Um modelo de simulação de crescimento e desenvolvimento do feijoeiro Carioca (Phaseolus vulgaris L.), cultivar de crescimento indeterminado e parcialmente trepador (Tipo III), é usado para examinar as prioridades e a dinâmica da alocação dos produtos da fotossíntese. O modelo é válido para os dados obtidos em Londrina, PRA simulation model for the dry bean (Phaseolus vulgaris L.) indeterminate large guide (type III), cv. carioca is presented and is used to examine the priorities and allocation dynamics of photosynthate. The model is valid for the data of Londrina, PR

Carnajal, Blanca Luz Pinilla

Guimarães, Maria de Fátima

Gutierrez, Andrew Paul

Miglioranza, Edison

Villacorta, Amador

English

A simulation model for the dry bean (Phaseolus vulgaris L.) indeterminate large guide (type III), cv. carioca is presented and is used to examine the priorities and allocation dynamics of photosynthate. The model is valid for the data of Londrina, PR.Um modelo de simulação de crescimento e desenvolvimento do feijoeiro Carioca (Phaseolus vulgaris L.), cultivar de crescimento indeterminado e parcialmente trepador (Tipo III), é usado para examinar as prioridades e a dinâmica da alocação dos produtos da fotossíntese. O modelo é válido para os dados obtidos em Londrina, P

