## Articulo

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## versión impresa ISSN 2007-0934

### Rev. Mex. Cienc. Agríc vol.7 no.5 Texcoco jun./ago. 2016

Articles

Economic optimization of N, P, K and planting densities in corn and bean intercropping

1Universidad Intercultural del Estado de México. Libramiento Francisco Villa S. N. San Felipe del Progreso, Estado de México. C. P. 50640. Tel: 01 712 123 59 63 Ext. 118. (horaciosm@colpos.mx).

2Campo Experimental Valle de México-INIFAP. Carretera los Reyes-Texcoco, km13.5, Coatlinchán, Texcoco, Estado de México, C. P. 56250. (aturrent37@yahoo.com.mx; gonzalez.adrian@inifap.gob.mx).

3Edafología Campus Montecillo. Colegio de Postgraduados. C. P. 56230. Carretera MéxicoTexcoco km 36.5 Montecillo, Estado de México. (jicortes@colpos.mx; vvolke@colpos.mx).

4Genética- Campus Montecillo. Colegio de Postgraduados. C. P. 56230. Carretera MéxicoTexcoco km 36.5 Montecillo, Estado de México. (camen@colpos.mx).

Abstract

The objective was to determine the best dose of fertilizer and planting density (D) for the cultivation of corn 'H-155' and black bean shrub '8025' three topological arrangements (AT). The selection criterion was the biggest gain, relative efficiency of land (ERT) and relative efficiency of gain (ERG). An experiment is established in split plot in the Valley of Mexico Experimental Station, in 2012. There were three large plots of corn and beans AT: 1) Simple corn and beans (CSMF); 2) intercalated in two alternating rows (MMFF); and 3) interspersed in an alternating groove (MFMF). The small plot consisted of 25 treatments of a rotatable central composite design with 5 levels of nitrogen (N), phosphorus (P), potassium (K) and D. The grain yield (Ym) and stover (Yr) was determined corn and bean grain yield (Yf). The greatest gain ($33 942) was obtained MMFF with the combination 34-0-40 kg of N-P-K and 29 500 plants in 0.5 ha corn and 11-0-30 kg of N-P-K and 80 000 plants 0.5 has of bean. In MMFF maximum ERT was 1.29 and ERG was 2.01. Most ESRD in MFMF was 1.27 with a 1.58 ERG, both associated with a high level of Ym 7.09 0.5 t ha-1. Keywords: Zea mays L.; Phaseolus vulgaris L.; central composite design rotatory and net income Resumen El objetivo fue determinar la mejor dosis de fertilizante y densidad de plantación (D) para el cultivo de maíz ´H-155´ y frijol negro arbustivo ´8025´ en tres arreglos topológicos (AT). El criterio de selección fue la mayor ganancia, eficiencia relativa de la tierra (ERT) y eficiencia relativa de la ganancia (ERG). Se estableció un experimento de parcelas divididas en el Campo Experimental Valle de México, en el año 2012. Las parcelas grandes fueron tres AT de maíz y frijol: 1) cultivo simple de maíz y frijol (CSMF), 2) intercalados en dos surcos alternos (MMFF), y 3) intercalados en un surco alterno (MFMF). La parcela chica constó de 25 tratamientos de un diseño central compuesto rotable con 5 niveles de nitrógeno (N), fósforo (P), potasio (K) y D. Se determinó el rendimiento de grano (Ym) y rastrojo (Yr) de maíz y el rendimiento del grano de frijol (Yf). La mayor ganancia ($33 942) se obtuvo en MMFF con la combinación 34-0-40 kg de N-P-K y 29 500 plantas en 0.5 ha de maíz y 11-0-30 kg de N-P-K y 80 000 plantas en 0.5 ha de frijol. En MMFF la máxima ERT fue 1.29 y ERG fue 2.01. La mayor ERT en MFMF fue 1.27 con una ERG de 1.58, ambas asociadas a un nivel alto de Ym de 7.09 t 0.5 ha-1.

Palabras clave: Zea mays L.; Phaseolus vulgaris L.; diseño compuesto central rotable e ingresos netos

Introduction

The corn and bean intercropping has several objectives including the efficient use of important resources such as water, light and nutrients, in economic and agronomic terms. It has been reported complementarity between maize and beans because they make better use of resources when they are interleaved than simple crops (Willey, 1990; Johanne and Lynch, 2012), which is reflected in higher performance (Li et al., 2001; Malezieux et al., 2009), the same level of inputs, and is attributed to topological arrangement of the crop.

