o mnmze he dfference beween he opml nd he rel resuls n grculure wer nd nuren flow n sol hve been observed ye from severl specs [5 9 83]. There ws creed specl drsclly smplfed nuren-n-sol model by ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

4 Ldány e l.: An gro-ecologcl smulon model sysem Erdély [5] wh he specl m h cn be bul no he food web populon dynmcl model o complee wh he mos mporn boc effecs. The dfferenl equon sysem of he nuren-n-sol model consss of hree equons: hey follow he chnge of wer onc nuren nd orgnc mer. Wer conen of sol As he plns cn bsorb onc nuren soluon only wer conen of sol plys s mporn role n vl processes s he onc nuren conen of sol. The wer conen of sol s reduced mnly by evporon (of sol nd pln) by ke-up nd wer run-off; ncresed mnly by he precpon nd werng. These fcors re dependng mongs ohers on emperure globl rdon he relve wer holdng cpcy nd he growng re of he pln s well s he wer holdng cpcy nd he curren wer conen of he sol. These effecs re nvolved n our model neverheless oher properes of sol such s he moun of crbon doxde he effec of wnd ec. re gnored. Wer conen of sol V he () h pon of me cn be clculed wh he help of he wer conen of sol V he h pon of me mulpled by n evporon erm Π ke-up erm Ω nd moreover dded o precpon werng nd wer run-off erm : Ψ V = Π Ω Ψ. V Evporon erm Π s derved from he poenl evpornspron formul due o Turc (n: Szász [79]) h s gven for he cse wer conen s no lmed nd s correced for he cse wer conen does be lmed whch s he rel cse n Hungry. Evporon erm Π s dependng on he dly emperure he dly globl rdon vlue nd he curren wer conen of sol. The more he wer conen s he greer he re of evporon s hus he less he evporon erm Π s; < Π < nd s endng o s he wer conen ends o zero. Tke-up erm Ω s dependng on he dly bomss growh db nd on he relve wer holdng cpcy of he pln. The more he dly growh db of he bomss s he less ke-up erm Ω s nd wh db ke-up erm Ω ends o. recpon werng nd wer run-off erm Ψ s dependng on he dly precpon he dly moun of werng nd he wer holdng cpcy of sol. Ionc nuren nd orgnc mer conen of sol Denoe by he dly onc nuren soluon conen of sol h depends of course K on he dly wer conen of sol V. Ionc nuren soluon conen of sol K K () h pon of me cn be clculed by onc nuren soluon conen of sol he he h pon of me mulpled by ke-up erm I n eroson erm E nd dded o decomposon erm D nd n rfcl ferlzer erm : K = K I E D K r K r. ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

5 Ldány e l.: An gro-ecologcl smulon model sysem Tke-up erm I (< I <) s dependng on he relve nuren conen of he pln derved from s need for onc nuren nd on he dly bomss growh db. I s obvous h he more he dly bomss growh db s he less ke-up erm I s nd s he dly bomss growh db ends o zero ke-up erm I goes o. Eroson erm E (< E <) expresses he fc h n cse wer s lmed n sol onc nuren soluon s lso lmed by whle n cse wer s unlmed onc nuren soluon s lmed by onc nuren h s unble o be ken up by he pln. Eroson erm E depends on he solubly of he dfferen knds of onc nuren. The greer moun of onc nuren s erosed he less moun of s erosble so eroson erm E ends o. Orgnc decomposon erm he h pon of me D cn be expressed by he formul D = ( ξ ) D Dbom Dof where ξ < denoes he dly percen of he decomposed orgnc mer he moun of he developed orgnc mer n sol nd ulzble orgnc ferlzer dded. The rfcl ferlzer erm ferlzer dded. K r D of D bom denoes denoes he moun of s equl o he moun of he ulzble rfcl A food web sesonl populon dynmcl model An gro-ecosysem s dreced mnly by he nercons mongs he populons lvng n he gro-ecosysem ogeher. Severl ndrec or hdden ypes of nercons h cn no be expressed s dfferen knds of merl flow such s compeon he ndrec nercons h cn be derved from he escpe from or he defence gns common predor s well s he so-clled op down nd boom up regulons re nvolved n our food web populon dynmcl model. To smule he nercons dscree dfference equon sysem s used. The generl equon of he web model s bsed on hree elemens: he frs one s o express he cvy of he ndvdul dependng on he emperure he second one s o descrbe he effec of he quly nd he quny of nuren of plns nd/or pess nd he hrd one s o dsply he effec of he predors. The model s bsed on he nuren-n-sol model defned bove. To descrbe he nercons n he food web dscree dfference equon sysem wh seven equons s used ech equon s for cern elemen or of he sysem he () h pon of me. The generl form of he dfference equon s where = he curren moun of he bomss of one of he populons or he () h nd he h pons of me re denoed by nd respecvely; ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

6 Ldány e l.: An gro-ecologcl smulon model sysem he cvy erm of he ndvdul s denoed by dly verge emperure T ; denoes he so-clled nuren erm; denoes he so-clled predon erm. In wh follows he erms of he generl equon re chrcerzed. Acvy erm nd s dependng on he To forecs he me nd he mss of he locl ppernce of pes generons he soclled clsscl emperure-sum mehod s wdely used however s ofen unrelble nd n hese cses he errors cn rush que hgh. To vod hs prmerc cvy funcon h uses he d of he onl Lgh-rp ework nd he dly verge emperure d s npu hs been creed by specl opmson process by évész [73]. Our model s bsed on he de h ws ppled by évész nmely he groecologcl process for ech ndvdul s defned no by he emperure self bu by he so-clled cvy funcon r h s non-lner funcon of he dly verge emperure T: s : T s ( T ) = exp( r : T r ( T ) = ( T b )) exp( c f ( s ( T ) s ( T )) ( T d )) exp( b ) exp( c d ) where b c d nd f re suble consns relve o ndvdul. Acvy funcon r expresses h he ndvduls do no develop under low emperure crcumsnces; whle he emperure ncreses he ndvduls develop n ncresngly rpd re up o cern pon; hgher emperure s s opml for he ndvduls he developmen s mpeded peculrly o he ndvduls sensvy. Acvy erm s derved from he cvy funcon r by lner rnsformon: : T A r ( T ) B. The rnge of erm s nrrow nervl round number : In he cse he emperure s unfvourble < he effec of he erm s mpedmenl. In he cse he emperure s fvourble > he effec of he erm s supporng. Term s connuous monoonously ncresng unl he emperure s opml nd monoonously decresng f he emperure s hgher hn s opml (gs. nd 3). ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

