Madhuram: A Simulation Model for Sweet Potato Growth

Transcription

1 World Journal of Agrcultural Scences 4 (): 41-54, 8 ISSN IDOSI Publcatons, 8 Madhuram: A Smulaton Model for Sweet Potato Growth K. Somasundaram and V.S. Santhosh Mthra Department of Computer Scence and Applcatons, Gandhgram Rural Insttute, Gandhgram, Dndgul Dstrct, Taml Nadu, Inda Abstract: In ths paper a process model for smulatng the growth of sweet potato has been proposed. Vegetatve developmental days (VDD) and reproductve developmental days (RDD) were calculated to predct crop phenology. Crop growth was dvded nto three phases,.e., the frst phase from plantng to tuber ntaton, the mddle phase from tuber ntaton to the begnnng of tuber bulkng and the fnal phase from the begnnng of tuber bulkng to harvest. Vne growth rates n terms of RDD were worked out for all the phases. Leaf producton was assumed to be related to the length of lfe of ndvdual leaves and the average leaf area was assumed to be nversely related to the number of leaves retaned. A new algorthm for predctng branchng events was developed. Solar radaton and photosynthess were calculated usng standard methods. Part of the photosynthates produced was used for provdng energy for the mantenance and growth processes. The remanng was allocated to leaves, stem and tubers n proporton to ther growth rate. The model predcted yelds were n good agreement wth the correspondng observed values n most of the cases. Predcton of number tubers was also reasonably accurate. However, predcton of number of leaves and branchng devated consderably from the observed value. Key words: Sweet potato computer smulaton crop smulaton INTRODUCTION Sweet potato s grown n nearly all parts of the tropcal and sub tropcal world and n warmer areas of temperate regons. The crop has been a staple food crop for many tropcal communtes for centures and t contnues to be an mportant source of food n many poor countres. Sweet potato s rch n carbohydrate [1] and vtamns []. Ths paper descrbes a growth smulaton model development for sweet potato, whch predcts the crop phenology n response to envronmental factors and computes total dry matter producton and ts dstrbuton. Parameters of three sweet potato varetes Sree Arun, Sree Bhadra and Sree Rethna were estmated for evaluatng the model. Usefulness of ths model for computng the mpact of stress effect due to water, potassum and ntrogen defct/ defcency on fnal yeld s also dscussed n ths paper. Background: Several studes have been reported on the relatonshp between plant parts and sweet potato tuber yeld [3, 4]. Bourke [5] showed the dependence of tuber yeld on total plant dry matter. Earler studes ndcated that dstrbuton of assmlate to the tuber s more mportant than total photosynthate producton n determnng the fnal tuber yeld [6, 7]. Accordng to Bouwkamp [8], sweet potato crop mght be ether source or snk lmted, dependng on the cultvar, envronment or canopy management. [9] observed that the formaton of storage roots of sweet potato n the feld dd not retard the vne growth but proceeded concurrently wth the growth of the tops. They also noted the effect of envronmental factors on the growth of sweet potato. Increase n storage root growth wth fluctuatng temperatures was attrbuted to the ncrease n the rate of translocaton of carbohydrates from the tops to the roots and the nfluence on mneral nutrton and water uptake. [1] dentfed mean tuber weght and number of tubers as the most mportant yeld components n sweet potato. Another concluson from ther study was that the varaton n yeld occurred n sweet potato due to the nfluence of season, plantng materal and tuber development. The realzaton of tuber yeld after tuber ntaton, depends on the capacty of the shoot system to produce assmlate and the development of the tubers to produce a snk for such assmlate [11]. [1] showed that long days enhanced the shoot development and retarded the tuber growth and vce versa for short day. They also observed a Correspondng Author: Dr. K.Somasundaram, Gandhgram rural nsttute, Dndgul dstrct, Taml Nadu, Inda 41

2 World J. Agrc. Sc., 4 (): 41-54, 8 smlar nverse relatonshp between day length and number of branches. Short days were found to promote tuber bulkng. Sweet potato was dentfed as a short day plant wth a crtcal photoperod of 13 h [13]. Accordng to [14], short days retard shoot growth and enhance tuber development. [15] observed that early tuber ntaton, hgh rate of tuber bulkng, long perod of tuber bulkng and large number of tubers were mportant n ncreasng the tuber yeld of sweet potato. Though there does not exst a smulaton model for sweet potato growth, growth smulaton models are avalable for other tuber crops. GUMCAS model [16] of cassava descrbed the growth of cassava reasonably well. In ths model, phonologcal development of the crop was calculated n terms of developmental day. For computng developmental day, a vegetatve clock, whch s a functon of temperature and a reproductve clock, whch s a functon of temperature and photoperod, were assumed. Relatonshps between envronmental parameters (day length, temperature, solar radaton, mosture content and relatve humdty), growth parameters and development of sweet potato are modeled n ths work. The fnal model was obtaned by combnng all these sub-models and was then used for smulatng the growth of the plant under dfferent envronments. The proposed model also computes both the potental (stress free) tuber yeld of sweet potato n a gven envronment and also the yeld n the presence of stresses created by the shortage of water, potassum and ntrogen and when there s no stress. MATERIALS AND METHODS Structure of the model: Wth ths background, we propose a growth smulaton model (Fg. 1) for sweet potato and the envronmental drvng varables of the model are: Fg. 1: Relatonal dagram llustratng the relatonshp of envronmental factors wth growth and producton of sweet potato. Boxes represent state varables, valves are rate varables, oval s the auxlary varable and clouds are the drvng varables and other envronmental varables. Sold lnes and broken lnes represent the flow of matter and nformaton respectvely 4

