utkrantivadi aakraman vishleshan

utkrantivadi aakraman vishleshan, jyala anukulansheel gatishilata asehi mhanatat, haah ganiteey modelling tantrancha eka sanch aahe joou alaingik punarutpadak loksankhyetil vaishishtyanchya dirghakalin utkranticha abhyas karnyasathi vibhedak samikaranancha vapar karato. abhyasat asalelya loksankhyetil utparivartan aanee naisargik nivadibaddalachya khaleel chaar gruhitkanvar heey aadharit aaheh
utkrantivadi aakraman vishleshanamule model mapdandanvar paristhiti olakhane shakya hote jyasathi utparivartit loksankhya nasht hote, nivasi loksankhyechi jaaga ghete aanee/kinwa nivasi loksankhyesah sahastitva thevate. dirghakalin sahastitvala (utkrantichya kalmananusar) 'utkranti shakha' mhanoon olakhale jaate. jevha fandya padatat, tevha utparivartak swatahla vatavaranat dusra rahivasi mhanoon sthapit karato.
utkrantivadi aakraman vishleshanacha kendrabindu mhanje utparivartak aakramankshamta. jevha too alp sankhyene nivasi loksankhyet aanala jaato tevha utparivartanachya dirghakalin ghatankiy vadhichya darasathi hii ganiteey abhivyakti aahe. aakramanachi tandurusti sakaratmak asalyas, nivasi jivanni tharavalelya vatavaranat utparivartit loksankhya vadhu shakate. aakramanachi tandurusti nakaratmak asalyas, utparivartit loksankhya vegane namshesh hote.
parichay aanee parshvabhoomi.
naisargik nivadidvare utkrantiche moolbhut tattva charles darwin yanni tyanchya 1859 chya 'aun daad origine auph speesheej' yaa pustakat spasht kele hote. tyaa velee jaree vadgrast asale taree, kendriya kalpana yaa tarkheparyant mothya pramanat badalalya naheet, jaree aata varshachya jaivik aadharabaddal barech kahee dnyat aahe. darwinne aapale yuktivad tondi vyakt kele, parantu tevhapasoon utkrantichya siddhantala aupcharik swaroop denyasathi anek prayatna kele gele aahet. paryavaraniy tapashilanchya kimmativar varshache model banavnare loksankhya anuvanshashastra, anek thikani janukanni prabhavit kelelya parimanatmak vaishishtyancha samavesh karnare parimanatmak anuvanshashastra aanee utkrantivadi khel siddhant jeey anuvanshik tapashilankade durlaksh karatat parantu uchch patalivaril paryavaraniy vastavad samavisht karatat, visheshtah konatyahi dhoranache yash loksankhyemadhye konatya varanvartevar dhorane khelali jaatat yavar avalambun asate, hii sankalpana varanvarta avalambitva mhanoon olakhali jaate.
anukool gatishilata haah 1990 chya dashakat vikasit kelelya tantrancha eka sanch aahe, joou phenotype vyakt vyakt vaishishtyanmadhil lahan utparivartananche dirghakalin parinam samajoon ghenyasathi vikasit keela gela aahe. teey loksankhyechya gatishilatecha utkrantivadi gatishilateshi sambandh jodatat aanee khel siddhantatun varanvartevar avalambun nivadichya moolbhut kalpanecha samavesh aanee samanyikaran karatat.
moolbhut kalpana.
anukulansheel gatishilatechya done moolbhut kalpana mhanje naveen utparivartak disu lagatat tevha nivasi loksankhya gatishil samatolamadhye asate aanee rahivasi asalelya vatavaranat durmil asatana asha utparivartananchya prarambhik vadhichya daravarun tyanchya antim bhavitavyacha andaj lavala jaau shakato. jevha utparivartanancha prarambhik ghatankiy vaadh darr mhanoon mojala jaato tevha yaa darala aakraman ghatank mhanoon olakhale jaate aanee jevha utparivartit vyakti aayushyat utpann karat asalelya santatinchi apekshit ekoon sankhya mojate tevha moolbhut punarutpadak sankhya mhanoon olakhale jaate. yala kadhikadhi utparivartananchi aakramankshamta mhanatat. 