The milpa system intercropped with fruit trees has been designed to promote food security, income, employment and family environment. In this system, corn, some legumes and fruit are interleaved in stripes. The system responds to the needs of small production units (usually 2 to 2.5 hectares divided into several properties), high degree of economic and social marginalization. Under these conditions and with a traditional management, staples maize and beans are produced with insufficient income to meet the needs of food and household income.

In crop production, seed, variety and fertilizers are considered among the most important inputs, as they constitute a significant proportion of production costs (Volke, 1982). The classic econometric method to establish the optimum economic dose soil fertility studies can be summarized as follows: 1) design and establish factorial experiments with various forms of fertilization and treatment design according to the investigator; 2) it is assumed that nutritional deficiencies are reflected in the observed yields and performance approaches in terms of a function of input levels, showing as much as possible the law of diminishing returns and 3) the dose of nutrients is obtained that produce the farmer the maximum net income per hectare (Martínez and Martínez, 1996; Barrios-Ayala et al., 2003; Volke et al., 2005; Barrios et al., 2008).

The relative efficiency of land (ERT) is the most commonly used measure to compare the productivity of intercropping (Vandermeer, 1989; Rezaei-Chianeh et al., 2011) under arable land constraints. The ERT monoculture represents the area required for the performance of polyculture at the same level of inputs (Vandermeer, 1989). In a variation of the formula of ERT may include net income to integrate economic and biological factor in the equation relative efficiency of the ERG gain.

The objective of this research was to determine the best combination of N, P, K and planting density for growing corn ´H-155´ and black bean shrub '8025' in different topological arrangements, defined in terms of profit or net income, the relative efficiency of land and the relative efficiency of total income. The assumption was that the effect of the topological arrangement without significantly increasing doses of N, P and K, planting density and cost, corn and shrubs interspersed bean increase performance and profits compared with those of monocultures at the same level of inputs.

Materials and methods

In the spring-summer (april 10-november 17, 2012) an experiment was conducted in the Valley Experimental Field of Mexico (CEVAMEX) "El Horno", the National Institute of Forestry, Agriculture and Livestock (INIFAP). The site, with fluvisol haplic floor (19° 29’ north latitude, 98° 53’ west longitude) has an elevation of 2 280 msnm. The average temperature during the growing season was 19.5 °C and precipitation of 315 mm.

An experimental design with three treatments divided large plot and 25 small plot treatments, with a repeat parcels handled. The large plot corresponded to the topological arrangement of white ´H-155´ and black bean '8025' in: A) simple culture of corn and bean (CSMF); B) two rows of corn alternating with two bean (MMFF); and C) a groove corn alternating with one bean (MFMF) (Figure 1).

In each topological arrangement were evaluated the nitrogen factors (N), phosphorus (P), potassium (K) and plant density (D). Space exploration ranged from 30 to 150 and 0 to 50 kg N; 0 to 60 and 0 to 50 kg P2O5; 0 to 40 and 0 to 30 kg K2O; and 31.5 to 43.5 and 60 to 120 plants in 0.5 ha of maize and beans, respectively. The combination of these factors resulted in 25 small plot treatments according to a central composite design rotatory (Table 1). This design was based on a factorial design 24 (two levels of factors: N, P, K and D in which the levels of each variable were coded as -1 and +1 increased by eight axial points coded as -2 and +2, and a center point coded as 0 (Barrios-Ayala et al., 2003; Volke et al., 2005). Thus, the number of treatments small plot by the central composite design rotatory corresponded to the formula 2k+2k+n; i.e, 24+24+1= 25 treatments, randomly distributed the three topological arrangements (75 total treatments). The treatments were perfectly aligned small plot field. Each treatment of small plot consisted of four rows of 0.8 m wide by 2.12 m, with the two center rows as useful plot.

Table 1 List of treatments of small plot tested in topological arrangements CSMF, MMFF and MFMF.