3 World J. Agrc. Sc., 4 (): 41-54, 8 Maxmum temperature ( C) Mnmum temperature ( C) Sunshne hours (h) Maxmum relatve humdty (%) Mnmum relatve humdty (%) and Sol mosture content (mm) where, d base Tbase < Td T opt :HD = T opt T base T T hgh d Topt < Td T hgh :HD = T hgh T opt T T () Crop phenology: The phenology of sub model explans the relatonshps between dfferent plant parts and the envronmental varables durng the development of sweet potato. Growth phases of sweet potato are dfferent as compared to other flowerng crops. Its growth s dvded nto three phases [13]. Intal phase of extensve growth of fbrous roots. Durng ths phase vnes have only moderate growth rate. Mddle phase where vnes grow extensvely and fast. Tubers are ntated and there s a tremendous ncrease n leaf area. Fnal phase where tuber bulkng occurs. Very lttle growth of vnes and fbrous roots. Intally leaf area stays constant and then decreases. Under tropcal condtons frst phase last for almost four weeks and the second phase lasts up to about seven weeks after plantng. Very lttle tuber ntaton occurs after seven weeks [17]. Phenologcal development of the crop s calculated on each day n terms of developmental days (Dd). The Dd s calculated usng the method followed by [16]. Photoperodc effect (?) s calculated usng the emprcal formula whch was developed by cubc curve fttng on the data taken from [18]: DL φ=.988dl DL where DL s the day length (h) and s the number of days after plantng (DAP). Crtcal photoperod for sweet potato s taken as 13 h. Optmum temperature for the growth of sweet potato(t opt ) s taken as 5 C [18]. The base temperature for the growth of sweet potato (T base ) s calculated as 8.1 C. The hghest temperature at whch sweet potato grows (T hgh ) s taken as 38 C [11]. Calculaton of Dd: Hourly ncrements n developmental tme (HD, DD/day) are calculated accordng to: Td T base,td T hgh :HD = (1) Tmn + Tmax T d = + (Tmax T mn) cos(.618(h 14))/(3) where, h = tme of the day, T mn and T max = Mnmum and maxmum temperature of the day. = mn max = h= 1 4 ( ) Rv f(t,t ) HD/4 Sweet potato s an ndetermnate crop. The plant contnues to produce branches and leaves even after flowerng. So throughout the lfe of the crop, two types of developmental days are calculated. Vegetatve Development Day (VDD): Here only vegetatve clock [16] s consdered for calculatng Dd. VDD s the sum of vegetatve development rates (Rv) tll date. Reproductve Development Day (RDD): RDD s calculated as the sum of reproductve development rates (Rr) tll date. Ths s computed usng the same method as n [16] by modfyng Rv wth?, as: Rr = Rv φ (4) Tuber ntaton: The end of frst phase of the growth s marked by the begnnng of tuber ntaton. Tubers are found to be ntated when RDD.e., SRr reaches a partcular value (ntbr). Ths value was computed to be same for all varetes. Producton of tubers: Once the frst tuber s ntated further producton of tubers s contnued tll the end of the mddle phase. The end of mddle phase s marked by the begnnng of tuber bulkng. The Value of SRr, after the producton of one tuber, should reach at least tbr_gap, before the next tuber s produced. Ths value s computed separately for the three varetes Sree Arun, Sree Bhadra and Sree Rethna. Tuber bulkng: [17] reported that tuber ntaton happens after four weeks and tuber bulkng after seven weeks of plantng under tropcal condtons. [19] suggested that under non tropcal condtons, frst phase lasts up to 9.5 weeks after plantng and the second 43

