In Tamaulipas, sugarcane is planted in an area of 62 000 ha in seven municipalities (^{SIAP, SAGARPA, 2014}). This area is area supply three engenho: Aaron Saenz, El Mante and San Miguel del Naranjo. In the last 36 000 ha are planted with 86% under rainfed. Three municipalities of Tamaulipas, Antiguo Morelos, Nuevo Morelos and Ocampo, are zones supply this engenho, representing 53% of total plantings. The average yield in the 2012-2013 harvest was 69 Mg ha^-1 to 8.6 Mg ha^-1 sugar changing in recent years 42-73 Mg ha^-1 (^{Cañeros, 2014}), due to the distribution of precipitation and nutritional management since it has been widely applied at a dose 120-60-70, without considering aspects such as variety, soil type, plant cycle, crop management (fertilization) and climate (^{Thorburn et al., 2007}).

In rainfed areas, loss of fertility for crop stalks and residue burning in the field (^{Lal, 2009}) is a common problem resulting from the extraction of nutrients from sugarcane. This results in a reduction in the profitability of the crop, which are practices necessary to maintain soil fertility and efficient use of chemical fertilizers (^{Lal, 2009}). This poses a growing threat to production in the sugarcane areas.

For optimum plant growth, the nutrients must be adequate and balanced amounts in accordance with the time of crop demand. Sugarcane is one of the high consumption of fertilizers and crops respond well to the application (^{Gopalasundaram et al., 2012}). The use of chemical fertilizers is an important practice for sugarcane to reach high yields; however, currently, the need to conserve the environment but especially its high cost (^{Franco et al., 2011}) implies an appropriate and effective use to ensure maximum utilization (^{Salgado et al., 2003}). Timely and efficient application of fertilizers will enable the early establishment of a large population of crushing stems, component of utmost importance in defining the yield. Therefore, this study aimed to identify the optimal dose of NPK economy that optimizes yield in the field and juice quality of sugarcane in the area of influence of engenho San Miguel del Naranjo was raised under conditions rainfed.

The experiment was established in sugarcane area Ocampo, Tamaulipas, supply area engenho San Miguel del Naranjo, located in the Naranjo, SLP. varieties MEX CP 72-2086 and 79-431 were evaluated cycles soca 2010 - 2011 in sugarcane plots established in two locations: Ejído La Muralla and Ejído Las Flores respectively; both locations under rainfed.

The local climate is subtropical with an average temperature during the experiment at 25 °C and rainfall of 1685 mm. Before and after the establishment of the experiment the recommended tasks were performed in the area after the cut: destroncone, ripping, two crops and weed control.

In order to generate the fertilization treatments we used as the basis the recommended dose by the engenho 120-60-70 and through the design by San Cristóbal (Martínez, 1986) the following levels of exploration were generated; N: 103, 112, 120 and 128; P: 41, 51, 60 and 69 and K: 46, 58, 70 and 82 kg ha^-1, respectively. The combination of these factors led to 12 treatments according to the recommendations of the design used, in addition to the control treatment. The 13 treatments were distributed in accordance field under a randomized complete block with four replications. The fertilizer was applied in two parts; the first on February 13, 2010, 50% of N and total P and K; the second on July 18, 2010, the rest of N.

The fertilizer was applied at one side of the band in a trench groove 10 cm deep and then capped. The size of the experimental plots were four rows 1.3 m wide by 10 m long and useful plot two central rows. The harvest was performed manually when the cane was between 12 and 13 months of age in CP 72-2086 and Mex 79-431 respectively. The study variables were: stem diameter (mm) and length of internodes (cm); at harvest height stems were measured, the quality based on determinations of °Brix with a digital refractometer (Model 300051, Thomas Scientific) and field yield (Mg ha^-1), for which the stems of the useful plot were weighed on a clock balance of 100 kg capacity and were converted to Mg ha^-1.

In all variables an analysis of variance was applied (^{SAS, 2010}), the mean separation test of Tukey (p= 0.05) was used to establish statistical differences. For the economic analysis proposed by ^{CIMMYT (1988)} method was used. Fertilizer costs ($kg^-1 of nourishment:N= $21.95; P= $ 19.5; K= $14.83) were considered, cost of labour ($3 010 00 ha), manual cutting cost ($136.07); moving costs ($65.00 t) and the price per ton of cane ($776.99) for the year 2011.

The Figure 1 shows that in the period of the experiment, after the application of treatments, precipitation was 1 685 mm, mainly in the months of July to September 2010, which met the crop water requirements; this period coincides with the maturation stage of the crop. Temperatures during the growing period were averaged 32 and 17 °C as máximum and minimum respectively, which are favourable for growing (^{Moore and Botha, 2014}). With these conditions of temperature and soil moisture, the plant generally showed good growth and normal development.

Figure 1 Precipitation and maximum and mínimum temperatures during the development of the cultivation of sugarcane. 2010-2011. 

The Table 1 shows the results of analysis of variance of the different variables under study are presented. The fertilization treatments had a significant effect (p˂ 0.05) in the studied variables, except for °Brix. The varieties responded to NPK fertilization treatments but not in yield. The coefficients of variation (CV) were less than 11%.

Table 1 Effect of combined application of N, P and K in two varieties of sugarcane in different variables of the plant, juice quality and low yield in rainfed in southern Tamaulipas. 