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A MODEL OF DRY BEAN GROWTH AND DEVELOPMENT: CULTIVAR CAROCA 1 AMADOR VILLACORTA2, ANDREW PAUL GUTIERREZ3, MARIA DE FÁTIMA GUIMARÃES, BLANCA LUZ PINILLA CAFIVAJAL e EDJSON MIGLIORANZA 4 ABSTRACT - A simulation model for lhe dry bean (Phaseolus vu/garis L.) indeterminate large guide (type III), cv. carioca is presented and is used to examine the priorities and aflocation dynamics of photosynthate. The model is valid for the data ci Londrina, PR. Index terms: plant modeling, stochastic model, population dynamics. MODELO DE CRESCIMENTO E DESENVOLVIMENTO DO EEIJOEIRO: CULTIVAR CARIOCA RESUMO - Um modelo de simulação de crescimento e desenvolvimento do feijoeiro Carioca (Phaseolus vulgaris L.), cultivar de crescimento indeterminado e parcialmente trepador (Tipo III), é usado para examinar as prioridades e a dinâmica da alocação dos produtos da fotossmntese. O modelo é válido para os dados obtidos em Londrina, PR. Termos para indexação modelagem de plantas, modelo estocástico, dinâmica populacional. INTROINJCTION Dry bean (Phaseolus vulgaris L.) is a plant that presents four growth habits: determinate (type 1), indcterminate small guide (type II), indeterminate large guide (type III) and indetenninate climbing (type IV). Bean physiologists attempt to understand plant growth and matter partitioning, using the simplified growth analysis to define with greater precision the contribution of piant type to eventual economic yield (Brandes et ai. 1972, Mosjidis 1975, Fanjul eI ai. 1982). Today mathematical models of field erops are becoming useful tools for a better understanding of lhe processes of cmp growth and yield, and, furthermore, can assess the effects of pests upon thesc processes. The dry bean model (type III) is similar in both structurc and function to a cotton model 1 Accepted for publication on April 19, 1989. 2 Eng. - Agr., Ph.D., Instituto Agronômico do Paraná (IAPAR), Caixa Postal 1331, CEP 86001 Londrina, PR, Brazil. Prof., Ph.D., Dlv. of Biol. Control, University of California, Berkeley, USA. ' Eng. Agr. M.Sc., Fundação Univ. Estadual de Londrina, Dep. de Agron, Londrina, PR, Brasil. describeci by Gutierrez et ai. (1975). Wang eI ai. (1977) and Gutierrez et ai. (1984). The major objectives of this work werc to expand the cotton plant model framework to dry bean, to examine the pattern of photosyntttate aliocation and to develop a model sufficiently flexible for Iinking pcst modeis for developing management strategies in dry beans. The mathcmatical model uscd by Gutierrez et ai. (1984) for cotton and Gutierrez & Baumgaertner (1984a, b) for alfalfa was based on a distributed delay model of Manetsch (1976) and Vansickie (1977). In this model, lhe distribution developmental times are characterized by an Erlang function. A canopy model is used with sub-populations of Icaves, stem, root and fruit. The model follows lhe dynamics of ali plant parts by age, and in addition includes lhe number dynamics for fruits. Ali plant part modeis are linked va the metabolic p001 model for photosynthate aliocation, while whoie plants are Iinked via deasity dependent competition for light, nutrients, water and other resources. Complete information on lhe metabolic pool model for energy acquisition and aliocation cari be found in Gutierrez et ai. 1987. The model is conceptually a time Pesq. agropec. bras., Brasília, 25 (3):365-370, niar. 1990 366 	 A. VILLACORTA et ai, varying life table. While deterministic, it simulates stochastic deve lopment. MATERIAL AND METHODS Two plots of 30 m x 15 m of the dry bean, cultivar carioca were planted at a density of ten planta per m2 on September 2, 1983 at the Experimental Station of the State University of Londrina. The original experiment had irrigated (Piot 1) and unirrigated (Piot 2) plots, but extensive rains feil throughout the season and supplemental irrigation was not needed. The crops were protected from insect injury and diseases by applications of insecticides and fungicides, and agronomic practices were the sarne in both plots. From each treatment three replicates were randomly selected, consisting of four healthy plants pulled from a meter row, every other day during Lhe crop cycle. The biomass was partitioned into leaf minus petiole, stem plus root, and fruit. The stem samples included the tap root, bul no effort was made to collect smailer roots. The leaf area of the plants was estimated using a leaf meter, and the relaiionship of leaf area Lo leaf ciry matter estimated. Fniit were categorized and counted as buda, fiowers and pods. Ali samples were oven dried for four days at 60°C, then weighed to an accuracy of±0,01 g. Solar radiation (Ca1 2 day' = 0.484 w/m2) and maximum and minimum temperature used to run the model were obtained from the weather station maintained by lhe Instituto Agronômico do Parami (IAPAR), Londrina, PR, located at five kilometers from Lhe experimental area. Degree days (°D) calculations were made above a threshold of 5°C, after the method of Frazer & Gilbert (1976). A separated experiment was used to