4 World J. Agrc. Sc., 4 (): 41-54, 8 phase from 9.5 weeks to 16 weeks after plantng. From these data the DAP on whch tuber bulkng starts (DAP tb ) s calculated as: DAP DAP t t tb = tb (5) where, DAP t = DAP on whch tuber ntaton happens, t = 4 and 9.5 weeks after plantng under tropcal and non tropcal condtons respectvely, tb = 7 and 16 weeks after plantng under tropcal and non tropcal condtons respectvely. Vne growth: Vne growth s more vgorous n the mddle growth phase compared to the ntal and fnal growth phases. Vne length (VL) was calculated as a functon of phenologcal growth rate. Ths growth s further modfed n terms of dry matter accumulated n vnes. dvl ' = dvl ( DMV 1 DMV ) ( DMV DMV ) 3 where, dvl = ncrease n VL on DAP, DMV -1, DMV - and DMV -3 = Dry matter n vnes on -1, - and -3 DAP respectvely, ' vlen dvl =,>1 = vlen1 Rr,= n Rr = where, Rr = growth rate of reproductve clock on DAP, Number of leaves: Leaves are the man source of assmlates whch s utlzed for the growth of the plant and for ncreasng the tuber weght. The number of leaves (LF) produced depends on the rate of leaf producton durng ths perod and the length of lfe of ndvdual leaves. Sweet potato contnues to produce leaves tll the harvest []. The number of leaves per plant at any pont of tme vares wdely among cultvars [1]. In ths study, the number of leaves per plant s calculated n terms of the phenologcal growth rate as well as the dry matter accumulated to the leaves. (6) (7) respectvely, LA -1 and LA - = Leaf area on -1 and - DAP respectvely, ALA - = Average leaf area on - DAP, nobr = number of branches on DAP. lfactor s a cultvar dependent constant. Leaf duraton: In ths study, the lfe of ndvdual leaves of sweet potato was worked out emprcally as 3 RDD and usng ths value, leaf fallng was smulated. Leaf area: Leaf area vares wdely among cultvars and at dfferent growth perods dependng on the number of leaves retaned on the stem and ther sze [1]. The followng emprcal equaton 9, shows the relatonshp between average leaf area (ALA) and LF. lafactor ALA = (9) log(lf) An ntal ALA (larea) s assumed for each cultvar tll at least three leaves are formed. lafactor s a parameter specfc to cultvars. Leaf area ndex (LAI) can be computed as: ALA LF LAI = (1) spacng where, spacng s the product of dstance between rows and the dstance between plants wthn the rows. Branchng: [1] observed an nverse relatonshp between day length and number of branches produced (BR). SRr requred for branch ntaton (br1) and the SRr between branchng events (br_gap) are calculated for the varetes Sree Arun, Sree Bhadra and Sree Rethna. The steps followed for predctng branchng are: Intalse: BR=. Determne DAP on whch branchng s ntated (DAP br1 ); BR=1; DAP on whch branchng happens (brday) = DAP Calculate the number of days requred between two branchng events (brgap) as: DAP br1 brgap = br_gap (11) br1 dlf DML DML LA LA 1 1 DML 1 DML ALA Rr lfactor + nobr = (8) where, dlf = ncrease n LF on DAP, DML, DML -1 and DML - = Dry matter n leaves on, -1 and - DAP 44 BR=BR+1; f (DAP-brday) brgap, brday = brday+1; f (DAP-brday)> brgap, brday+ brgap Rr br_gap and = brday brday+ brgap Rr br_gap and = brday

5 BR=BR; f brday+ brgap Rr < br_gap. = brday World J. Agrc. Sc., 4 (): 41-54, 8 Length of the branches and the number of leaves on t are assumed to ncrease at the same rate as that of the man stem. Snce short days promote the growth rate of the crop as well as the producton of branches, branchng event s predcted when the crop grows at a rate hgher than that of the expected rate. Calculaton of solar radaton: Solar radaton absorbed by the plant was calculated usng the method suggested by []. Drect and dffused solar radatons are calculated separately. Calculaton of photosynthess: Rate of leaf photosynthess (PL, KgCO ha -1 h -1 ) s calculated usng the equaton 1 [18] as: PLEA PAR PL = PLMX 1 exp PLMX (1) where, PLEA = ntal lght use effcency (Kg CO ha - 1 h -1 (Jm - s -1 ) -1 ), PLMX = Maxmum rate of leaf photosynthess (Kg CO ha -1 h -1 ), PAR = Photosynthetcally actve radaton whch s about 5% of the solar radaton receved. PL was computed separately for drect and dffused rradance. PLEA and PLMX are specfc to cultvars and they vary wth temperature. Effects of temperature on PLEA and PLMX are explaned by equatons 13 and 14 respectvely, whch were developed by least square curve fttng on the data from [18]. PLEA =.187TMEAN.1TMEAN (13).151TMEAN + PLMX = PLMX_opt.69TMEAN (14) where, PLMX_opt = PLMX at 5 C (ths s a varetal parameter), TMEAN s the mean temperature of on th DAP whch s calculated usng the method suggested by [3]. Daly gross canopy photosynthess s calculated from the leaf photosynthess rate usng equaton 15 []. Pc = Ls. PLs + Ld. PLd (15) where, Ls and Ld are components of LAI n drect and dffused sunlght respectvely, PLs and PLd are components of PL n drect and dffused sunlght respectvely 45 A fracton of the daly gross photosynthate s used for the mantenance process n the plants. Ths process ncludes resynthess of degraded protens and mantenance of on-gradents across cell membranes. The energy for ths process s derved from the photosynthates by mantenance respraton. Mantenance coeffcent m represents the daly mantenance respraton rate (Kg CH O ha -1 d -1 ) and the equaton 16 represents ts varaton wth temperature [4]. (TMEAN )/1 m =.Rm (16) where, Rm = m at C. Another fracton of the dry matter wll be converted nto structural parts and the effcency of convertng substrate to structure s called growth effcency (Y) and ts value s assumed to be constant n ths model. Proporton of the gross photosynthate allocated to the shoot process (?) s assumed to be 8% n ths model. Daly net canopy photosynthess s calculated usng []. L Pn ce = Pg ( 1 η( 1 Y )) Y.m ξ (17) where, Pn ce = Daly net canopy photosynthess (Kg CO ha -1 d -1 ), Pg = Daly gross canopy photosynthess (Kg CO ha -1 d -1 ), L = LAI,? = Leaf area rato (m (g dry weght n CO equvalents) -1 ). Pn ce computed usng equaton 17 s converted nto Kg dry weght wth the help of the equaton gven by []. Pn ce Pn = (18) 1.65 where, Pn = Daly net canopy photosynthess (Kg ha -1 d -1 ). Parttonng: Photosynthates remanng after the mantenance and growth processes wll be stored n dfferent parts and storage organs. Growth rate of ndvdual parts of the plant provdes a measure of ther compettve ablty as snk [5]. In sweet potato, competton between stems and leaves for the avalable supply of assmlates contnues for a long perod. Growth rate of each plant part s computed n terms of ncrease n leaf area, for estmatng the photosynthate allocated to them. Growth rate of vnes (fv ) on th DAP s calculated usng equaton 19 as the product of ncrease n leaf area and dry matter accumulated n vnes per ncrease n leaf area on th DAP. fv = (LA LA ) wt_vl (19) 1