*, **, *** significativo a p≤ 0.05, 0.01 y 0.001 respectivamente; ns= no significativo a p˃ 0.05

These results confirm the need for fertilizers as an option to increase the yield of sugarcane, as indicated by ^{Palma-López et al. (2000)}; ^{Salgado et al. (2001)} and ^{Gopalasundaram et al. (2012)}. The response to treatment x variety interaction indicates that fertilization depends on the variety.

Plant height is quite important in the production of sugarcane and the selection of new varieties. The plant height, expressed as the length of crushing stems (LTM) is presented in Table 2, which shows that the T6 (N₁P₁K₃) had the highest and treatment T1 (N₀P₀K₀) had the mínimum length of crushing stems; this response represented an increase of 25%. The increase in the length of crushing stems (4-25%) resulting from the application of treatments (NPK) was also a result of increased stem diameter (9-11%) and internode length (9-23%) depending on this treatment and variety.

Table 2 Effect of combined application of NPK treatments in sugarcane under rainfed yield and other variables in southern Tamaulipas. 

En columnas, letras iguales indican no diferencias entre tratamientos (Tukey, 0.05).

This confirms that, the optimal dose of NPK will depend on soil type and variety (Palma-López et al., 2001; ^{Salgado-García et al., 2011}). However, this suggests the need to continue this research in sugarcane area of southern Tamaulipas. The length of crushing stems was increased to 19% by increases in N application from level 0 (N₀P₀K₀) to level 1 (N₁P_nK_n) significantly (p<0.05) but higher increases in N were not significantly different (p> 0.05) at level 1.

Similar responses to increases in N rates were reported by ^{Muchovej and Newman (2004)}; ^{Madhuri et al . (2011)}; ^{Saleem et al. (2012)} and ^{McCray et al. (2014)}. For the effect of P, level 1 (N_nP₂K_n) showed a significantly higher length on crushing stems (p< 0.05) than the level 0 (N₀P₀K₀) and similar to level 2 (N_nP₂K_n). The application of K at different levels increased significantly (p< 0.05) on crushing length stems, but within levels no significant differences, so it is assumed that the best level of K was level 1 (N_nP_nK ₁) with an increase of 16% over the level 0 (N₀P₀K₀).

The different fertilization treatments did not significantly modify the quality of cane juice sugar (°Brix) at the time of harvest. The answer in the quality of cane juice was also observed by ^{Salgado-García et al. (2000)}; although, ^{Xu et al. (2010)} found that high doses of N, P and K itself had a significant increase in the quality of the juice. Data in Table 2 shows that, the lowest cane yield (66.1 Mg ha^-1) was in treatment N₀P₀K₀ (control) which is quite similar to the average of engenho San Miguel del Naranjo in the harvest 2012 -2013 of 69 Mg ha^-1 (^{Cañeros, 2014}). Different levels of N, P and K had a varied effect on yield of sugarcane.

The highest yield was observed in treatment N₁P₁K₁ with 112.2 Mg. ha^-1 differing significantly from other treatments and cane improves yield by 41% compared to treatment N₀P₀K₀ and differs from treatment recommended by engenho San Miguel del Naranjo (7%) (N₃P₃K₃). This means that, the recommended dose was not adequate for the production of sugarcane, so it is necessary to continue research in this area of Tamaulipas and define the optimal dose and economical soil type and for each variety. Similar situations in response to fertilization have been observed in other studies (^{Salgado et al., 2003}).

Both varieties of sugarcane showed a statistically similar yield (p˃ 0.05) in its response to N fertilization (Table 3). Significant yield increases with increasing doses of N were observed up to 103 kg ha^-1 (104.2 Mg ha^-1), while at higher doses yield tends to decrease. Fertilization treatment dose 103-41-46 had the highest yield of sugarcane outperforming the control treatment in 70% and treatment 120-60-70 recommended by engenho San Miguel del Naranjo 7%. The best fertility treatment met the requirements of both varieties because at very high doses, the response of plants was reduced. However, ^{Muchovej and Newman (2004)} indicated that exceeding 170 kg ha^-1 per dose did not increase in biomass and yield of sucrose. Moreover, the effect of phosphorus had a significant response at a dose of 69 kg ha^-1 (107.5 Mg ha^-1); although, similar to the dose of 41 kg ha^-1 (101.4 Mg ha^-1) indicating the possibility of considering an acceptable level 1 phosphorus. The variety Mex 79-431 was higher (p˂ 0.05) CP 72-2086 in stem diameter and °Brix but with similar yield (p˃ 0.05).

Table 3 Effect of combined application of NPK on two sugarcane varieties under rainfed yield and other variables in southern Tamaulipas. 

Medias de variedades con la misma letra son iguales (Tukey 0.05).

Both varieties showed a similar behaviour in response to fertilization K. At a dose of 46 kg ha^-1 the maximum yield was obtained (102 Mg ha^-1) and at higher doses was observed field yield was similar to this dose or a tendency to decrease. The economic analysis indicated that fertilization treatments 103-41-46 for the dose that produced the best yield, with a rate of return to variable capital of $ 1.85 and $ 3.01 for varieties CP 72-2086 and Mex 79-431 respectively, in both cases being higher return rate.