Introduction

The potato requires large amounts of nutrients, due to their need to fill tuber. When the goal is to improve the yield and quality of potato, the amount should be given importance, the type of nutrient and its application programming (^{Coraspe et al., 2009}).

The production of seed potatoes in greenhouses in Mexico within the formal system of seed production, NOM041-FITO-2002 ^{SENASICA (2014)}, is made by using organic substrates (coconut fiber, rice hulls and peat) and inorganic (tezontle, perlite, sand and gravel) and mixtures thereof. Fertilization in some cases is a solid foundation mixed with the substrate and fertigation using complete formulations of NPK and Ca, which is complemented by foliar applications of nutrients according to the stage of crop development; in some cases, are used general hydroponic nutrient solutions as ^{Steiner (1961}). One of the great problems of seed production tuber greenhouse is the poor stability of the results, which coupled with high densities used, 45 to 100 plants m², reduces the yield per plant, so it is important to determine the NPK fertilizer levels in national varieties under local conditions (^{Flores et al., 2009}).

The performance is influenced by genotype, environmental conditions, intercepted radiation, physiological state of tubers employees or in vitro plants, planting density and nutrition is one of the most important factors for high performance and improve quality physical and health of tubers, so that nutrients should be applied in the time demanded by the plant and suitable for growing concentrations. Of the essential elements for plants, nitrogen (N) is a structural component of nucleic acids, amino acids and proteins; potassium (K) is required for activation of certain enzymes, carbohydrate translocation and regulation of osmosis; while phosphorus (P) is involved in energy processes in nucleic acids, phosphorus sugars, alcohols and lipids.

The process tuberisation is influenced by the nutritional balance (^{Struik and Wiersema, 1999}), photoperiod (^{Martínez et al., 2001}), total radiation, radiation intercepted by the plant, CO₂, temperature, genotype and nutrition (^{Struik and Wiersema, 1999}).

The nutrition is critical in the development and performance of the potato; nitrogen and potassium are the elements found in potatoes in large quantities; high concentrations of nitrogen lengthen the growing season and delay the onset of tuber; also they reduce tuber yield and quality; while low concentrations act contrary (^{Giletto et al., 2003}). Management of nitrogen fertilization is important for regulating the growth and development of potato cultivation as well as to minimize the risks of contamination by nitrites (^{Zebarth and Rosen, 2007}). The N content of 60 to 100 days of development of the potato, the tuber in relation to total plant nitrogen varies from 81 to 89% in the varieties Hilite Russet and Russet Burbank (^{Alva et al., 2002}).

In field applications, 200 kg ha^-1 of this element increases the amount of foliage and remains active after 70 days of crop development (^{Da Silva, 2000}) constant. ^{Giorgetta et al. (1993)} mention that the phosphorus is important in the establishment of the plant and generating stolons; glasshouse tested concentration of 72 mg L^-1 of P, applied as triple superphosphate, where they managed to obtain 385 minitubers per m², of which 53% weighed between 5 and 40 g. In addition, ^{Chapman et al. (1992}); ^{Rozo and Ñústez (2011)} evaluated three levels of phosphorus (50, 100 and 150 kg ha^-1) as P₂O₅ results in equal performance with each other and higher than the control level of zero kg ha^-1.

With respect to potassium ^{Rozo and Ñústez (2011)} mention that potassium deficiency can result in decreased performance and size of tubers. ^{Mc Dole et al. (1978)} state that some quality factors such as dry matter, specific gravity, sugar content, flesh color and the phenomenon of hollow heart are affected by potassium fertilization.

^{Coraspe et al. (2009)} conclude that the sequence of maximum accumulation of macronutrients in leaf and root vegetables in hydroponics in the variety Atlantic was K>N>S>Ca>P>Mg. However, no difference in nitrogen requirement depending on genotype; in this regard, ^{Love et al. (2005)} evaluated the requirements of N in three genotypes: Bannock Russet, Gem Russet and Russet Summit, where they found they had different nitrogen requirement compared to Russet Burbank.

Different studies on potato hydroponics in greenhouses have been made, where the plant will provide all the nutritional requirements you need. ^{Boersig et al. (1988)} compared the NFT and ARM systems for the production of mini-tubers. ^{Simko (1991)} differentiated the process of in vitro and in hydroponics tuberisation. Meanwhile, ^{Chil et al. (2001)} evaluated the effect of the temperature of the nutrient solution for the production of minitubers, and found that their number was increased to 15 °C than at temperatures higher than 20, 25 and 30 °C; Additional foliar concentration of nutrients such as N, K, Ca and Mg is increased at high temperatures; meanwhile, phosphorus is not affected.