6 World J. Agrc. Sc., 4 (): 41-54, 8 where, LA and LA -1 = Leaf area on and -1 DAP respectvely, wt_vl= s a cultvar dependent constant. Growth rate of leaves (fl ) on th DAP s calculated usng equaton, as the product of ncrease n leaf area and dry matter accumulated n leaves per ncrease n leaf area on th DAP. fl = (LA LA ) wt_la () 1 where, wt_la = s a cultvar dependent constant. Growth rate of tubers (ft ) on th DAP s calculated usng equaton 1 ft DMT 1 = dntbr (1) ntbr 1 = (LA LA 1) wt_ntbr, f number of tubers on DAP> and that on -1 DAP= where, dntbr = Rr TBR K WS ntbr = Rr TBR WS, -1 1 K Rr -1 = growth rate of reproductve clock on (-1) th DAP, TBR K = Effect of stress due to potassum shortage on number of tubers, DMT -1 = Dry matter n tubers on -1 th DAP, wt_ntbr= s a cultvar dependent constant. Dry matter stored n vnes (ddmv ), leaves (ddml ) and tubers (ddmt ) on th DAP are estmated usng the equatons, 4 and 6 respectvely. fv ddmv = Pn, f tdm> () tdm where, ddmv = Dry matter allocated to stem on th DAP, tdm = fv + fl + ft, Pn = Net photosynthetc rate on th DAP. DMV = DMV + ddmv, f > (3) 1 where, DMV and DMV -1 = Dry matter n vne and branches on th and (-1) th DAP respectvely. fl ddml = Pn, f tdm> (4) tdm DML = DML + ddml, f > (5) 1 DML and DML -1 = Dry matter n leaves on th and (-1) th DAP respectvely. ft ddmt = Pn, f tdm > (6) tdm where, ddmt = Drymatter allocated to tubers on th DAP. DMT = DMT + ddmt, f > (7) 1 where, DMT and DMT -1 = Dry matter n tubers on th and (-1) th DAP respectvely. Water stress on crop growth: The effect of water stress on crop growth s computed usng the method suggested by [6]. Snce the data on wnd speed s not commonly avalable, Prestly-Taylor method s used n ths model for calculatng reference evapotranspraton (ET ). Water stress (WS) s calculated usng [6]: wtr dep WS = wtr RAW (8) where, wtr = water avalable n the sol (mm), dep = water depleted from root zone (mm), RAW = readly avalable water (mm), wtr was calculated usng the formula [6]: wtr = 1 ( FC PWP) root_depth (9) where, FC=feld capacty, PWP=permanent wltng pont, root_depth = maxmum effectve root depth. Raw was calculated usng the formula [6]: where, raw = wtr dep_fctr (3) dep_fctr = P +.4(5 ET) (31) table where, P table = water depleton factor at no stress, ET c = crop evapo transpraton. Et c was calculated as: ETc = ET cropfactor (3) dep was calculated usng the formula: c where, ddml = Drymatter allocated to leaves on th DAP. dep = dep1 (rfall roff) rrgaton capllaryrse + ETc + percolaton (33) 46