yaa kalpanancha vapar karnyasathi, ganiteey pratimane utkrantishil badalatoon jaat asalelya vaishishtyancha spashtapane samavesh karane aavashyak aahe. jaree paryavaranachya badalatya bhagat keval sadhyachya loksankhyechi loksankhya asel, taree paryavaran aanee loksankhyechya gatishilata yaa donhinche varnan yaa pratimane kele pahije. tyanantar aakramanacha ghatank nishchit keela jaau shakato. heey katheen asoo shakate, parantu ekada nishchit jhaale qee, anukuli gatishilata tantre model sanrachanepasun swatantrapane lagoo kelee jaau shakatat.
eksaman utkranti.
samaan vaishishtyansah asalelya vyaktincha samavesh asalelya loksankhyela monomorphic mhanatat. anyatha spashtapane sangitalele naslyas, vaishishtya hii eka vastavik sankhya manali jaate aanee r aanee m heey anukrame monomorphic nivasi loksankhyeche aanee aakramankari utparivartanache vaishishtya moolya aahe.
aakraman ghatank aanee nivad pravanata.
aakraman ghatank sootra _ 1 chee vyakhya nivasi (aar) neey vatavaranatil suruvatichya durmil utparivartanacha apekshit vaadh darr mhanoon kelee aahe, jyacha arth pratyek phenotypechi (vaishishtya moolya) varanvarta jevha jevha samtol vatavaranachya itar serve pailuncha andaj lavnyasathi purese asate, jase qee jansankhyikiy rachana aanee
sansadhananchi upalabdhata. pratyek aar sathee, aakraman ghatank haah suruvatichya durmil utparivartakane anubhavalela tandurusticha bhupradesh manla jaau shakato. utkrantichya khelachya siddhantapramanech pratyek yashasvi aakramanabarobar bhupradesh badalato, parantu utkrantichya shastriy drushtikonachya ulat, nehmi uchch tandurustichya dishene anukool prakriya mhanoon.
aapan nehmich asey gruheet dharoo qee rahivasi tyachya jansankhyikiy aakarshanavar aahe aanee parinami serve aar sathee sootra _ 2, anyatha loksankhya anishchit kalasathi vadhel. 
nivad pravanata hii sootra _ 3, sootra _ 4 vareel aakraman ghatankacha utaar mhanoon paribhashit kelee jaate. jarr nivad pravahache chinh kinchit jaast (qamee) vaishishtya moolye asalele sakaratmak (nakaratmak) utparivartak asel tarr teey yashasviritya aakraman karoo shakatat. heey resheey andajanusar aahe 
jeey jevha jevha sootra _ 6 asate.
jodichya drushtine-aakramakta bhukhand.
aakraman pratipadak haah durmil utparivartakane anubhavalelya tandurustichya bhupradeshache pratinidhitva karato. mothya (anant) loksankhyemadhye, jyache sootra _ 1 sakaratmak aahe, teey keval vaishishtya moolya sootra _ 7 asalele utparivartak saksham asatat.
yashasvipane aakraman kele. aakramanacha samanya parinam assa aahe qee utparivartak rahivashanchi jaaga gheto aanee durmil utparivartak badalanmule anubhavala jaanara tandurusticha bhupradesh. aakramanachya parinami parinami malikecha parinam nirdharit karnyasathi jodinusar-aakramak bhukhand (pips) anekada vaparale jaatat. heey pratyek nivasi vaishishtyachya mulyasathiche sootra 9 darshavtat, serve utparivarti vaishishtyanchya mulyansathiche sootra 7, jyasathi sootra 1 sakaratmak aahe. lakshat ghya qee sootra _ 1 heey karn sootra _ 3 varr shoonya aahe. pipsmadhye durmil utparivartakane anubhavalelya tandurustichya bhupradeshancha anulamb reshanshi sambandh aahe jithe nivasi vaishishtya moolya sootra _ 9 sthir aahe.