^{Novella et al. (2008)} found that solutions 1 ds m^-1 can be used for the production of seed tubers in a greenhouse, and that the increase in the electrical conductivity to 5.8 ds m^-1 does not affect the number of minitubers indoor hydroponic systems; also they mention that originated from tubers plants produce fresh weight, dry matter and higher than those arising IAF from plants in vitro. On the other hand, ^{Simko (1991)} evaluated mixtures of substrates and two nutrient solutions for hydroponic cultivation of potatoes. Meanwhile, ^{Muro et al. (1997)} studied the influence of the nutrient solution substrates (peat and sand) and ^{Flores et al. (2009)} planting density on yield of seed potatoes, and mentioned that the higher the density decreases the number of tubers per plant. Also, ^{Mc Collon (1978)} mentions that a nutritional imbalance with high concentrations of phosphorus and low zinc in the nutrient solution produces high tuber yield.

Therefore, the objectives of this research were to: 1) determine the concentrations of NPK suitable for the production of potato clone 020342.1 under hydroponics conditions; and 2) assess the yields of minitubers under greenhouse conditions.

Materials and methods

Two experiments were established of september to december 2012 in a greenhouse in Zinacantepec, Mexico. The location is 19° 17’ 21” north latitude and 99° 42’ 49” west longitude and a height of 2 640 msnm (^{García, 2004}; ^{INEGI, 2008}). The average temperature of experiment 1 was 15.5 °C and Experiment 2 of 14.3 °C with highs of 36 and lows of -0.9 and -1.5 °C respectively.

The 1.8 L pots were used volume, horticultural grade vermiculite from 1 to 4 mm in diameter. The 020342.1 clone industry was used with quality and tolerance to internal staining caused by tuber syndrome purple potato tip; minitubers selected were from 12 to 15 mm in diameter with a single outbreak and virus-free.

Irrigation was done with the use of droppers 8 L h^-1 with four outputs distributor. They programmed with a programmer Hunter PRO-C model, four irrigations the first two weeks, followed by five the next four weeks, and seven the last six weeks, depending on the stage of crop development; spending was 33 ml per pot in each irrigation for a maximum flow of 231 ml per pot.

The experimental design was randomized complete block with three replicates for NPK and four levels for each factor, which gives a total of twelve treatments (^{Martínez, 1996}). Concentrations in mg L^-1 were 100, 150, 200 and 250 of nitrogen; 30, 80, 130 and 180 for phosphorus; and 250, 300, 350 and 400 of potassium. The resulting 12 treatments have the following combinations of NPK: T1 (100-30-250); T2 (200-30-250); T3 (100-130-250); T4 (200-130-250); T5 (100-30-350); T6

(200-30-350); T7 (100-130-350); T8 (200-130-350); T9 (15080-300); T10 (250-80-300); T11 (150-180-300) and T12 (15080-400). For this purpose 12 supplemented nutrient solutions Mg 45 mg L^-1, 200 mg L^-1 Ca, 3 Fe-EDTA, 0.5 Zn, 0.5 Cu, 0.5 B. The pH was adjusted to 6.0 and conductivity of various 2 were 2.6 ds^.m^-1. The results of the experiment were analyzed using the statistical package SAS version 9.0 (^{SAS, 2002}).

Furthermore, the concentration of chlorophyll was evaluated, which was measured by the method of ^{Lichtenthaler and Wellburn (1983)}; then Spad readings were taken and the value was substituted in the regression equation. Other variables were: IAF, which took an 80 Accupar ceptometro, plant height, number, fresh weight and diameter of tubers. For all variables was made corresponding analysis of variance and comparison of means (^{SAS, 2002}).

Results and discussion

Foliar area index

In all treatments, the IAF increased in the first samples (31 and 41 DDE); maximum growth occurred in the treatment T12 with 1.0 of IAF, and at 41 DDE the IAF a considerable increase in the T6 and T12 treatments was reached; after october 26, this treatment began to decline so that for the last date (november 19), the average was 3.71. Something similar happened in treatments T8, T9 and T11 in the last sampling date IAF decreased to 3.9, 3.4 and 3.5, respectively. Unlike the above, T1, T2, T3, T4, T5 and T6 treatments they showed increased IAF through sampling dates, without tending to decrease as in the case of T12 (Figure 1). Treatments with lower content of N showed high IAF values to the third sampling date (October, 20), whereas treatment with high concentrations of N was the T10; from second date presented values IAF 3.0, which also occurred with T6, T11 and T12 treatments 200, 150 and 150 mg L^-1 of nitrogen. Another important factor influencing performance are the high values of the IAF and the duration thereof; this is observed for treatment T6 and T12 showed consistency in increasing IAF during the cycle of potato clone 020342.1 and had higher performance in number and biomass of tubers.

Average experiments 1 and 2.