7 World J. Agrc. Sc., 4 (): 41-54, 8 where, dep1=water content n the root zone at the end of the prevous day, rfall=precptaton, roff=runoff from the sol surface, rrgaton=net rrgaton depth that nfltrates the sol, capllaryrse=capllary rse from the groundwater table, ETc=crop evapotranspraton, percolaton=water loss out of the root zone by deep percolaton. WS s multpled wth Rr before summng t to check whether tbr_gap s reached whch marks the producton of a tuber n the mddle phase. Potassum stress on crop growth: The most mportant macro element for sweet potato s potassum whch s benefcal to the prncpal physologcal processes [1]. Potassum fertlzers ncrease the number of tubers of sweet potato [7]. Potassum ncreases the rate of photosynthess as well as the translocaton of the photosynthates []. Equaton 34 s formulated to estmate the effect of potassum stress on tuber producton. They are developed wth the assumpton that, when there s no potassum applcaton there are TBR K number of tubers at 9 DAP. Nnenty DAP s selected n ths case because the short duraton hgh yeldng varetes are usually ready for harvest at 9 DAP under tropcal condton. Another assumpton s that when more potassum s added t ncreases the number of tubers lnearly tll the maxmum possble values TBR KM s reached. KM TBR s the quantty of potassum whch s requred to attan TBR KM. Values of the parameters TBR KM, KM TBR and TBR K are estmated usng the data from [8]. TBR K TBR KM TBR K K + TBR K KM TBR = (34) TBR KM Ntrogen stress on crop growth: Ntrogen s a valuable component for the development of aeral parts of sweet potato [1]. Increasng ntrogen applcaton ncreases the sze of ndvdual leaves [9]. Ntrogen potassum mxture s mportant for ncreasng the number and weght of tubers. Ntrogen stress on mean tuber weght (TWT N ) s gven by equaton 35. As n the case of potassum Samplng schedule s gven n Table 1. stress, ths equaton s developed wth the assumpton that, when there s no ntrogen applcaton there s a mean tuber weght of TWT N. Smlar to potassum, another assumpton made here s that, when more ntrogen s added t ncreases the mean tuber weght lnearly tll the maxmum possble value TWT NM s reached. NM TWT s the quantty of ntrogen, whch s requred to attan TWT NM. Values of the parameters TWT NM, NM TWT and TWT N are computed usng the data from [7]. 47 TWT N TWTNM TWT N N + TWT N NM TWT = (35) TWT Estmaton of parameter values: The parameters requred to smulate the growth of sweet potato were estmated by conductng a feld experment at Mtranketan, Thruvananthapuram, Inda, whch s stuated at 8.5 N lattude. Sol type at the ste s clayey. Three varetes Sree Arun, Sree Bhadra and Sree Rethna were planted n Randomsed block desgn wth three replcatons. Sree Arun s a spreadng varety of 9-1 days duraton, wth an average yeld of -8 T/ha. Sree Bhadra s a sem-spreadng varety of 9-95 days duraton, wth an average yeld of -7 T/ha. The varety Sree Rethna s of spreadng type and 9-1 days duraton. Its average yeld s about -6 T/ha. Vne cuttngs of 15 cm length were planted n rows taken 6 cm apart. Plant to plant spacng followed was 5 cm wthn each row. As a control measure aganst sweet potato weevl, cuttngs were dpped n.5% monocrotophos and kept for 1 mnutes before plantng. Agro technques recommended by Central Tuber Crops Research Insttute (CTCRI), Thruvananthapuram, Inda were followed. Vne cuttngs were planted on May 4, 4 June 4, 4 September 4, 7 October 4 and 3 November 4. Fertlzers were appled at the recommended dose of 5 Kg N, 5Kg P O 5 and 5 Kg K O per hectare. Half of the recommended dose of N and K O and full P O 5 were appled as basal dose and the remanng dose was top dressed one month after plantng. Destructve samplngs were done to collect data on followng plant attrbutes. Vne length Number of leaves Leaf area Number of flowers Number of tubers Fresh and dry weghts of vne, leaves and tubers Length of branches and Number of leaves n branches Model evaluaton: To evaluate the performance of developed model, feld experments were carred out at Mtranketan, Thruvananthapuram for three seasons usng three varetes Sree Arun, Sree Bhadra and Sree Rethna. Data were collected from CTCRI, Thruvananthapuram and Regonal centre (RC) of CTCRI, Bhubaneswr also to test the performance of the model. Weather data of each of the ste were also collected. NM

8 World J. Agrc. Sc., 4 (): 41-54, 8 Table 1: Samplng schedule of the feld experment to estmate crop parameters Date of plantng Samplng dates Harvest date , , and , and , , and , , and , and Mtranketan, Thruvananthapuram: For testng the model, an experment feld was conducted n the same ste to estmate the crop parameters. The same agro technques were followed. Three sets of data were collected for each varety by plantng the crop n three dfferent dates, 18 June 4, 4 July 4 and 4 July 4. Three varetes Sree Arun, Sree Bhadra and Sree Rethna were planted. Data collecton was done on 11 st, 9 th and 11 st days after plantng respectvely. CTCRI, Thruvananthapuram: The second ste was CTCRI, Thruvananthapuram, Inda, whch s located at 8.5 N lattude. Sol type at the ste was clayey. Data were collected from the same three varetes, whch were kept n the nsttute germplasm collecton. Agro technques recommended by CTCRI were followed for rasng the crops. The plantng was done on 1 January 6 and data were collected when the plants were 116 days old. Data on plant attrbutes were collected smlar to data collecton done for Mtranketan, Thruvananthapuram. RC of CTCRI, Bhubaneswr: The thrd ste was Regonal centre of CTCRI, Bhuvaneswar, Inda, whch was located at 1.5 N lattude. Sol type at the ste was sandy loam. Data were collected from the varetes Sree Arun and Sree Bhadra whch were kept n the nsttute germplasm collecton. The crop was rased as per the agro technques of CTCRI. The plantng was done on 5 September 5 and data were collected on 14 th day. Data on plant attrbutes were collected smlar to data collecton done for Mtranketan, Thruvananthapuram. RESULTS (TMIN ) of 3 C and 3 C respectvely and obtaned the value of ntbr as: 4 7 ntbr = Rr (36) = 1 tbr_gap: The varetal character tbr_gap, was computed separately for the three varetes Sree Arun, Sree Bhadra and Sree Rethna, usngthe equaton: tblk ntbr tbr_gap = (37) notbr where, tblk = SRr for seven weeks after plantng wth TMAX and TMIN of 3 C and 3 C respectvely, notbr= Number of tubers produced by the plant. vlen1 and vlen: The parameters vlen1 and vlen were computed usng the equatons 38 and 39. vlen1 = VL n = 1 Rr (38) where, VL = VL on th DAP, Rr = Rr on th DAP, n = number of days. VL vlen= mn log Rr = 1 (39) where, Rr = Rr on th DAP, mn = number of days. lfactor, lafactor and larea: Value of the parameter lfactor and lafactor were estmated usng equatons. Estmaton of parameter values: Requred parameter values for the model development were computed based on the data collected as gven below: ntbr: Snce the feld experment was conducted under tropcal condton, SRr for four weeks after plantng was worked out wth maxmum temperature on th day (TMAX ) and the mnmum temperature on th day 48 lfactor = where, LF = LF on th DAP. n LF = 1 Rr (4) = ( ) (41) lafactor log LF ALA