 Tratamiento Maíz Frijol N P2O5 K2O D N P2O5 K2O D (kg 0.5 ha-1) (pl 0.5 ha-1) (kg 0.5 ha-1) (pl 0.5 ha-1) 1 60 15 10 34 500 12.5 12.5 7.5 75 000 2 60 15 10 40 500 12.5 12.5 7.5 105 000 3 60 15 30 34 500 12.5 12.5 22.5 75 000 4 60 15 30 40 500 12.5 12.5 22.5 105 000 5 60 45 10 34 500 12.5 37.5 7.5 75 000 6 60 45 10 40 500 12.5 37.5 7.5 105 000 7 60 45 30 34 500 12.5 37.5 22.5 75 000 8 60 45 30 40 500 12.5 37.5 22.5 105 000 9 120 15 10 34 500 37.5 12.5 7.5 75 000 10 120 15 10 40 500 37.5 12.5 7.5 105 000 11 120 15 30 34 500 37.5 12.5 22.5 75 000 12 120 15 30 40 500 37.5 12.5 22.5 105 000 13 120 45 10 34 500 37.5 37.5 7.5 75 000 14 120 45 10 40 500 37.5 37.5 7.5 105 000 15 120 45 30 34 500 37.5 37.5 22.5 75 000 16 120 45 30 40 500 37.5 37.5 22.5 105 000 17 30 30 20 37 500 0 25 15 90 000 18 150 30 20 37 500 50 25 15 90 000 19 90 0 20 37 500 25 0 15 90 000 20 90 60 20 37 500 25 50 15 90 000 21 90 30 0 37 500 25 25 0 90 000 22 90 30 40 37 500 25 25 30 90 000 23 90 30 20 31 500 25 25 15 60 000 24 90 30 20 43 500 25 25 15 120 000 25 90 30 20 37 500 25 25 15 90 000

Nota: los fertilizantes utilizados fueron urea (46 % N), superfosfato de calcio triple (46% P2O5), y cloruro de potasio (60% K2O).

Sowing was manual and on it all the P, K and a third of the N corn and all three elements applied to beans; the remaining two thirds of N were applied to the first hoeing corn.

The experiment was maintained without restriction moisture by furrow irrigation and weeding was manual. Bean harvest was 125 days after planting; plants of each experimental unit were removed entire plot, dried in the shade, is peel and weight of the clean grain stubble was recorded. From this data was estimated the grain yield in 0.5 ha (Yf).

The corn was harvested at 221 days after sowing. All ears of each useful plot were harvested, weighed and shelled. Grain moisture at harvest time was determined with a John Deere portable meter (SW 16060®, Ill. EEUU). The grain yield Ym with 14% humidity, was estimated to 0.5 ha, occupied by corn on topological surface arrangements. The corn stover was cut and weighed the day after the corn harvest. Stubble moisture was determined by gravimetric method and was considered to calculate the yield of stover (Yr) in 0.5 ha at 14% moisture.

With dataYm, Yr and Yf observed each treatment was calculated the relative efficiency of land (ERT) (Vandermeer, 1989) and the relative efficiency of the gain (ERG), with the following equations:

ERT=Ybean intercroppingYbean monoculture+Ymaize intercroppingYmaize monoculture

ERG=INmaize intercroppingINmaize simple crops+INbean iintercroppingINbean simple crops

Where: profit or net income (IN); corresponded to total income (IT); minus total cost (CT), according to relationship IN= IT-CT. The IT of each species was obtained by multiplying the yields of corn stover and grain for their respective prices at the point of sale, ditto for the grain of beans. The CT was the sum of the variable cost (CV) plus the fixed costs (CF). The CV of each treatment was the sum of the quantities of N, P, K and D multiplied by its respective price (Volke, 1982). The price list considered in the calculation is presented in Table 2.

Table 2 Price list, in 2012, considered in the calculation of the optimum economic dose.