7 Ldány e l.: An gro-ecologcl smulon model sysem (T) for nd _ Tem perure Dy 3 gures 3. : Acvy erm of emperure ( C) for he culved pln weeds nd nd polyphgous. 3: Acvy erm of dy for culved pln. uren erm uren erm s due o performnce he followng properes of he ndvduls n he model: In he cse nuren s unlmedly vlble (under fxed ll oher crcumsnces) he bomss of s ncresng mxml re denoed by Κ. In he cse nuren s lmed he bomss of s ncresng more slowly sgnng or decresng. In he cse nuren s jus s much s needed he moun of he bomss s nerly consn ( ). In he cse nuren decreses excessvely he ndvdul s gong o de ( ). In he cse he ndvdul s n compeon wh noher consumer he chnge of bomss s nfluenced by he moun of he bomss of he oher consumer ogeher wh some wegh prmeers. A polyphgous ( or ) consumes from he dfferen populons n proporon o he mouns nd he nurve vlues of s nuren-bomsses. Term h ssfes ll he properes bove wll be consruced sep by sep he followng wy. rs we gve he proporon of he dly moun of ol vlble nuren reduced by he moun of necessry nuren nd he moun of ol vlble nuren more excly he proporon (-)(ol vlble nuren necessry nuren) ol vlble nuren s follows: = = K = K K K K ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

8 Ldány e l.: An gro-ecologcl smulon model sysem = = = =. Coeffcens denoe he weghs of he nrrows runnung from populon Y o Y consn > s ny number due o vod numercl errors durng dvson. I s obvous h >. As he nex sep we nroduce funcon ν = x x f x f ) ( : ( > x ) h subsung x by ssfes ll he properes bove bu he frs one becuse s lm remns under Κ even n cse nuren s unlmedly vlble. oe h we choose > ν such h < ν lnκ /ln holds. Consder funcon Κ = mx ) ( : x x g x g ν ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

9 Ldány e l.: An gro-ecologcl smulon model sysem x gure 4. uncons f (smooh lne) nd g (doed lne). h s lner connuous srcly monoonously decresng whenever consn f x. uncon : ( ) = g( ) f ( ) ssfes ll he properes bove ncludng (): If < h s o sy f nuren s unlmedly vlble: If holds. If < ν x < nd kes Κ ν : ( ) =. hen Κ so subsung Κ by Κ we ge h propery () h s o sy f nuren s jus enough or shor : ( ) = so n he cse nuren s jus enough ( ) hen hus () s ssfed. uncon s monoonously decresng hus () holds. In cse h s o sy he ndvduls re srvng s consequence hey re gong o de so (v) holds. ropery (v) follows from he consrucon of s we see h he decrese of he bomss of he nuren-populon s cused by he consumers-ncompeon ogeher. ropery (v) follows from he consrucon of gn wh he brke effecs ν nd. ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

10 Ldány e l.: An gro-ecologcl smulon model sysem redon erm redon erm ssfes he properes of he bomss-chnge s follows: Whle he bomss of he consumer-populon s ncresng he nurenpopulon s decresng slower nd slower re nd he sme me he decresng moun of he bomss of he nuren-populon s n mpedng fcor for he consumer-populon. Whle he consumer-populon s ncresng slower sgnng or decresng however he moun of he bomss of he nuren-populon s gong o sgne or even o ncrese. Consder he cse of polyphgy. rom he one nuren-populon s spec he effec of he oher nuren-populon s on he one hnd posve (whle he oher s beng consumed he one cn escpe) on he oher hnd s negve (he oher nuren-populon s mkng he consumer-populon sronger by nourshng ). The bove effecs of he nercons re que complex. Our m ws o gve he smples model ever whch descrbes he bove properes s excly s possble. I cn be proved h erms µ = µ = µ = µ = µ = µ = ssfy ll he bove properes where µ denoes speed fcor nd > s ny number due o vod numercl errors durng dvson. ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

11 Ldány e l.: An gro-ecologcl smulon model sysem ulplers nd re o express he brekng effec n cse more predors re n compeon. The oher poperes cn be derved n smlr wy we dd before for nuren erm. The connecon of he nuren-n-sol nd he food web models Inpu d ppled by he models cn be devded no four groups: Dly d such s precpon emperure werng globl rdon ferlzon ec. These knds of d hve been vlble n Hungry for ens of yers. Consns reled o he pln sol onc nuren or speeds of boprocesses ec. These knds of d cn be obned by esmon or fng. Srng vlues lke V K D ec. These knds of d cn be gned by e.g. sol survey. Oher knds of d such s he growh of bomss db defned by orgnc mer db : = mx ( ) for ll populons D bom developed n sol defned by Dbom = mn ( ) for ll populons ec. h re he oupus of he food web model nd npus of he nuren-n-sol model on he oher hnd he vlble nuren n sol h s he oupu of K he nuren-n-sol model nd he npu of he food web model. I s relzed such h one sep s ken by he nuren-n-sol model s oupu would be npu no he food web model one sep s ken by whch rgh fer. Hvng he oupu of he food web model he nuren-n-sol model cn be sred gn. A cse sudy for he populon dynmcl model. Smuled resuls bsed on dly verge emperure nd precpon d mesured n 98 Debrecen Hungry The models descrbed bove ws esed wh rel emperure nd precpon d ogeher wh fcous bu rel proporonl srng vlues K V S nd. The prmeers of he cvy erms s well s he coeffcens j nd he consn Κ were se such h hey cn demonsre he dfferen emperure sensvy nd some oher properes of he dfferen populons. In g. 3 cn be seen h for he dfferen populons he dvngeous effec of cvy erm > ppers dfferen pons of me n sprng nd furhermore h bou he h dy of he yer here ws perod wh exremely hgh emperure nd no precpon whch ws more or less mpedng for every populon. ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