utkrantivadi ekeri dhorane.
nivad pravanata sootra _ 4 utkranti badalachi disha tharavate. jarr too sakaratmak (nakaratmak) asel tarr kinchit jaast (qamee) gunavishesh asalele utparivartak samanyapane aakraman karel aanee rahivashanchi jaaga gheil. pann sootra _ 4 nahise jhalyas kaay hoil? asha velee utkranti thambali pahije asey disate. haah eka sambhavya parinam asala taree, sarvasadharan paristhiti adhik guntaguntichi aahe. vaishishtye kinwa dhorane sootra 17 jyasathi sootra 18, utkrantivadi ekvachani dhorane mhanoon olakhale jaatat. asha bindunchya jawal, durmil utparivartakane anubhavalela tandurusticha bhupradesh sthanik patalivar 'sapat' asato. heey teen gunatmakdrushtya bhinn marganni ghadu shakate. pratham, cubic karyachya kathichya bindupramanech eka apghatit prakaran jethe maryadit utkrantichya utkrantichya sthanik 'sapatpana' chya pudhe netat. dusare mhanje, eka tandurusti kamal jee utkrantivadi sthir ranniti (ess. ess.) mhanoon olakhali jaate aanee jee ekada sthapit jhaali qee, jawalchya lokandware aakraman kelee jaau shakat nahee.
utparivartak. tisare, kiman tandurusti, jyamadhye vighatankari nivad hoil aanee loksankhyechi done aakaranmadhye shakha hoil. yaa prakriyela utkranti shakha mhanatat. jodidar aakramankshamatechya rachnet ekeri dhorane aadhaltat jithe sakaratmak aakramankshamatechya pradeshachi seema karnala chhedate. 
ekada nivad pravanata kalalyavar ekeri dhorane shodhali jaau shakatat aanee tyanche vargikaran kele jaau shakate. ekvachani dhorane shodhanyasathi, nivadicha pravanata jyaa gunansathi nahishi hote teey shodhane purese aahe, mhanje.eae. sootra 17 shodhanyasathi, asey sootra 20. nantar moolbhut gananetoon dusari vyutpann chachani vaparoon tyanche vargikaran kele jaau shakate. sootra 17 varr moolyamapan kelele dusare vyutpann nakaratmak (sakaratmak) asalyas dhoran sthanik tandurusti kamal (kiman) darshavate. mhanoon, utkrantivadi sthir dhoran sutrasathi _ 17 aamchyakade aahe
jarr heey dhoran utkrantivadidrushtya asthir asel aanee jarr teey abhisaran dekhil sthir asel tarr utkrantivadi shakha akheris udbhavatil. ekvachani dhoran sootra _ 17 heey thode qamee kinwa thode jaast vaishishtyapurn moolyansah abhisaran sthir monomorphic loksankhya honyasathi, sootra _ 17 chya jawal asalelya vaishishtyapurn moolyansah utparivartakanni abhedya asane aavashyak aahe. heey houu shakate qee sootra _ 17 chya shejari asalele nivad pravanata sootra _ 4 heey sootra _ 28 sathee sakaratmak aanee sootra _ 29 sathee nakaratmak asane aavashyak aahe. yacha arth assa qee sootra _ 9 chey karya mhanoon sootra _ 4 chaa utaar
sootra _ 17 varr nakaratmak kinwa samatulya aahe
varr dilele abhisaran sthiratecha nikash aakraman ghatankachya ghatankachya vyutpannancha vapar karoon dekhil vyakt keela jaau shakato aanee yethe vicharat ghetalelya sadhya prakarananpeksha adhik vistar karnyasathi vargikaran parishkrut kele jaau shakate.