 Concepto Precio ($) Costos fijos Renta de la tierra, seguro agrícola (12%), barbecho, rastra, surcado, jornales para riego, cuota de agua, deshierbe, cosecha maíz y corte frijol 6260.00 ha-1 Costos variables N 18.39 kg N-1 P 23.75 kg P-1 K 14.71 kg K-1 Precio de la unidad de incluyendo transporte, aplicación manual, interés por el crédito bancario 12% para el ciclo agrícola Costo de mil plantas maíz-frijol. Costos de siembra 24.45 mil plantas-1 Precios de venta Precio rastrojo empacado y transportado al punto de venta 796.00 t-1 Precio del grano de maíz desgranado y transportado al punto de venta 3742.06 t-1 Precio del grano de frijol desvainado y transportado al punto de venta 11444.90 t-1 Fuente: Volke (1982); FIRA (2012); INIFAP (2012); SE (2012), información de productores locales. Using SAS program (SAS Institute, 2005), the regression models for the dependent variables were adjusted: IN, Ym, Yr and Yf. The general model equations was: Dependent variable= µ + a1 + a2 + N + P + K + D + NP + NK + ND + PK +PD +KD+ N2 + P2 + K2 + D2 + a1N + a1P + a1K + a1D + a1NP + a1NK + a1ND + a1PK + a1PD + a1KD + a1N2 +a1P2 + a1K2 + a1D2 + a2N + a2P +a2K + a2D + a2NP + a2NK + a2ND + a2PK + a2PD + a2KD + a2N2 + a2P2 + a2K2 +a2D2 + a2D2 + e Topological arrangements were included as auxiliary variables (dummy) that in the case of three topological arrangements took values of: a1= 0 and a2= 0 for settlement CSMF, a1= 1 and a2= 0 for MMFF and a1= 0 and a2= 1 for MFMF. The response of topological arrangements was the algebraic sum of terms without "a" plus counterparts terms corresponding to the effect of management factors; that is, that all terms with "a" in the equations are differences in response between topological arrangements (Barrios et al., 2003; Barrios et al., 2008). The factors were coded into five levels, equally spaced, as: n= (N-115)42.5,p=(P-55)27.5,k=(k-35)17.5 and d=(D-127.5)18 The regression procedure (backward sls= 0.2) included significant factors (p< 0.05) for each dependent variable. With IN equation resulting from an optimization program in SAS® which showed the maximum net income (NI) or gain with its combination of N, P, K and D of each topological arrangement it was made. Once known the level of factors that maximized the gain in the three topological arrangements optimum economic dose (DOE) simple crops of corn and beans to compare with other arrangements at the same level of input was considered. For this input levels of the DOE they were replaced in the regression equations to determine the effect of the topological arrangement Ŷm, Ŷr, Ŷf. Results and discussion With the equation of estimated net income (ÎN) (Table 3) the DOE that maximized the gain of each topological arrangement was obtained. The biggest gain was$33 942 and was achieved with the topological arrangement interleaved with the combination MMFF per hectare of 34-0-40 kg of NPK and 29 500 maize plants and 11-030 kg of NPK and 80 000 plants beans (Table 4), since this arrangement is needed less N, which according to Lithourgidis et al. (2011) is an environmentally important aspect intercropping systems because it involves less use of inputs and production costs. This "DOE" in the MMFF system is suitable for the case of a producer who has satisfied the requirements of maize and beans from the family diet and is interested in the maximum net income.

Table 3 Regression equations of net income, grain yield and corn stover and bean grain.

 Variable Ecuación de regresión R2 ÎN= 23381+4858.8019a2+887.3316k-993.5592n2+1569.4156d2+1590.327a1np+1722.9694a1n2- 1286.7531a2k2-2136.6628a2d2 0.49 Ŷm= 4.8456+0.3685n+0.1441p2+0.6437a1+0.3592a1n+0.4240a1np-0.3831a1p2+1.1548a2+0.2959a2n- 0.2817a2k+0.4324a2pd 0.48 Ŷr= 5.6934+0.1214n-0.1231n2+0.4701a1+0.2280a1d+0.1897a1np+0.1826a1pd+0.8687a2 0.48 Ŷf= 1.0897+0.0472n+0.0457k+0.1352d+0.1056d2+0.1004a1-0.0791a1d-0.1686a2-0.1173a2d 0.51

Table 4 Optimization N, P, K and planting density in three topological arrangements corn and bush beans, based on the most profit.

 Arreglo topológico N Dosis óptima económica D ÎN Max IN P2O5 K2O kg 0.5 ha-1 pl 0.5 ha-1 ($ha-1) ($ ha-1) CSMF Maíz 86 0 23 33.5 Frijol 24 0 17 62.0 Total ha-1 110 0 40 94.5 28 895 28 895 MMFF Maíz 34 0 40 29.5 Frijol 11 0 30 80.0 Total ha-1 45 0 70 109.5 33 42 33 942 MFMF Maíz 90 0 34 35.0 Frijol 25 0 26 83.5 Total ha-1 115 0 60 118.5 31 491 30 472

ÎN= ingreso neto estimado. CSMF cultivo simple de maíz y de frijol; MMFF= dos surcos de maíz alternados con dos de frijol;y MFMF= un surco de maíz alternado con uno de frijol. Max IN= máximo IN del arreglo topológico.