12 Ldány e l.: An gro-ecologcl smulon model sysem Dly verge emperure 3 C Dy gure 5. Bomss chnge of culved pln weeds nd monophgous nd nd polyphgous s well s predor ; smuled resul bsed on he dly verge emperure mesured n 98 Debrecen Hungry. ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

13 Ldány e l.: An gro-ecologcl smulon model sysem Compre emperure d wh bomss d of he dfferen populons n g. 5. (or he cvy erms see gs. nd 3.) The bomss of culved pln (from he ls yer) hd been slowly decresng ll sprng hen fer hvng reched s opml dly verge emperure (n June) ws ccelerngly ncresng. The growh cme o pon of sndsll bou he h dy nd fer reched s exended mxml re ws quckly decresng. Weed prefers low emperure. I sred o ncrese que erly rher nensvely. In he mddle of summer ws decresng becuse of hgh emperure. Afer he verge dly emprure fell below 5 C ncresed gn nd sred gn o decrese que le n uumn. In s grph one cn see he effec of flucung emperure n le uumn. Weed prefers hgher emperure. I sred o grow very quckly erler hn culved pln. Afer he 5 h dy ws decresng que fs bu he speed of decrese ws lower nd lower. The cvy erm of monophgous s smlr o he one of s nurn hus her bomss grphs re smlr oo jus wh shor me shf. onophgous consumes he weed h prefers hgher emperure hough s opml emperure s slghly lower. Therefore sred o ncrese b ler nd slowler hn weed nd he sme s for s bomss decrese. olyphgous consumed from he erly weed very few s dslkes low emperure however sred o grow slowly. The decrese of he erly weed lef s mrk on he grph of he pes. As he bomss of he culved pln sred o ncrese quckly he one of he polyphgous followed nd sred o decrese jus fer he culved pln s bomss subsded. redor cn choose from hree knds of nuren. I sred o grow bou he 5 h dy sble re reched s exended mxmum wh he mrks of flucung emperure n le uumn/erly wner whch s followed by very quck decrese. Smuled resuls bsed on he dly verge emperure nd precpon d mesured n Debrecen Hungry In g. he sesonly relve o he populons cn be seen well. Whle yer 983 ws he mos fvourble for he culved pln yeld n 98 ws que poor (g. 6). The effec of he mld wner n 98 8 s consderble on he grph of he erly weed. Besdes sesonly cn be seen n he grph of he weed whch prefers wrm weher h he dfferen condons n dfferen yers mply grphs wh dfferen mxmum slope nd convexy properes. oce he effec of wrmer (98) nd cooler (984) summer on monophgous h prefers wrm weher. The grph of monophgous h consumes he less sensve weed seems o be he mos sble one. Smlrly o weed polyphgous prefers cool weher hus yers 98 8 were more fvourble hn he ones fer. The grph of predor cn be sd o be he less chngeble. ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

14 Ldány e l.: An gro-ecologcl smulon model sysem Dly emperure Debrecen Hungry gure 6. ve-yer (98 84) smulon resuls of he food web model for ech elemen of he web. ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

15 Ldány e l.: An gro-ecologcl smulon model sysem henology model Applyng he bove models he obvous queson s how he number of ndvduls cn be derved from gven moun of bomss. ore excly f he phenologcl phses of he populon ogeher wh her bologcl properes re known how cn one defne he number of he ndvduls n he phses gven pon of me? The followng model solves hs problem. ecll he de menoned n he secon cvy erm ws nroduced nmely h he gro-ecologcl process s no defned by emperure self bu by he soclled cvy funcon snce he effec of he sme emperure on he ndvduls s very dfferen n dfferen phenologcl phses. Thus nsed of cumulve emperure we nroduce cumulve cvy cum h = = h SW h wh he help of whch he enerng des of he phenologcl phses cn be defned. h h Cumulve cvy cum cumules he vlues of cvy erms of ndvdul from srng pon of me relve o (le us sy he frs sprng pon of ) n he cse phse h holds where h denoes one of E (for he egg se of he h generon =... g ) L j (for he j h lrv se of he h generon j =... l ) nd I (for he mgo se of he h generon). h To express he phse h holds we nroduce funcon SW for populon of n phenologcl phse h pon of me : where SW h : = h ( SW ) h> E mn mn L h [ mx{ ( Cum Tm ) } ] ( SW ) h h h h h { mn[ mx{ ( m k m ) } ] mn[ mx{ ( Cum Tm )}] } * h ( SW ) h> L h> L f f f f = h = E > > nd nd nd h > E h = L h > L h T m denoes he mnmum of cumuled cvy of h s necessry o ener phse h; h m denoes he curren verge mss of n ndvdul n s se n phse h; h m denoes he verge mss of n ndvdul enerng phse h; g nd l denoe he numbers of generons nd lrv phses reled o respecvely; * ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