estirnate the maximum pod growth rate. Approximately 500 flowers were isolated and tagged the sarne day, and ten of them were collected every other day until fuJi growth; the samples were oven dried at 60°C, and weighed. This data was used Lo estimate rate of pod growth. RESULTS AND JJLSCUSS1ON The pararneters for the modei are given in Table 1. Data from the PIot 1 was used Lo estimate the parameters, the vegetative Pesq. aropec. bras., Brasilia, 25(3):365-370, mar. 1990 phenology and growth rates, while a separata experiment was used to estimate maxiznum pod growth rates (Fig. 1 and 2). In Fig. 3 lhe dry matter leaves, pods and stem plus root (A) and Lhe number of fruit parts (buds, fiowers and pods) per plant are presented (B). Leaf and stem plus root pmduction slowed considerably due to carbohydrate stress when Lhe demand for dry matter in pods increased sharply (i.e. Lhe supply - demand ratio). The declines in stem plus roots and leaf dry matter after Limes 1.100 °D were due to the shedding of senescing leaves and petioles. Apparently Lhe bean plants suffcred water stress which causes a faster than normal Jeaf abscission rate. The declines in late season pod dry matter is explained by the fact that mature TABLE 1. Parameters for carioca cv. comon bean. (1) Average Iongevity of: Growth rates Leaves 6400D 0.048 gI01) Stem (to woody tissue) 1000 01) 0.009g101) Root (to woody tissue) 10000D 0.006 gI0D (2) First fruit branch at 10 plants per m2 	 59001) (3) Growth demands  -Leafgrowth( A L) A L mean change in leaf demand from t to t + At .. A Lt + A t 	 Lt.DLP. A t = .0085 Lt. A t where DLP is Lhe compounding rate per A S + A t = Lt.DSP. A t = .099 St A t - Root growth ( A R) A Rt + A t DRP. A L1 + A t = .125 At1+ At - Bud demand (DB); a = age DB = .0000569 g/budf°D = growth rate per bud (0<a<355°D) - Frult demand (DF) DF 	 .0037 glpod/°D = growth rate per pod (355 	 a 	 11300D) A MODEL OF DRY BEAN GROWTH AND DEVELOPMENT 	 367 TABLE 1. Cont. (4) Rate of fruit point production (RFP) RFP = .4 buds/Di) or 0.4. °D per day (5) Average developmental Limes on the phenology ofone pod AgeO O Agel 175°D Age2 210°D Age 3 355 °D Age4 1130 0D AgeS 1355°D (6) Shed windows for fruit due to carbohydrate stress Buds (0<a<25 if s/d<1) Pods(150<a<700 0D il sld<1) s supply d = demand (7) 33 decimeter square of leaf area per g leal.  pods were not included in Lhe ficld samples (Fig. 3A). The observed fruit number patterns are presentcd in Fig. M. In beans, Lhe production of new fruits slowed or stopped due to carbohydrate stress when pods began their rapid growth. The fruit dynamics patterns are smoother because of shorter postflower delay in rapid fruit growtii. This result is consistent with Lhe extensive data publishcd for cotton by Gutierrez et al. (1975, 1984) and Viliacorta et ai. (1985). In Fig. 4 the simulation resuits are presented, as observed in Lhe field data. Plant subunits grow exponentially until fruits begin rapid growth causing sharp curtailment in growth rates of the other plant subunits. With respect to Lhe dry matter rctained, only a sniali amount is iost via shed fruit; the model predicts that bean may be kept growing vegetatively if enough fruits are removed to 15 10 cc uJ u, 40 5 o  O 	 100 	 200 	 300 	 400 	 500 	 600 	 700 	 800 	 900 	 1000 PHYS!OLOG!CAL AGE (DO> 50C) FIG. 1. Average dry matter accumulation in Carioca cv. bean pods plotted on phy-siological time (°D> 5°C). Pesq. agropec. bras., Brasifia, 25(3):365-370, mar. 1990 368 	 A. VILLACORTA et ai. 5 5 	O 	 500 	 200 	 XC 	 400 	 50(7 	 400 	 714 	 XC 	 XC 	 IXC 	 1100 OIIYSIOLOGICAL AGE 00 50(7) FIG. 2. Average dry matter accumulation in carioca cv. bean, pod shell and seed plotted on physiological time (°D> 5°C). 	- 	 A. 	 o Leaves Pods cc o 	100 - 	 1 • 	 : (Ti-IOUSANOS) OD more meaningfull picture of aliocation emerges from plotting dumulative total aflocated respiration and combined growth and ieproduction to the total acquired (Fig. 4D) Bean appears to be an efficient plant, assimilating ca. 47% of the cnergy produced, compared, for example, wfth 27% in cotton (Gutierrez et aI. 1987). In Lhe model, the stochastic development and Lhe interaction of temperature and solar radiation on bean growth are presented, while water and nitrogen effects are not included. A beans is not available in Lhe literature to validate the simutated information. Daily rates of energy aliocation show the dynamics, but a B. 150j 1_O 100- : UBuds  .Howers 4 u. •Pods -; .G14 0.3 	 0.7 	 li 	 1.5 (Ti-IOUSANOS) 00 FIG. 3. Dry bean growth and dcvetopment: A) dry matter aHocation to leaves, stem plus root, and pods; B) numbers of fruit buds, fiowers and pods. Data plotted on degree days above 5 0C using 1983 weather data from Londrina, PR. Brazil. The lines represdnt stmulated values, two arrows indicate discrepancy because in tbe tieJd samplfng of mature pods was not included. avoid carbohydrate stress. This prediction is consistent with field observations, raising a question about the definitions of determinate and indeterininate growth habits (Fig. 4A). The sirnulated pattems of