9 World J. Agrc. Sc., 4 (): 41-54, 8 4 (a) RMSE = (a) RMSE = (b) RMSE = (b) RMSE = (c) RMSE = (c) RMSE = Fg. : Observed Vs predcted tuber yeld (T/ha) for the varetes (a) Sree Arun (b) Sree Bhadra and (c) Sree Rethna where, ALA =ALA on th DAP. Value of larea was estmated separately for all the three varetes from feld observatons. br1 and br_gap: SRr requred for branch ntaton (br1) and the SRr between branchng events (br_gap) were calculated separately for the three varetes from feld observatons. wt_vl, wt_la and wt_ntbr: Value of these parameters were estmated as follows: DMV wt_vl = LA (4) DML wt_la = LA (43) DMT wt_ntbr = LA (44) Fg. 3: Observed Vs predcted values of number of tubers for the varetes (a) Sree Arun (b) Sree Bhadra and (c) Sree Rethna Values of the crop parameters estmated for the three varetes Sree Arun, Sree Bhadra and Sree Rethna are gven n Table. These values are the average of the fve data sets whch were collected under dfferent weather condtons. Model evaluaton: Usng the model, tuber yeld of the varetes at each ste were computed. In Fg. a-c observed values of tuber yeld were plotted aganst the predcted ones. From these fgures, t s observed that the predcted values are reasonably close to the observed values. The number of tubers predcted was plotted aganst the observed values n Fg. 3a-3c. The plot of observed Vs predcted for the number of leaves and the number of branches for all the varetes are shown n Fg. 4a-4c and 5a-5c respectvely. Predcted values of number of branches devated consderably from the observed values n many cases. 49

10 World J. Agrc. Sc., 4 (): 41-54, (a) RMSE = (a) RMSE = (b) RMSE = (c) RMSE = (b) RMSE = (c) RMSE = Fg. 4: Observed Vs predcted values of number of leaves for the varetes (a) Sree Arun (b) Sree Bhadra and (c) Sree Rethna Fg. 5: Observed Vs predcted values of number of branches for the varetes (a) Sree Arun (b) Sree Bhadra and (c) Sree Rethna Table : Crop parameter values estmated for Sree Arun, Sree Bhadra and Sree Rethna Parameter Sree Arun Sree Bhadra Sree Rethna ntbr tbr_gap vlen vlen lafactor lfactor br br_gap larea wt_vl wt_la wt_ntbr Senstvty analyss: An average cultvar was defned for conductng senstvty analyss. Average of the parameter values estmated for Sree Arun, Sree Bhadra and Sree Rethna were taken as the parameter values of the average cultvar. Senstvty of the fnal output (T/ha) to the perturbatons n each plant parameter was computed. Senstvty (ß) (Table 9) was estmated usng equaton 45 as the rato of the fractonal change n yeld to the fractonal change n a partcular parameter [16]. dy/y β n = (45) dp / P n where, ß n = ß value of the parameter n, Y = Default tuber yeld when all the parameter values are optmum (Table 6), dy = Yeld when parameter value changed Y, P n = Optmum value of the parameter n, dp n = Parameter value after change - P n. n 5