16 Ldány e l.: An gro-ecologcl smulon model sysem from o s cused by he fc he nex phse hs been enered. h h h k s proporon consn m s mulpled by whch n order o obn he mxmum mss of n ndvdul n phse h nd fnlly relon > for phses mens ler phse hn. h uncon SW equls o f nd only f he populon of hs more hn zero number of ndvduls n phse h gven pon of me nd equls o else. The h chnge of he vlues of funcon SW from o s cused by he fc cumuled cvy hs reched he mnmum h s necessry for n ndvdul o ener phse h nd/or by he one he mss of ndvdul hs reched he mxmum n ndvdul n phse h cn even hve; Wh he help of funcon s follows: corr g SW correced food web bomss model cn be creed E I E I h h = ( SW )( SW ) W ( ) SW I ( ) SW LS χ. = The correced food web bomss model bove ssfes he followng properes: In wner here s no growh; n hs cse funcon W of expresses he bomss-wse cused by wner weher. Durng he mgo phse consumpon s suspended; n hs cse funcon I s he sme s of he orgnl food web bomss model excep erm whch s now denclly equl o. h There s loss n bomss enerng new phse; funcon LS of denoes h he moun of wh chrcersc funcon χ h s equl o f nd only f s he pon of me phse h enered nd s equl o zero else. I s obvous h here mus be pon of me phse s enered frs nd he sme me here mus be noher one whch he process of memorphoss s fnshed h for he whole populon. Ths mens h funcon SW h swches on/off he phses hs o be smoohed s follows: where p E E g = SSW = SW p L SSW p h h h = SW * ( p ) h L L L mn mx L L T T g = cum T L = SW = for every h > L. h h h h m c m h p mn mx SW h h h ( c c ) m Ths mens h h p s equl o zero unl phse h s enered. In he cse he mnml vlue of cvy h s necessry o ener phse h hs been reched ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

17 Ldány e l.: An gro-ecologcl smulon model sysem monoonously decreses from o zero. A he pon of me whch he whole process h of memorphoss s fnshed becomes o be equl o nd lso keeps o be zero. I s esy o see h p for ll phses h SSW =. nlly he numbers of ndvduls n ll phses wll be clculed s follows. Se ou from n esmed srng vlue of he number of ndvduls srng pon of me n phse E : E oi = E m from whch he numbers of ndvduls of ler phses cn be derved f h E : oi h h h h s h s = oi p mn oi oi h h mn h ( ) χ χ w m m where denoes funcon o express he re of srvng of populon of χ s pon of me clculed wh he help of he vlble moun of nuren (denoed by v U ) s well s ne he necessry moun of nuren (denoed by U ) s follows: v U s χ = mn. ne U Consn < w h < denoes he re of mxmum moun of wegh h cn be loosed whou dyng. Ths formul s suble o express he followng properes of he populons: The sum of he numbers of ndvduls does no ncrese n ny phse excep f h = E for =... g. Durng he memorphoss from phse h no he nex one denoed by h he number of ndvduls n phse h s decresng endng o whle he number of ndvduls n phse h s ncresng. The decrese of he bomss of cn be cused on he one hnd by he fc h n cse nuren s shor he ndvduls re losng her weghs nd on he oher hnd by he one he populon s consumed by noher populon. The number of ndvduls n he frs cse does no chnge whle n he ler cse s decresng. In cse nuren s shorer hn s necessry for he ndvduls even o keep beng n exsence he number of ndvduls s decresng becuse of srvon. oe h he loss of bomss durng he memorphoses hs been ye subrced from he bomss of. The curren verge mss of n ndvdul n phse h pon of me cn be obned s: SSW h ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

18 Ldány e l.: An gro-ecologcl smulon model sysem m h m = f h E nd h I h oi L j = m f h = I j = l E m else h where E s belongng o he sme generon s h. Therefore he number of eggs of ler generon hn he frs one s L j E E db oi = ( = 3... g j = l ) m h s o sy he number of eggs cn be derved from he whole bomss growh db durng he very ls phse jus before mgo phse whch s prcclly equl o he bomss of eggs. The spl exenson model In wh follows smplfed spl exenson model of he bove gro-ecosysem model wh he help of whch spce specfc complex ecologcl model cn be obned wll be dscussed. The modules of he spl sysem re srongly conneced o nd dependen from ech oher however ech of hem works ndependenly oo. The model nroduced n hs pper descrbes jus n only prey predor or pln pes relon nd s bsed on wo ssumpons: opulons hve gre number of ndvduls (hypohess of bundnce). Indvduls belongng o he sme populons re dencl n every dynmclly relevn specs (hypohess of unformy). There s no need o consder he hrd ssumpon known n populon dynmcs nmely he hypohess of ergodcy. Every ndvdul perceves he sme envronmen round self. Ths semen s rue exclusvely n he homogeneous prs nsde n n nhomogeneous pece of feld. An nhomogeneous pece of feld ws dvded no 5 5 prcels nd ws consdered o be seprely homogeneous. In ll he prcels he number of plns (Z) nd he number of pess (H) re known. Smule he prcels wh neghbour model. The qunes of he elemens of he food chn n he dfferen prcels re vryng dynmclly n me. A he () h pon of me he quny of pess n cell depends on he quny of he nuren vlble here nd he number of he pess nvdng from he neghbourhood. There re ndvduls of wo knds of pess represened n he model he frs one s ckng fronlly (loclly) he second one cks globlly. H = w H H j ( j ) Qj Wj j L j ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