Figure 1 Foliar area index of the clone 020342.1 at 31, 41, 46, 52, 64 and 75 DDE experiment NPK in hydroponics.  

Plant height

In relation to plant height, analysis of variance indicated that there were significant differences between treatments in both experiments, and the average of these (Figure 2). The treatments presented plants were taller T10 an average of 47 cm, with 43 cm T8, high in N; and 45 cm to T11, T9 with 42 and T12 with 42 cm; all were statistically different with T1, T2, T3, T4, T5 and T7 treatments. Moreover, interaction between N and K, and N and P was presented; Additional treatments showed different responses according to the dose of K applied in the nutrient solution.

Treatments with the same letter are the same, Tukey p< 0.05.

Figure 2 Average height of plants NPK experiment in clone 020342.1 in hydroponics. 

Performance minitubers

The yields of fresh weight of tuber clone 02342.1 are statistically different in all treatments (Table 2). The average yield of the experiment ranges from 167.27 to 216.95 g; treatments with lower yields are T7 with 167.27 g, T4 and T1 with 172.88 with 174.24 g; treatment with the lowest fresh weight has the lowest concentration of N, which demonstrates the importance of P and N in the potato tuber. Treatments with the highest yields were T3 with 202.28 g, the T10 with 216.69 and 216.95 g with T6. As can be seen, the best treatments contain high concentration of nitrogen (200 and 250 mg L^-1) and potassium concentrations (300 and 350 mg L^-1); while the T3 treatment has lower content of nitrogen and potassium, but with higher content of phosphorus; T2 contains high concentration of nitrogen and low phosphorus, which also has good production in fresh weight. This indicates that there is a balance between the three main elements NPK to achieve high yields (greater than 198 g).

Table 2 Fresh weight of tubers and comparison of means from clone 020342.1 NPK experiment in hydroponics. 

Tratamiento	Media de peso fresco de tubérculo (g)
1. 100N-30P-250K	174.24 def
2. 200N-30P-250K	198.47 abc
3. 100N-130P-250K	202.28 ab
4. 200N-130P-250K	172.88 ef
5. 100N-30P-350K	179.31 cdef
6. 200N-30P-350K	216.95 a
7. 100N-130P-350K	167.27 f
8. 200N-130P-250K	193.25 bcd
9. 150N-80P-300K	185.66 cbdef
10. 250N-80P-300K	216.69 a
11. 150N-180P-300K	186.92 bcde
12. 150N-80P-400K	191.48 bcde

Tratamientos con la misma letra son iguales, Tukey p< 0.05.

The results agree with those mentioned ^{Ayalew and Beyene (2011)} who with 280 kg ha of K has increased performance in field 10 ton more compared with treatment of 200 kg ha potassium. In addition, ^{Muro et al. (1997)}; ^{Simko (1991)} evaluated the influence of two nutrient solutions for hydroponics potato, finding tuber very good yields with high concentrations of this element. ^{Mc Collon (1978)} mentions that high concentration of phosphorus and low zinc in the nutrient solution gives higher yields twice to commercial. Finally, ^{Flores et al. (2009)} studied planting density on yield of seed potatoes and found that the higher the density decreases the number of tubers per plant.

In the Figure 3 shows more clearly the difference between treatments. However, the results are not consistent with respect to the P content in the solution, so we can say that the P concentrations evaluated was not final in the production of tuber fresh weight; These results agree with those reported by ^{Muro et al. (1997)}, who found that increasing the concentration of phosphorus in nutrient solutions employed, not performance increases.

Treatments with the same letter are the same, Tukey p< 0.05.

Figure 3 Comparison of tubers fresh weight (g) produced in greenhouses clone 020342.1 for NPK experiment in hydroponics.  

As it regards the total number of tubers is observed (Figure 4) that there is difference between treatments. Treatments increased production of mini-tubers per plant were the T8 with 18.6 tubers, with T12 with 18.2, T10 with 18.1 and T6 with 16.8. It is noted that the N influenced the number of tubers in three of the four solutions of which concentration was higher than the 200 mg L^-1; likewise, treatment with the highest number of minitubers was presenting 130 mg L^-1 of P. This results agree with those reported by ^{Alva et al. (2002)}; ^{Giorgetta et al. (1993)}, who mentioned that N is very important for potato yield, and P is important in the generation of stolons and performance.

Treatments with the same letter are the same, Tukey p< 0.05.

Figure 4 Total number of tubers produced in the greenhouse by clone 020342.1 for NPK experiment in hydroponics. 

On the other hand, treatments with fewer tubers were T4 with 10.5, T5 with 11.7, T7 with 13 and T1 with 12.2. The same behavior for larger tubers of 15mm diameter was observed (Table 3).

Table 3 Number of tubers >15 mm gases produced by clone 020342.1 on NPK experiment in hydroponics. 