Coding for the five levels of the study factors:

n= (N-115)42.5,p=(P-55)27.5,k=(k-35)17.5 and d=(D-127.5)18

a1= coding MMFF and a2= MFMF as dummy variables (dumb) that can take the value 0 or 1 for its effect on the response variable. ÎN= net income estimate. Ŷm, Ŷr and Ŷf= estimated corn grain, corn stover and grain bean yields respectively.

The DOE estimated equation IN showed that is not required of P, in any topological arrangement, to achieve maximum income, this may be because the soil of the experimental site has been getting high and constant doses of fertilizers in the last 20 years, leaving a possible nutrient reservoir at least P. The MMFF arrangement provided $5 046.00 more profit and arrangement MFMF$2 595.00 more than the CSMF. These DOE for MMFF and MFMF arrangements are useful for producers who decide to adopt technology based on revenues generated (Seran and Brintha, 2010).

Vandermeer (1989) indicates that comparisons between topological arrangements must be made at the same level of inputs; thus, in the present study by contrasting earnings intercalated in these conditions system were obtained Ŷm, Ŷr and Ŷf, with their respective regression equations (Tables 3 and 5). Under these conditions it was also observed that the greatest gain was obtained with the arrangement MMFF ($29 293.00 ha-1) compared to the CSMF ($28 895.00 ha-1). At this level of input variable and fixed costs were the same in the topological arrangements so the difference between them was due to the performance of the two species. The MFMF arrangement in accordance with the treatment 20, the greater was obtained Ym observed at 7.09 t in 0.5, which equals 14.18 t in 1 ha dispersed system. However, it was not treating or topological arrangement with which the highest gain was obtained ERT or greater, since there was a depression in bean yield compared to that obtained in CSMF. The decrease of 12-55% in performance or soya bean intercropped with maize has been reported by other authors (O'Callaghan et al., 1994; Lesoing and Francis et al., 1999; Matusso et al., 2014). The revised literature suggests that this is due to interspecific competition for light, water and nutrient advantage seen in corn. Corn has more leaf area and root distribution (Hai-Yong et al., 2013) that beans; thus, interleaving corn intercepts more photosynthetically active radiation that transforms grain biomass (Tsubo and Walker, 2002).

Table 5 Maximum and minimum values observed relative efficiency of land (ERT) in maize culture and bush beans in MMFF, and their respective values of relative efficiency of the gain, net income, grain yield and corn stover and grain bean.

 Tratamiento Maíz Frijol ERT ERG IN ($) Ym Yr Y-1 N-P2O5-K2O D N-P2O5-K2O D (kg 0.5 ha-1) (pl 0.5 ha-1) (kg 0.5 ha-1) (pl 0.5 ha-1) ($ ha-1) (t 0.5 ha-1) 13 120-45-10 34 500 37.5-37.5-7.5 75 000 1.29 1.66 26 653 5.64 6.39 1.27 1 60-15-10 34 500 12.5-12.5-7.5 75 000 1.26 1.44 28 789 5.36 6.46 1.29 18 150-30-20 37 500 50.0-25-15 90 000 1.22 2.01 25 469 5.93 6.2 1.16 4 60-15-30 40 500 12.5-12.5-22.5 105 000 1.21 1.39 33 942 5.94 6.33 1.68 6 60-45-10 40 500 12.5-37.5-7.5 105 000 1.2 1.37 30 695 5.72 6.14 1.55 7 60-45-30 34 500 12.5-37.5-22.5 75 000 1.01 1.01 27 316 6.04 5.22 1.19 15 120-45-30 34 500 37.5-37.5-22.5 75 000 0.99 0.99 24 060 5.07 5.64 1.33 12 120-15-30 40 500 37.5-12.5-22.5 105 000 0.89 0.84 26 900 5.27 6.38 1.42 19 90-0-20 37 500 25-0-15 90 000 0.88 0.78 21 644 5.21 5.36 0.87 25 90-30-20 37 500 25-25-15 90 000 0.83 0.7 19 633 4.6 6.3 0.94

The ERT older were 1.29 observed in the MMFF treatment system 13; while the maximum ERT MFMF was 1.27 in the treatment 20 (Tables 5 and 6). A value of ERT in MMFF 1.29 means that 1.29 is required is simple to achieve crop yields single crop, compared to the same level of inputs. On average, the ERT of the MMFF and MFMF systems was greater than one. Under production conditions where arable land is a limiting factor ERT is a good indicator to choose the best combination of inputs that maximizes.