19 Ldány e l.: An gro-ecologcl smulon model sysem where: = H b Z c f else H Z b c. H denoes he quny of he pess n he h prcel (kg) Z expresses he quny of he plns n he h prcel (kg) H b coeffcen ses he proporon such h = f he quny of he Z c pln s jus enough for he pes. If he suon s unfvourble < whle n cse << ll he pess nend o depr from he prcel. Seng coeffcen s of gre mpornce from he spec of he model becuse hs fcor deermnes prncplly wheher pes should bndon he prcel or he prcel s consdered s suble or even del o remn here. rmeers b nd c re o vod numercl errors durng he clculons. They denoe he qunes of he so-clled survvng ndvduls h re syng for (shor) whle n cells whou suble lvng crcumsnces. I s obvous h b<<h nd c<<z /. w s speed fcor of compulson o emgre h ses he srengh of wll o leve cell. Wh he help of hs fcor he pess cn be chrcerzed ccordng o he dfferences n her wys of emgron. or exmple some of hem depr very quckly f he condons chnge o b unfvourble whle ohers would bndon he errory ler no so rpdly. If H b < Z c hen funcon kes he vlue of. In hs cse he quny of he plns s suffcen for he pess he pess do no nend o depr from he errory. The quny of he w pess h re gong o sy n he nex cycle s expressed by H. I s obvous h he greer he proporon H Z s he closer o zero funcon s whch mens h some of he pess mgh be gong o sy n he prcel bu more of hem ry o bndon. If he errory s del ( = ) hey would no wn o leve he prcel. By he sum w H j ( ) Qj Wj j cn be clculed how mny pess rrve from he res of he prcels j o he observed prcel where b c ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

20 Ldány e l.: An gro-ecologcl smulon model sysem Q j = ( x x j ) ( y y j ) The coordnes of he exmned prcel re denoed by (x y ). The coordnes of h prculr prcel from where he pess re rrvng re denoed by (x j y j ). The re of ckng bly h descrbes how fr pes cn go s denoed by v. I ws necessry o buld hs fcor no he model becuse he mesure of nfecon depends grely on he dsnce of he prcels. In he cse v>> he cker cn be consdered s he only one ckng fronlly. If v he pes cn pper everywhere sooner or ler. nlly c) H c =. ( Z j c) H c Wj j ( Z cor W j shows how desrble gven prcel s. If W j s gre pes would more lkely go owrds he prcel. I s possble h prcel s hghly desrble bu s oo fr n hs cse he pess re gong o choose less fvourble bu closer prcel. A cse sudy for he spl model A very smple cse sudy n whch here re compleely he sme qunes of vlble nuren n every prcel of he 5 5 feld s demonsred s follows. In one of he corner prcels here pper some pess. Ths smple s se for pes wh medum emgron bly. The bles below show he chnges ll sble suon s se n. In g. 7 spredng process cn be seen where pess ppered n he upper lef corner. All he prcels conned uns of plns s lmen. The qunes of he pess re shown on he lef sde grphclly on he rgh sde numerclly. I cn be seen h he pess moved every me n he drecon wh he more del (greer) proporon of pln nurens per pess. In he curren suon he vlue of s se o. The process of spredng wll connue unl he vlue of funcon reches so he proporon flls below. H Z j b c v. Ths model hs mny possbles of progress n. o only he pln lmen bu lso he smulneous presence of more pess nd plns cn be descrbed. Even he effecs of he relef cn be bul no hs model. ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

21 Ldány e l.: An gro-ecologcl smulon model sysem gure 7. Temporl-spl quny of pess n des 9. ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

22 Ldány e l.: An gro-ecologcl smulon model sysem Applcon of he se-plnes The bove menoned spo-emporl smulon models offer new possbles o use he mulvre se-plnes. Execung he ecosysem food web model for one yer we ook ou d of every enh dy o obn he reference dbse nd o mke he ndrec ordnon. or smple vsulson of he se-plne we cn use Excel dgrms. or more deled represenon nd furher nlyss of he objecs (plces / des) nd oher reled nformon n mny pon of vews he use of IS progrm s recommendble. In he followngs we demonsre wo cse sudes whch smule he emporl chnges of dfferen prcels n n nhomogeneous feld. The effecs of dfferen nuren mouns The moun of he vlble nurens cn sgnfcnly nfluence he ses of n gro-ecosysem. In g. 8 we cn exmne n smuled suon. The smulon shows he resuls of prcels wh dfferen vlble nurens he sme perod n sprng nd he begnnng of summer. The modere nd hgh nuren levels come from n ddonl nuren dosge fer 5 dys of he smulon so he hree rjecores hve he sme orgn. In he fgure we cn see h he rjecores more nd more dffer from ech oher. As he nuren moun s ncresng he rjecores go o he lef nd down. We know from oher resuls h hs re mens he beer condons for he culved pln. The observed chnges n he ses help he mpc ssessmen of ferlzng. The effec of dfferen pln proecon mehods Smlrly o he ferlzng he dfferen pln proecon mehods cn be consdered s groechncl remens. In hs cse we smuled he use of pescdes decresng he densy of he ffeced populons on gven dy. All oher prmeers kep her vlues. mens selecve nsec conrol gns monophgous pes he oher remen ws generl zoocde (g. 9). In hs cse he chnges re no connuous s n he former exmple seps from pon o he oher cn be observed n ccordnce wh our expecon.the resuls chnge n he sme drecon bu wh dfferen res. Of course he generl zoocde whch effecs ll he four nsec populons proved o be mos drsc compred wh he orgnl se. In boh exmples we cn observe h he rjecores re smlr o ppe. Ths shpe comes from he sesonl dynmcs (Hufngel nd ál [38]) whch proved o be very srong effec hgh modere low gure 8. The effecs of dfferen nuren mouns. ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