age struture and numbers of fruits are presented in Fig. 413, and follow the pattems observed in Lhe field data. Daily aflocation of dry matter to plant subunits is prescnted in Fig. 4C. The daily dry matter acquisition and aliocation date for Pcsq. agmpec. bras., Brasília, 25(3):365.370, mar. 1990 more advanced model that describes the interactions of cassava, pests and the introduction of natural enemies as modified by weather, soil nitrogen and water Ievets, is presented by Gutierrez et al. (1988). Nontheless, with Lhe bean model at its current stage of development, Lhe resultant simulation was highly satisfactory. Presently, the development of the plant model is a prerequisite for evaluating pest damage and A MODEL OF DRY BEAN GROWTH AND DEVELOPMENT 	369 01 li)  20 1 -J a. 'e 	Stem & Root 	hed 30 Resee O 	 ri 1m, 01 	 0.3 	 0.5 	 0.7 	 0.9 	 1.1 	 1.3 	 13 1- z LU 1.) z >. -1 a O Leaves 	 D Fniit 	.J Stern & Root 	 fl Resprration 4 	/ O - T O 	 20 	 40 	 60 	 50 (THOUSANDS) 00 > 5 400 	 600 	(THOUSANDS) 	 TOTAL (g) 00> 5 FIG, 4. Per plant simulated dry bean growth and deve!opment: A) dry matter aflocation to leaves stem plus root reserves, and shed and retained fruit; B) numbers of frults produced, fruit buds, floiers, pods and total shed fruits; C) daily aliocation patterns to plant subunits, and D) aUocatíon frac-tions. Data plotted on clegree days above 5 0C using 1983 weather data from Londrina, PR, Brazil. for developing integrated pest management FANJUL, 	L.; 	 KO}IASEÍI-SEIIBATA, 	 1.; 	strategies for their control, leading ultimately 	IJERNANDEZ-HOLOCOTZY, E. Yield to an efficicnt crop management. potential and stratiíied growth analysis of an interminate clirnbing pole bean (Pliaseolus vulgaris) in Mexico. Expi. Agric., REFERENCES 	 1:I67-175, 1982. 	BRANDES, D.; ViEIRA, C.; MAESTRI, M.: 	 FRAZER, B.D. & CILBERT, N.E. Coccinellids and 	GOMES, F.R. Efeitos da população de plantas 	 aphids, a qualitativc study of the impact of 	e da época de plantio no crescimento do 	 adult lady birds (Coleoptera:Coccinellidae) 	feijoeiro (Pitaseo/us vu/çarjs L.) 1 - Mudanças 	 preying on field popufations of pea aphids 	morfológicas e produção dc inatria seca. 	 (llomoptcra;Aphididae). J. Entomol. Soc. 	Expericntiae, 14:1-49, 1972. 	 B.C., 73:33-56, 1976. 160 (THOUSANDS) 00> 5 600- D. 120 400 z o uJ a. b 300 ec 	 5O Ftowers e o w i 200 40-  /41 - 100 o _ 	 6u0 - 0— O 1 	 1 o ['esq. agroec. bras., Brasília, 25(3):365-370, mar. 1990 370 	 A. VILLACORTA et ai. GUTIERREZ, A.P. & BAUMGAERTNER, J.V. Muititrophic levei models of predator-prey-energetics. 1 Age specific energetics mo-deis pea aphid Acyrthosiphon pisu.'n (Harris) (Homoptera: aphididae) as an exampie. Can. Ent., 116:924-932, 1984a. GUTIERREZ, A.P. & BAUMGAERTNER, J.V. Muititrophic levei modais of predator-prey-energertics. ii A realistic model of plant- herbi-vore-parasitoid-predator interactions. Can. Ent., 116933-949, 1984b. GUTIERREZ, A.P.; FALCON, L.A.; LOEW, W.B.; LEIPZIG, P.A.; BOSCH, R. vari den. An analysis of cotton production in California:A model for Acala cotton and the effects of defoliators on its yield. Environ. EntomoI. 4:125- 136, 1975. GUTIERREZ, A.?.; PIZZÃMIGLIO, M.A.; DOS SANTOS, W.J.; TENNYSON, R.; VILLACORTA, A.M. A general distributed delay time varying life table plant population model: cotton (Gossvpiutn hirsurwn L.) growth and development as an example. Ecol. Modeling, 26:231-249, 1984. GUTIERREZ, A.P.; SCHULTHNESS, F.; WILSON, L.T.; VILLACORTA, A.; ELLIS, C.K.; BAUMGAERTNER, J.V. Energy aquisition and allocation in Plants and insects: A hypothesis for the possible role of hormones in insect feeding patterns. Cais. Entomol., 119:109-29, 1987. GUTIERREZ, A.P.; WERMELINGER, B.; SCHULTHNESS, F.; BAUMGAERTNER, J.V.; HERREN, 1-LR.; ELLIS, C.K.; YANINEK, I.S. Analysis of the biological control of cassava pests lis Africa: I. Simulation of carbon, Nitrogen and Water dynainics is cassava. Iournal Applied Ecology, 25, 901-920, 1988. MANETSCH, T.J. Time varying distributed deiays and their use in aggregate modeis of iarge sys-terns. IEEE Trans. Syst. Man Cybcin, 6:547-553, 1976. MOSJIDIS, Ch. J. Distribución de ia matena seca entre los órganos aéreos de varias cultivares de frijoi (Phaseolus vulgaris L.) Fitoec. Lat., Venezueia, 1 1(1):29-33, 1975. VANSICKLE, J. Attrition in distributed delay mo-deis. IEEE. Trans. Syst. Man Cybcrn., 7:635-638, 1977. VILLACORTA, A.; GUTIERREZ, A.P.; DOS SANTOS, W.J.; PIZZAMIGLIO, M.A. Aed-use do crescimento e desenvolvimento do algo-doeiro no Paraná. Um Modelo de simulação da variedade IAC 17. Pesq. agropec. bras., Brasilia, 20(1):115- 128, 1985. WANG, Y.H.; GUTIERREZ, A.P.; OSTER, G.; DAXL, R. A popuiation model for cotton growth and development: coupling cotton-her-bivore interactions. Cais. Entomol., 109:1359-1374, 1977. Pcsq. agropec. bras., Brasflia, 25(3):365-370, mar. 1990 

Modelo de crescimento e desenvolvimento do feijoeiro: cultivar carioca

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A model of dry bean growth and development cultivar carioca

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