Tratamiento	Media
	T>15 mm	TT
1. 100N-30P-250K	9.47 ef	11.22 g
2. 200N-30P-250K	11.44 cd	13.08 de
3. 100N-130P-250K	9.78 ef	11.52 fg
4. 200N-130P-250K	8.92 f	10.59 g
5. 100N-30P-350K	10.02 def	11.77 gf
6. 200N-30P-350K	13.74 ab	16.81 bc
7. 100N-130P-350K	10.54 ed	13.07 ef
8. 200N-130P-350K	14.52 a	18.68 a
9. 150N-80P-300K	11.36 cd	13.77 de
10. 250N-80P-300K	14.30 a	18.13 ab
11. 150N-180P-300K	12.47 bc	15.30 cd
12. 150N-80P-400K	14.21 a	18.27 ab

T>15 mm = tubérculos mayores de 15 mm de diámetro; TT = tubérculos totales. Tratamientos con la misma letra son iguales, Tukey p< 0.05.

Here treatments highlighted T8, T10, T12 and T6, which were statistically equal to 14.52, 14.3, 14.21 and 13.7 minitubers respectively. When comparing treatments T8 and T6, we can see the positive influence of phosphorus in the production of minitubers, for while the T6 contains only 30 mg L^-1, treatment T8 contains 130 mg L^-1.

In general, treatments with higher potassium content, regardless of the concentration of phosphorus, had a higher number of minitubers, both total and over 15 mm in diameter (Table 4).

Table 4 Distribution of diameters (%) of minitubers in clone 020342.1 for NPK experiment in hydroponics. 

Tratamientos	Diámetro
	40 mm	30 mm	25 mm	20 mm	18 mm	15 mm	>15 mm
1. 100N-30P-250K	1.8	21.6	23.3	22.1	8.1	7.6	15.6
2. 200N-30P-250K	3.3	24.5	22.4	18.7	7.3	6.6	17.2
3. 100N-130P-250K	1.7	25.7	21.4	18.6	9.3	7.9	15.4
4. 200N-130P-250K	3.7	21.3	23.4	19.3	9.1	7.4	15.7
5. 100N-30P-350K	0.9	22.1	23.6	20.5	9.6	8.4	14.9
6. 200N-30P-350K	0.8	16.4	21	24	11.2	8.5	18.3
7. 100N-130P-350K	0	14.6	21.8	23.8	11.1	9.4	19.4
8. 200N-130P-350K	0	12.6	19.4	23.2	12.7	9.9	22.3
9. 150N-80P-300K	0.1	14.5	22.4	25.8	11.7	7.8	17.8
10. 250N-80P-300K	0.4	14.5	18.7	21.9	12.7	10.5	21.3
11. 150N-180P-300K	0.2	14	20.4	24.7	12.6	9.6	18.5
12. 150N-80P-400K	0	11.4	18.7	24.3	12.5	10.9	22.2

This is consistent with what was found by ^{Chapman et al. (1992)} and ^{Singh and Lai (2012)} who mentioned that the higher the concentration of K, has increased crop yield, both in field and greenhouse. As you can also see that in treatments with lower concentration of nitrogen they had fewer minitubers; however, production increased when used 200 to 250 mg L^-1 of this element is presented. In addition, these results are consistent with that found by ^{Novella et al. (2008)}; ^{Muller et al. (2007)}, who report that the electrical conductivity of the nutritive solution 1 to 5.8 ds m^-1 does not affect the number and performance of minitubers. It can also be seen in Table 4 that the distribution of the diameters of minitubers per treatment, is different; so, T2 and T4 treatment with 200 mg L^-1 of nitrogen and 250 mg L^-1 of K, regardless of the concentration of P, showed the highest number of minitubers over 40 mm in diameter, followed by T1 and T3 with lower nitrogen content.

Also, treatments 1 to 5, for the diameter of 30 mm, showed the highest values; i.e. tubers had fewer but larger diameter otherwise treatments with T8, T10 and T12. The minitubers larger amount of less than 15 mm, where the percentage was higher than 20% diameter was presented; It highlights the T12 (150N-80P-400K) treatment with 22%. In general, the experiment showed the highest production of minitubers for diameters of 20 and 25 mm. The opposite turned out to treatments T1 to T5, which increased production corresponded to the diameters of 25 and 30 mm.

Conclusion

Under greenhouse conditions, concentrations above 200 mg L^-1 of N, phosphorus 130 and 250 mg L^-1 of K favor the production of potato minitubers in hydroponics in perlite.

The clone 020342.1 studied, with these concentrations of NPK in the nutrient solution, showed higher performance in number of minitubers, number of tubers smaller diameter, IAF, chlorophyll content, plant height (47 cm) and greater performance.