Table 6 Maximum and minimum values observed relative efficiency of land (ERT) in maize culture and bush beans in MFMF, and their respective values of relative efficiency of the gain, net income, grain yield and corn stover and grain bean.

 Tratamiento Maíz Frijol ERT ERG IN ($) Ym Yr Yf N-P2O5-K2O D N-P2O5-K2O D (kg 0.5 ha-1) (pl 0.5 ha-1) (kg 0.5 ha-1) (pl 0.5 ha-1) ($ ha-1) (t 0.5 ha-1) 20 90-60-20 37 500 25-50-15 90 000 1.27 1.58 28 184 7.09 6.46 0.97 22 90-30-40 37 500 25-25-30 90 000 1.26 1.56 25 856 6.85 6.82 0.75 17 30-30-20 37 500 0-25-15 90 000 1.25 1.53 23 408 6.09 6.62 0.62 13 120-45-10 34 500 37.5-37.5-7.5 75 000 1.23 1.51 25 648 6.06 6.53 1.03 6 60-45-15 40 500 12.5-37.5-7.5 105 000 1.14 1.22 30 472 6.71 7.05 1.15 10 120-15-10 40 500 37.5-12.5-7.5 105 000 0.91 0.85 28 222 6.46 6.42 0.89 23 90-30-20 31 500 25-25-15 60 000 0.91 0.82 28 043 6.8 6.9 0.83 12 120-15-30 40 500 37.5-12.5-22.5 105 000 0.88 0.79 27 569 6.6 6.39 1.04 21 90-30-0 37 500 25-25-0 90 000 0.83 0.63 18 934 4.91 6.97 0.68 2 60-15-10 40 500 12.5-12.5-7.5 105 000 0.82 0.67 20 795 5.06 5.86 0.81

In MFMF the ERT of 1.27 was accompanied by a high ERG (1.58) with a yield of grain like corn to 14.18 t ha-1 dispersed system level inputs of treatment 20 (Tables 1 and 6).

In the topological arrangement MFMF, treatment 6 (60-45-15 kg N-P-K and 40 500 maize plants more 12.537.5-7.5 kg N-P-K and 105 000 bean plants per hectare) was obtained the biggest gain ($30 472.00 ha-1) with a corn grain yield of 6.71 t ha-1 in 0.5 occupied by corn. In addition, unpublished data showed that the protein maize grain in the topological arrangement MFMF (8.6%) is higher than in MMFF (8.3%) and CSM (7.8%) compared to the same dose of N, P, K and D. Thus, treatment 6 MFMF would be choice for producers as to obtain a good yield of corn grain quality, which is important because corn obtain 39% of the protein in the daily diet (Bourges, 2013; Turrent et al., 2013). In terms of the higher net income ($33 942) it was obtained with the topological arrangement MMFF, treatment 4 (Tables 1 and 6).

Conclusions

In the maize crop ´H-155´ and black bean shrub '8025' the highest net income was presented with the interleaved topological arrangements (two rows of maize alternated with two bean and an alternating groove of each species) compared to simple crops.

In the topological arrangement of two rows of corn alternating with two bean was the biggest gain of $33 942.00 with the combination of inputs per hectare of 34-0-40 kg N-P-K in 29 500 plants of maize and was obtained 11-0 -30 kg N-P-K in 80 000 bean plants; i.e.$5 047.00 rather than single crop species. The effect of the same topological arrangement more profit was also generated when the level of N, P, K and planting density was constant in the comparison; and the maximum relative efficiencies of land and income were 1.29 and 2.01, respectively.

The greatest gain (\$30 472.00 ha-1) in the topological arrangement an alternating one groove corn bean was obtained with the combination 60-45-15 kg N-P-K and 40 500 of maize plants and 12.5-37.5-7.5 kg NPK and 105 000 bean plants per hectare MIAF. In this topological arrangement the highest relative efficiency soil was 1.27 and its respective relative gain efficiency was 1.58. Both were associated with high corn grain yield (7.09 t 0.5 ha-1) and a decrease in bean yields.

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Received: January 2016; Accepted: April 2016

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