11 World J. Agrc. Sc., 4 (): 41-54, 8 Weather data of Mtranketan, Thruvananthapuram durng the frst season (18 June 4 to 6 September 4) was used for makng ths analyss. Average of the 5% change on ether sde of the parameter value was used for computng ß. Default tuber yeld at ths ste when all the parameters are at optmum level durng the season for the average cultvar was computed as 31.5 T/ha. From Table 9 t s understood that branchng s the most senstve parameter n determnng tuber yeld. The parameters br_gap and br_1 play a major role n determnng the canopy sze of the plant and thus mportant n determnng the source potental of the plant. Hgh ß values for the parameters lafactor and lfactor reterates the mportance of vegetatve growth n determnng the fnal yeld. Other hgh rankng senstve parameters s ntbr. Ths parameter s very mportant for attanng good snk capacty whch s the most mportant factor n determnng dry matter producton and yeld. DISCUSSION MADHURAM model descrbes the growth of sweet potato reasonably well n the two envronments where t was evaluated. Most of the growth processes were modeled usng the emprcal data. Factors controllng branchng n sweet potato are not well understood and requre further research. Inverse relatonshp between day length and number of branches as reported by [17] was the bass of the branchng algorthm used n ths model. Reproductve growth rate becomes faster when day length s short and under such stuatons more branches are produced. But the model predcted values devated consderably from the observed values. Hence t appears that a better branchng algorthm wll mprove ths model to a large extent. Snce tuber ntaton s promoted by short day condtons [19], ntbr s computed as the sum of Rr s. From Fg. 3, t appears that the model explans the process of tuber ntaton reasonably well. Source snk relatonshps are explaned well by the model. Dry matter parttonng to tubers are smulated based on the basc dea that the source potental s the more lmtng factor n the ntal phase and the snk capacty s more mportant after the formaton of the storage roots [1]. Ntrogen and potassum stress on the plant was modeled wth a lot of assumptons. Though they nfluence many growth processes, the most mportant ones only were ncluded n ths model. Ths s an area where a lot of refnement can be made. 51 Table 3: Varaton n yeld at dfferent levels of sol mosture content for Sree Arun, Sree Bhadra and Sree Rethna durng the perod from 18 June 4 to September 4 Yeld (t/ha) Sol mosture Content (mm) Sree Arun Sree Bhadra Sree Rethna Smlarly water stress algorthm was ncluded n the model wth an assumpton that only mnmum data are avalable. Hence Prestly-Taylor method was followed for calculatng ET, though better methods are avalable. Smulaton scenaros: Ths model can be used for understandng the performance of the crop under dfferent sol and envronmental condtons. Yeld under dfferent levels of stress due to water, K and N can be smulated by ths model. Optmum value of nputs lke mosture content(mst), K and N at whch the tuber yeld s maxmum can also be found out usng ths model. Water stress on crop growth: Water stress computed usng equaton 8, s multpled wth Rr to compute dntbr on th DAP durng the mddle phase, by whch the rate of tuber producton s modfed. Table 3 shows the change n tuber yeld, under the nfluence of water stress. The tuber yeld (T/ha) were calculated for sweet potato varetes Sree Arun, Sree Bhadra and Sree Rethna whch were grown durng the perod from 18 June 4 to September 4 at Mtranketan Thruvananthapuram at dfferent levels of mosture content. To fnd the value of mosture content (mst) at whch YLD s maxmum, a quadratc curve s ftted to the yeld data obtaned at dfferent levels of mst for Sree Arun, Sree Bhadra and Sree Rethna usng SYSTAT 9.. YLD = a mst + b mst + c (46) where, YLD = Tuber yeld (T/ha), a, b and c are emprcal coeffcents. Values of a, b and c whch were computed for these three varetes are gven n Table 4. Value of mst at whch YLD s maxmum s found out separately for each varety by dfferentatng

12 World J. Agrc. Sc., 4 (): 41-54, 8 Table 4: Values of a, b and c computed for Sree Arun, Sree Bhadra and Sree Rethna at Mtranketan, Thruvananthapuram durng the perod from18 June 4 to September 4 Varety a b c Sree Arun Sree Bhadra Sree Rethna Table 5: Varaton n yeld at dfferent levels of potassum for Sree Arun, Sree Bhadra and Sree Rethna durng the perod from 4 July 4 to November 4 Yeld (T/ha) Quantty of K (Kg/ha) Sree Arun Sree Bhadra Sree Rethna Table 6: Values of ak, bk and ck computed for Sree Arun, Sree Bhadra and Sree Rethna at Mtranketan, Thruvananthapuram durng the perod from 1 July 4 to November 4 Varety ak bk ck Sree Arun Sree Bhadra Sree Rethna Table 7: Varaton n yeld at dfferent levels of ntrogen for Sree Arun, Sree Bhadra and Sree Rethna durng the perod from 4 July, 4 to 1 October, 4 Yeld (t/ha) Quantty of N (Kg/ha) Sree Arun Sree Bhadra Sree Rethna equaton 46 and then solvng t by assumng that the value of the frst dfferental s zero when YLD s maxmum. Maxmum yeld due to the effect of mosture content s attaned when the mosture content was 5.55, 5.5 and 5.63 mm for Sree Arun, Sree Bhadra and Sree Rethna respectvely and the YLD computed at ths mosture content were 36., and 4.5 T/ha respectvely. Potassum stress on crop growth: Potassum stress on the producton of tubers, whch s calculated usng equaton 34, s multpled wth Rr to compute dntbr on th DAP durng the mddle phase, by whch the rate of tuber producton s modfed. Through the nfluence on these processes, potassum stress results n a reducton n the fnal tuber yeld. The tuber yeld under dfferent levels of K were calculated for sweet potato varetes Sree Arun, Sree Bhadra and Sree Rethna whch were grown at Mtranketan, Thruvananthapuram durng the perod from 1 July 4 to November 4 are gven n Table 5. To fnd the quantty of potassum (K) at whch YLD s maxmum, a quadratc curve s ftted to the yeld data obtaned at dfferent levels of K for Sree Arun, Sree Bhadra and Sree Rethna usng SYSTAT 9.. Value of K at whch YLD s maxmum was found out separately for each varety as n the case of water stress. Maxmum yeld due to the effect of potassum s attaned when the K O appled was 81.5, and Kg/ha for Sree Arun, Sree Bhadra and Sree Rethna respectvely and the YLD computed at ths level of K O were 3.53, 4.44 and 8.93 T/ha respectvely. Ntrogen stress on crop growth: Ntrogen stress on the mean tuber weght, whch s calculated usng equaton 35, s multpled wth ddmt to nclude the nfluence of ntrogen stress on the tuber yeld durng the fnal phase. In ths w ay ntrogen stress reduces the fnal tuber yeld. The tuber yeld under dfferent levels of N were calculated for sweet potato varetes Sree Arun, Sree Bhadra and Sree Rethna whch were grown at Mtranketan, Thruvananthapuram durng the perod from 4 July, 4 to 1 October, 4 are gven n Table 7. To fnd out the quantty of ntrogen (N) at whch YLD s maxmum, a quadratc curve s ftted to the yeld data obtaned at dfferent levels of N for Sree Arun, Sree Bhadra and Sree Rethna usng SYSTAT 9.. YLD = an N + bn N+ cn (48) YLD = ak K + bk K+ ck (47) where, ak, bk and ck are emprcal coeffcents. Values of ak,bk and ck whch were computed for these three varetes are gven n Table 6. 5 where, an, bn and ck are emprcal coeffcents. Values of an,bn and cn whch were computed for these three varetes are gven n Table 8. Value of N at whch YLD s maxmum was found out separately for each varety as n the case of water