bahuroop utkranti.
yashasvi aakramanacha samanya parinam mhanje utparivartit vyakti rahivashanchi jaaga ghete. tathapi, itar parinam dekhil shakya aahet; visheshtah nivasi aanee utparivartit donhi tiku shakatat aanee nantar loksankhya dvirupi banate. loksankhyemadhye eka vaishishtya tikoon rahate asey gruheet dharoon, jarr aanee keval jevha tyacha apekshit vadhicha darr durmil asatana sakaratmak asel, tarr sootra 34 aanee sootra 35 yaa done vaishishtyanmadhil sahastitvachi aut ashee aaheh
aanee
jethe sootra _ 34 aanee sootra _ 35 yanna anekada morphs mhanoon sambodhale jaate. ashee jodee eka sanrakshit dvirupata aahe. serve sanrakshit dvirupatancha sanch sahastitvacha pradesh mhanoon olakhala jaato. chitratmakdrushtya, jevha jodinusar aakramakta aalekh karnavar pratibimbit keela jaato tevha yaa pradeshat paraspar aachchhadit bhag asatat. 
bahuroopi loksankhyemadhye aakraman ghatank aanee nivad pravanata.
aakraman ghatank dvirupiya loksankhyesathi thet samanyikrut keela jaato, kaaran done rupank sutrandware nirdharit kelelya vatavaranatil durmil utparivartakchya apekshit vadhichya darache sootra _ 40 aanee
sootra _ 35. sootra _ 34 kinwa sootra _ 35 chya jawal asalelya utparivartanasathi sthanik tandurustichya bhupradeshacha utaar aata nivad pravanandvare deela jaato.
aanee
vyavharat, dvirupiya nishchit karane anekada katheen asate
nivad pravanata aanee aakraman ghatank vishleshanatmakdrushtya, aanee anekada
sankhyatmak gananecha avalamb karava lagato.
utkrantivadi shakha.
utkrantichya kalat ekankik bindunjaval sanrakshit dvirupata udbhavane asamanya nahee, parantu tyache mahatva nivad sthir karnari aahe qee vighatankari yavar avalambun asate. nantarchya prakaranat, done aakaranchi vaishishtye utkranti shakha mhanoon olakhalya olakhalya prakriyet vegali hotil. gerritz 1998 eka aakarshak sadarikaran karate
vighatankari nivad keval tandurustichya kiman jawalach hote assa yuktivad. heey sanshodhanatmakdrushtya samajoon ghenyasathi, eka eka bindu jawal dvirupiya loksankhya sootra _ 34 aanee sootra _ 35 chaa vichar qaraa. satatyane 
aanee tevhapasoon 
dvirupiya loksankhyesathi tandurusticha paridrushya haah ekvachani dhoranachya jawal asalelya eka rupatmak rahivashasathi tyacha eka gondhal asala pahije.
vaishishtyapurn utkrantiche kathanak.
shakhannantarchi utkranti heey vaishishtyapurn utkrantichya kathanakancha vapar karoon spasht kele jaate. heey sahastitvache kshetra, utkrantivadi badalachi disha aanee nivadicha pravanata nahishi honare bindu fitness maxima kinwa minima aahet qaa heey darshavtat. utkrantimule dvirupiya loksankhya sahastitvachya pradeshabaher jaau shakate, asha paristhitit eka roop lupt hote aanee loksankhya punha ekada ekroopi hote.
itar upayog.
anukool gatishilata prabhavipane khel siddhant aanee loksankhya gatishilata ekatra karate. tyamule, utkranti loksankhyechya gatishilatevar kassa parinam karate yacha tapas karnyasathi heey khoop upayukt tharoo shakate. yatoon eka manoranjak nishkarsh baher yeto too mhanje vaiyaktik-stariy anukulan kahivela sampoorn loksankhya/prajati namshesh houu shakate, hii ghatana utkranti aatmahatya mhanoon olakhali jaate.