23 Ldány e l.: An gro-ecologcl smulon model sysem Orgnl Zoocde orgnl en. zoocde -.4 gure 9. The effec of dfferen pln proecon mehods Dscusson () Durng he smulon of he food web model he effecs of some exreml evens were exmned s well such s he exncon of populon h mgh cuse he exncon of he monophgous h consumes. Our furher plns re he surveys of he exhuson of sol he mnul nervenon lke ferlzon pln proecon werng ploughng sowng hrvesng (e.g. n Hufngel nd ál [38]) he longerm me seres he rsk nd sbly nlyss of he bove effecs he effec of exreme weher condons nd globl chnge. The models re nended o be generlzed for hghly complex food web sysems wh gre volumen populons nd o exend nd vlde hem for specl food web sysems. () The phenology model h ws nroduced bove ws creed orgnlly wh he followng ms: To swch on/off cern elemens of he food web model [53] h descrbes he bomss dynmcs of populons n n ecosysem. In hs wy he sesonl chnges of boh boc nd boc nercons of he exmned ndvdul cn be followed more excly. To conver he mesure of bomss for he number of ndvduls. In hs wy he resons of bomss chnge cn be seen well. Above ll mehodcl developmen of he generl model ws nended o gve hrough n exmple for pes populons. The model cn be embedded n smulon models wh dscree dfference equons. Smlr models n lerure hve probbly no ye been ppered. The phenology model cn be ppled n sudes of phenologcl evens of pess even ndependenly of he food web model. In ddon o n modellng ecosysems s expeced o be ppled n pln proecon prognoscs s well o mprove he phenology model furher nvesgons re plnned such s: sochsc generlzon spl generlzon [9 3 73] n pplcon for pes populons wh dfferen phenologes vldon nd fng for rel d ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

24 Ldány e l.: An gro-ecologcl smulon model sysem n nvesgon of he vlded model for que dfferen weher condons sudy of he effecs of exreme weher condons nd globl chnge. The sysems presened n hs pper re used for modellng he spo-emporl perns of grculurl ecosysems. The jon pplcon of he smulon models nd he se-plnes could help us o survey he effecs of he ecologcl nd groechncl condons n he sme sysem. If we cn f our model o rel feld monorng d oo wder rnge of nerpreons nd conclusons wll be obned. In hs cse he reference dbse self should conn boh rel nd smuled d h cn generlze he pplcon possbles of he se-plne sysems. Bsed on he cse sudes our sysems seem o be suble o solve he problems menoned n he nroducon so he sysems re sll under developmen. Acknowledgemens. We would lke o express our hnks o rofessor Zs. Hrnos for supporng our work Szen Isván Unversy Deprmen of hemcs nd Informcs. EEECES [] Brh S. Czárán T. & Oborny B. (996): Spl consrns mskng communy ssembly rules: A smulon sudy. ol eobo. hyox. rh 3: [] Bechn L. Bocch S. & ggore T. (999): Spl nerpolon of sol properes for rrgon plnnng. A cse sudy n ohern Ily. roc. of he s Inernonl Symposum odellng Croppng Sysems Lled Spn pp [3] Ber A. orr. Born. & rdn L. (): Use of CropSys o smule four-yer roon wh dfferen ferlzon levels. roc. of he nd Inernonl Symposum odellng Croppng Sysems lorence Ily pp [4] Bíró J. & Hufngel L. (): Bondkácó Heeroper közösségek lpján Blon vízrendszerében. Hdrológ Közlöny 8(5 6): [5] Beven e l. (994): TOODEL nd IDATB. Cenre for eserch on Envronmenl Sysems nd sscs. Techncl epor T /94. Lncser Unversy Lncser UK. [6] Boumn B.A.. (99): SBLEVO nd WWLEVO rowh models o smule crop growh opcl reflecnce nd rdr bckscer of sugr bee nd wner whe clbred for levolnd. CABO-DLO repor 63. CABO-DLO Wgenngen The eherlnds 6 pp. [7] Boumn B.A.. (993): OYZA_W ce growh model for rrged nd wer lmed condons. SA repor AB-DLO 67 pp. [8] Chen S. Zho B. Sockle C.O. Hrrson J. & elson. (): Use of models s decson suppor ools n dry nuren mngemen. ASAE per o S. Joseph I. [9] Cherov O.. & Komrov A.S. (995): On mhemcl heory of sol formng processes.. Theorecl bckground.. SO model of sol orgnc mer dynmcs. 3. Bsc des of mnerl phse modellng. ussn Acdemy of Scences. ushno eserch Cener. Insue of Sol Scence & hoosynhess. reprn 4 pp. [] Crsc A. oonen C. Ercol L. & Bnd. (): Sudy of he mpc of clme chnge on whe nd sunflower yelds usng hsorcl weher d-se nd crop smulon model. roc. of he nd Inernonl Symposum odellng Croppng Sysems lorence Ily pp. 9. [] Czárán T. (998): opulácó- és ársulásdnmk érben és dőben: ömeg- és objekumkölcsönhás modellek. In: ekee. (ed.) A közösség ökológ fronvonl. Scen Budpes pp ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