13 World J. Agrc. Sc., 4 (): 41-54, 8 Table 8: Values of an,bn and cn computed for Sree Arun, Sree Bhadra and Sree Rethna at Mtranketan, Thruvananthapuram durng the perod from 4 July, 4 to 1 October, 4 Varety an bn cn Sree Arun Sree Bhadra Sree Rethna Table 9: Results of senstvty analyss of the plant parameters for the average sweet potato cultvar Parameter Parameter value ß ntbr tbr_gap 3.33 vlen vlen lafactor lfactor br br_gap larea wt_vl.6 wt_la wt_ntbr.694 stress. Maxmum yeld due to the effect of ntrogen s attaned when the N appled was 85.11, 85.3 and Kg/ha for Sree Arun, Sree Bhadra and Sree Rethna respectvely and the YLD computed at ths level of N were 3.81, 3.98 and 8.6 T/ha respectvely. CONCLUSION In ths paper we have proposed a model for smulatng the growth of sweet potato. Ths model s bult usng varous sub models/ routes for predctng phenology, productvty and assmlates parttonng. These models were bult manly usng the data reported n lterature as well as those collected emprcally. Important stress factors lke water, potassum and ntrogen are also ncluded n the model. Feld experments were conducted at a locaton for fve seasons wth three dfferent varetes of sweet potato and the plant parameter values were estmated. Feld experment was also conducted at the same locaton for another three seasons and data were collected for testng the model predctons. Data were collected from another two stes also for evaluatng the model. The values predcted by the model were compared wth the feld observatons. There was a good agreement between the two n respect of tuber yeld, number of leaves produced and the number of tubers produced. However the predcton of number of branches devated from the observed values. Ths s the frst ever smulaton model developed for sweet potato. Assumptons made n ths model must be refned and further work should be done to address the real feld stuaton. AKNOWLEDGEMENT The second author thanks the Drector, CTCRI, Thruvananthapuram, INDIA for grantng study leave for carryng out ths study. REFERENCES 1. Ustmenko, C.G.V. and Bakumovsky, 198. Plants growng n the tropcs and subtropcs. Mr Publshers.. Vllareal, R.L., 198. Sweet potato n tropcs: Progress and problems. In: Vllareal, R.L. and T.D. Grggs (Eds.). Proceedngs of the 1 st Internatonal Symposum on Sweet Potato. AVRDC, Tawan, Chna, pp: Amarchandra, A. and J.P. Twar, Productvty potental of sweet potato (Ipomoea batatas Por). J. Root. Crops., 13: Wlson, L.A., 198. Tuberzaton n sweet potato (Ipomoea batatas (L.) Lam). In: Vllareal, R.L. and T.D. Grggs (Eds.). Proceedngs of the 1 st Internatonal Symposum on Sweet Potato. AVRDC, Tawan, Chna, pp: Bourke, R.M., Growth analyss of four sweet potato (Ipomoea batatas) cultvars n Papua New Gunea. Trop. Agrc., 61: Austn, M.E. and L.H. Aung, Patterns of dry matter dstrbuton durng development of sweet potato (Ipomoea batatas). J. Hortc. Sc., 48: Wlson, L.A., Use of rooted leaves and grafted plants for the study of carbohydrate metabolsm n sweet potato. Proc. Intl. Symp. Trop. Root Crops., 1: Bouwkamp, J.C., Growth and parttonng n sweet potato. Ann. Trop. Res., 5: Austn, M.E. L.H. Aung and B. Graves, 197. Some observatons on the growth and development of sweet potato (Ipomoea batatas). J. Hortc. Sc., 45: Lowe, S.B. and L.A. Wlson, Yeld and yeld components of sx sweet potato (Ipomoea batatas (L.) Lam.) cultvars. II. Varablty and possble sources of varaton. Expt. Agrc., 11:

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