25 Ldány e l.: An gro-ecologcl smulon model sysem [] Csörgs. & Hufngel L. (): Heeroper fjegyüesek Dunán. Hdrológ Közlöny 8(5 6): [3] Csörgs. & Hufngel L. (): Heeroper és Odon fjegyüesek yék-hol- Dun hínár állománybn. Hdrológ Közlöny 8(5 6): [4] Donell. Spllcc. rche. & pn. (996): Evluon os CropSys smulons of growh of mze nd wer blnce nd sol nre conen followng orgnc nd mnerl ferlzon ppled o mze. 4h Europen socey for Agronomy Congress Veldhoven-Wgenngen The eherlnds pp [5] Erdély É. (): A növények áll hsznosíhó ápnygmennység dőbel válozásánk modellezése. 6. gyr Bomer és Bomemk Konferenc SZIE ÁOK pp.8-9. [6] erenczy A. Hufngel L. écs. & észáros Z. (999): Bodverzás monorozás növényvédelm fénycspdhálóz d lpján. 5. gyr Bomer és Bomemk Konferenc BDT Szombhely pp [7] rncvgl. & rche D. (999): Comprson of croppng sysems models n he smulon of crop bomss nd gren lef re ndex developmen. s Inernonl Symposum odellng Croppng Sysems Lled Spn pp [8] brelle B. enssr S. & Houo S. (995): Anlyss nd feld evluon of he CEES models wer blnce componen. Sol scence Socey of Amerc Journl. [9] ál. (997): Az nformk eszközenek felhsználás kerészeben. Új Kergzdság 997(4): [] ál. (997b): Az nformk lklmzás leheősége zöldségermeszésben. TA knddáus érekezés Kerésze és Élelmszerpr Egyeem Budpes. [] ál. (998): Ökológ lpú szknácsdás nformácós rendszer. zdálkodás 4(): [] ál. & Hufngel L. (999): Víz élőhelyek állpoánk monorozás poloskközösségek lpján. Agrárnformk 999 DAE Debrecen pp [3] ál. & Hufngel L. (): Új módszerek z lklmzo rovrn monorozásbn. Lppy János-Vs Károly Tudományos Ülésszk övényvédelm Szekcó SZIE Budpes pp [4] ál. & Hufngel L. (): Combnon of ulvre ehods nd rphcl Dbse ngemen n Servce of Ecologcl onorng. 3rd EITA (vol ) groonpeller ESA onpeller pp [5] rdn L. Ber A. & orr. (998): Smulon of wo croppng sysems wh EIC nd CropSys models. Il. J. Agron. : [6] odwn D.C. & eyer W.S. (995): Blncng crop producon wh slny nd werble mngemen. nd Inernonl Symposum on Sysems Approches for Agrculurl Developmen Los Bnos hllppnes. [7] Hnsen S. Jensen H.E. elsen.e. & Svendsen H. (99): DAISY Sol ln Amosphere Sysem odel. o-forsknng fr ljosyrelsen r. A 7 pp. [8] Hrnos Zs. (99): Az lklmzkodó mezőgzdság rendszere: módszern kuások. KÉE Budpes. [9] Horváh L.. (): Térbel nhomogenások kezelésének módszern problémá precízós növényermeszésben. [Spl nhomogeny problems n precson frmng.] Szmulácó és monorng z grárökoszszémák vzsgálábn IV. Agrárnformk (Debrecen. ug. 7 8.) pp [3] Horváh L. ál. & Hufngel L. (3): odellng of spo-emporl perns of ecosysems n grculurl felds roceedng of EITA 3 Debrecen Hungry pp [3] Hufngel L. (n press) odellezés populácódnmkábn. Szemnárum köe SZIE Budpes. ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

26 Ldány e l.: An gro-ecologcl smulon model sysem [3] Hufngel L. észáros Z. ál. & erenczy A. (999): Temporl spl perns of ocune communes n Hungrn pple orchrds. Ac hyopholog e Enomolog Hungrc 34(4): [33] Hufngel L. Bkony. & Vásárhely T. (999): ew pproch for hb chrcerzon bsed on speces ls of quc nd semquc bugs. Envronmenl onorng nd Assessmen 58: [34] Hufngel L. Bkony. & Vásárhely T. (999): Sokválozós módszerek lklmzás víz és vízfelszín poloskákr épülő vízmnősíés rendszerekben. Álln Közlemények 84: 9 4. [35] Hufngel L. ál. erenczy A. & Ősz B. (999): Többválozós módszerek lklmzás rovregyüesek ér-dőbel zoocönológ monorozásábn. Informk felsőokásbn 999 DESZ Debrecen pp. 5. [36] Hufngel L. & Sollmyer B.E. (999): Zoocoenologcl pern of bug ssembles n he Szls nd yál srems. Opuscul Zoologc 3: [37] Hufngel L. ál. Ősz B. & észáros Z. (): opulon dynmcl sbly n servce of pln proeconl prognoss. Ac hyopholog e Enomolog Hungrc 36: [38] Hufngel L. & ál. (): Többválozós állposík-rendszerek lklmzás vlósés szmulál dsorok kezelésében. [ulvre se-plnes n servce of nlyss of feld- nd smuled d.] Szmulácó és monorng z grárökoszszémák vzsgálábn II. Agrárnformk (Debrecen. ug. 7 8.) pp [39] Jermy T. & Szelény. (958): Az ősz búz állársulás. Álln Közlemények 46: 9 4. [4] Jordán. (998): A áplálékhálózok szerkezee. Természe Vlág 9(6): [4] Jordán. (): Sesonl chnges n he posonl mpornce of componens n he rophc flow nework of he Chespeke By. Journl of rne Sysems 7:89-3. [4] Jordán. (): eje fjkölcsönhások. Természe Vlág 3(3): 98. [43] Jordán. & olnár I. (999): elble flows nd preferred perns n food webs. Evol. Ecol. es. : [44] Jordán. Tkács-Sán A. & olnár I. (999): A relbly heorecl ques for keysones. Okos 86: [45] Kb. Broek B.J. vn den & eddes E.A. (99): SWACO: A Wer ngemen nd Crop roducon Smulon odel. ICID Bullen 4(): [46] Keulen H. vn & Selgmn. (987): Smulon of wer use nrogen nuron nd growh of sprng whe crop. Smulon onogrphs udoc-dlo Wgenngen The eherlnds 38 pp. [47] Knsel W.. (ed.) (98): CEAS: A eld Scle odel for Chemcls unoff nd Eroson from Agrculurl ngemen Sysems. USA Dep. of Agrculure Conservon eserch epor o. 6. [48] Kropff.J. & Lr H.H. vn (eds.) (993): odellng crop-weed nercons. Wllngford: CAB Inernonl 74 pp. [49] Lr H.H. vn oudrn J. Keulen H. vn (eds.) (99): Smulon of crop growh for poenl nd wer lmed producon suons s ppled o sprng whe. Smulon epors 7 7 pp. [5] Ldány. (): Egy áplálékhálóz populácódnmk modellje. 6. gyr Bomer és Bomemk Konferenc SZIE ÁOK Budpes pp [5] Ldány.-Hufngel L. (3): A henology odel embedded n n Ecosysem odel for Agroecologcl rocesses roceedngs of EITA 3 Debrecen Hungry pp [5] Ldány. Erdély É. & évész A. (3): An Ecosysem odel o Smule Agroecologcl rocesses. roceedngs of EITA 3 Debrecen Hungry pp ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

27 Ldány e l.: An gro-ecologcl smulon model sysem [53] Ldány. & Erdély É. (): Kölcsönhás hálózok dőbel szmulácój. [A sesonl populon dynmcl model of food-web.] Szmulácó és monorng z grárökoszszémák vzsgálábn I. Agrárnformk (Debrecen. ug. 7 8.) pp [54] Lndemn.L. (94): The rophc-dynmc spec of ecology. Ecology 3: [55] Levn S. A. (978): opulon dynmc models n heerogenous envronmens. Ann. ev. Ecol. Sys. 7: [56] Lovelnd.J. ounsevell. Legros J.. os D. de l Armsrong A. lnsk J. jk K. Smo C. (eds.) (995): ACCESS. Agro-Clmc Chnge nd Europen Sol Subly: splly dsrbued sol gro-clmc nd sol hydrologcl model o predc he effecs of clme chnge on lnd-use whn he Europen Communy. Volume II: user mnul. 6 pp. [57] rorn. & Bellocch. (999): A revew of mehodologes o evlue groecosysem symulon models. Il. J. Agron. 3: [58] ols.j.. (99): orecsng orchrd pess for deque mng of conrol mesures. roc. Exp. & Appl. Enomol. Vol. EV Amserdm pp [59] ols.j.. (99): orecsng n ndspensble por of IB n pple orchrds. Ac hyopologc Enomologc Hungrc 7( 4): [6] onco S. Scco D. & rgnn C. (): Anlyss of he nfluence of dfferen envronmenl fcors n crop growh. VII. Europen Socey for Agronomy Congress Cordob Spn pp [6] urry J. D. (989): hemcl bology. Sprnger Verlg ew York. [6] ovk V. & jerck J. (99): Smulon of he sol-wer dynmocs n he roo zone durng he vegeon perod. II. The course of se vrble of sol wer below mze cnopy. Journl of Hydrology nd Hydromechncs 4: [63] ováky E. (99): rognoszzálás ervezés modellezés környezevédelemben. Aqu Kdó Budpes. [64] yls L. Hufngel L. ál. & észáros Z. (): Sesonl nd successve dynmcs of ocude ssembles bsed on lgh rp collecons n Julnn jor. roceedngs of he Lppy János & Vs Károly Scenfc Symposum (6 7. ov. Budpes) pp [65] Okubo A. (98): Dffuson nd Ecologcl roblems: hemcl odels. Bomhemcs Vol.. Sprnger Verlg Berln Hedelberg ew York. [66] Oen W. (994): Dynmcs of wer nd nurens for poed plns nduced by flooded bench fergon: expermens nd smulon. Thess. Wgenngen 5 pp. [67] mm S.L. (98): ood Webs. Chpmn nd Hll London. [68] mm S.L. Lwon J.H. & Cohen J.E. (99): ood web perns nd her consequences. ure 35: [69] odn J. (993): SY-TA Compuer progrms for mulvre d nlyss n ecology nd syshemcs. Absrc Bonc 7( ): [7] odn J. (994): ulvre nlyss n ecology nd syshemcs. SB ublshng The Hgue. [7] odn J. (997): Bevezeés öbbválozós bológ dfelárás rejelmebe. Scen Budpes. [7] évész A. & Horváh L. (): A fenológ prognózs új módszere 6. gyr Bomer és Bomemk Konferenc Budpes. [73] évész A. (): Új leheőségek z empírkus hőösszeg modellezésben. [ew opons for emprcl he-un modellng.] Szmulácó és monorng z grárökoszszémák vzsgálábn III. Agrárnformk (Debrecen. ug. 7 8.) pp [74] Scheurng I. János I.. Csllng Á. & ászor. (993): SOC defes chos: A new populon dynmcl model. In: ovk.. (ed.): roceedngs of he II Second Inernonl Conference on rcls n he url nd Appled Scences. London Amserdm. ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry

28 Ldány e l.: An gro-ecologcl smulon model sysem [75] Slvesr. Bellocch. zzoncn. & enn S. (999): Evluon of he CropSys model for smulng sol wer sol nre green re ndex nd bove-ground bomss of mze under dfferen mngemen. s Inernonl Symposum odellng Croppng Sysems Lled Spn pp [76] Söckle C.O. Donell. & elson. (3): CropSys croppng sysems smulon model. Eur. J. Agron. 8: [77] Svendsen H. Hnsen S. & Jensen H.E. (995): Smulon of crop producon wer nd nrogen blnces n wo germn gro-ecosysems usng he dsy model. Acceped n odellng of geo-bosphere rocesses. [78] Szász. (988): Agromeeorológ állános és specáls. ezőgzdság Kdó Budpes. [79] Ulnowcz.E. (983): Idenfyng he srucure of cyclng n ecosysems. h. Bosc. 65: [8] Ulnowcz.E.- Wolf W.. (99): Ecosysem flow neworks: loded dce h. Bosc. 3: [8] Vrg I. & Hufngel L. (): Temporl-spl perns of quc nd semquc Heeroper Lke erő. Opuscul Zoologc 33: 99. [8] Verberne E.L.J. Hssnk J. Wllgen. de roo J.J.. & Veen J.A. vn (99): odellng orgnc mer dynmcs n dfferen sols. eherlnds Journl of Agrculurl Scence 38: 38. [83] W A. S. (947): ern nd process n he pln communy. J. Ecol. 35:. [84] Wlson J. B. (994): Who mkes he ssembly rules? J. Veg. Sc. 5: ALIED ECOLOY AD EVIOETAL ESEACH ( ): ISS enkl B. Budpes Hungry