Introduction

Amaranth is one of the many crops domesticated and used in Mexico for more than 4000 years (^{Alejandre and Gómez, 1999}; ^{Alejandre et al., 2012}). It is also cultivated in other countries because of its great genetic diversity and phenotypic plasticity, which allows it to adapt to unfavorable conditions of temperature and humidity on slopes (^{Soriano et al., 2015}). In Aztec culture, amaranth was known as “huautli”, which had great commercial value, since it was used as currency of exchange because it was one of the taxes that 17 of the 20 provinces of the Aztec empire gave the “Gran Tenochtitlán “(^{Aguilar and Alatorre, 1978}).

The amaranth seed and leaf were used in religious ceremonies (^{Sauer, 1950}), which, together with the replacement of native crops by the introduced ones of the Old World (which were preferred by the Spanish), acted together to reduce the cultivation of amaranth drastically (^{Becerra, 2000}). Fortunately, the rooting of customs in the villages is very dynamic, and cultivation of amaranth has been maintained to date, albeit on a small scale, thanks to the knowledge and action of farmers’ groups (^{Sauer, 1979}; ^{Becerra, 2000}). It is for this reason that the agricultural potentials of sociocultural and biological systems in the course of coevolution are present in their knowledge systems (^{Kallis and Norgard, 2010}).

Some studies have revealed that before the arrival of the Spaniards, amaranth was grown in productive areas from what is now the state of Arizona in the United States of America to the central Mexican highlands (^{Bostid, 1984}). Knowledge about the management of amaranth cultivation was conceived on the basis of the trial and error method and experimenting to achieve a productive equilibrium, the conservation of the land and the cultural use of the products obtained from it (^{Abasolo, 2011}). The cultivation of amaranth allows the farmer to obtain economic resources that contribute income to the production unit (^{Sánchez et al., 2015}). Although the lack of organization of producers to sell grain has been a vulnerable aspect of the chain, because 80% of producers decide to sell to intermediaries, who set the price at harvest, this causes increase supply and demand (^{Ayala et al., 2014}).

The increase in the area of amaranth in Mexico is determined by the value of production, the yield and the average rural price (SIAP, 2015), the difference of the national average and the state with the largest area 54.55%. The relationship with productivity growth depends on the adoption of technological innovations, which are recommended according to the characteristics of the production area (^{Estrada et al., 2006}). Amaranth is cultivated under temporary conditions, tolerates drought and its yield may be greater or similar to that of other crops under equal circumstances, apart from being an alternative of production and adequate consumption to marginalized regions of the country (^{Barrales et al., 2010}). The crop is developed in small communities with water shortage and technology for production and processing in the producing regions of the country (^{De la O et al., 2012}). However, producers do not have an adequate technological package that allows them to increase their yields (^{Ayala et al., 2014}).

On the other hand, the crop is poorly associated with the availability of moisture and the needs of fertilizers defined by the characteristics of the soil. It is known that nitrogen is the most restrictive element in the growth of a crop, in amaranth it is mentioned that as the environment is more favorable, more N should be applied (^{Schultz-Schaeffer et al., 1989}; ^{Ramírez et al., 2011}). Although studies of amaranth varieties with levels of 0 to 180 kg ha^-1 of N are known, yield increased by 45% at the highest dose (^{Myers, 1998}). In another study on fertilization in amaranth varieties, they achieved higher yields, associated with the formulas 80-60-40 and 80-30-40 with 1 668.7 and 1 660.9 kg ha^-1, respectively, the variety DGTA reached the yield of 178.2 kg ha^-1 with the density of 100 000 plants ha^-1 (^{Ramírez et al., 2011}).

Among the Amaranth production parameters in Mexico, the state of Tlaxcala is the one with the highest area harvested (2 491 ha) and the highest production (3 509.4 t), followed by Puebla with 1 950 ha harvested and 2 188.7 t amaranth (^{SIAP, 2014}). In the state of Puebla, the municipality of Tochimilco produced 1 097 t representing 19.77% of national production and 50.12% of state production (^{SIAP, 2014}). However, Tochimilco records an average yield of 1 t ha^-1, which is far from the yield obtained in municipalities of the State of Mexico (1.95 t ha^-1) and the national average (1.31 t ha^-1).

On the other hand, due to the incorporation of animal manure (manure) and organic waste, the chemical fertilization that they make to the cultivation of amaranth is minimal, since in the first work they apply a bundle of diammonium phosphate DAP (18-46-00) mixed with two bundles of urea (46-00-00), equivalent to a dose of 55-25-00 kg of NPK per ha (^{Sánchez et al., 2015}). However, the fertilizer doses used in the region by local producers may vary when applying the fertilizer in first and second labor added to compost of worm, according to the amaranth production system. Therefore, the objective of the research was to evaluate the effect of organic-mineral fertilization on grain yield and height of amaranth plant; in addition, determine if there is any correlation between plant density and yield.

Material and methods

Experimental design and treatments

A completely random experimental block design with four replications was used, the experimental unit size was four furrows 2 m long by 2.4 m wide (0.6 m furrow) and the useful plot was the two central furrows and eliminating a forest on both sides. The treatments were obtained through the Plan Puebla I matrix (^{Turrent and Laird, 1975}).

The factors and levels of study were: nitrogen at four levels 20, 40, 80 and 100 kg ha^-1; phosphorus 0, 20, 40 and 60 kg ha^-1; commercial compost of worm at 4 levels 500, 1000, 2000 and 3000 kg ha^-1, plus 40 kg ha^-1 of potassium for fertilization treatments and a control treatment NPK (00-00-00) without application of compost as treatments additional. The total number of treatments was sixteen (Table 1). The variables evaluated during two crop cycles (2014-2015) were yield per m², yield per plant and plant height. The number of plants per experimental unit was also counted at the time of panicle cut in order to evaluate if there is a correlation between plant density and yield.

Table 1 Evaluated treatments. 

N= nitrógeno; P= fosforo; K= potasio; c= composta.

Results and discussion

With the statistical results the model is correct to explain the effect of chemical-organic fertilization on plant height, yield per m² and yield per plant of amaranth (Table 2), which were significant (p< 0.05), and highly significant (p< 0.01).

Table 2 Average squares and probability level for the variables plant height, yield per m2 and yield per plant in amaranth. 

^* = significativo en valor de Fc (α= 0.05); ^** = significativo en valor de Fc (α= 0.01)

The effect by organic-mineral fertilization on AP, RM² and RP is shown in Table 3, in general the plant requires amounts of N between 20 and 80 kg ha^-1, P between 00 and 40 kg ha^-1 and 1 to 3 t ha^-1 of worm compost. However, the highest height was achieved significantly (Tukey, p≤ 0.05), with the dose of 40 kg ha^-1 of N and the lowest level of phosphorus and 1 t ha^-1 of compost of worm; as the N and compost of worm (11, 1 and 3) remain constant, a low phosphorus response can be observed. Close results were found by ^{Ramírez et al. (2011)}.

Table 3 Effects by organic mineral fertilization on average values of variables in amaranth (2014-2015). 

N= nitrógeno; P= Fósforo; K= Potasio; c= composta; AP= altura de planta; RM² = rendimiento por metro cuadrado; RP= rendimiento por planta; CV= coeficiente de variación; DMS= diferencia mínima significativa.

When analyzing the variable RM², we found highly significant differences (Tukey, p≤ 0.05). It can be observed in Table 3 that the yield per m² higher is obtained in treatment 5 with the dose 80-20-00-1 kg ha^-1 and t ha^-1 of NPK and c, surpassing the rest of the treatments tested, the control was the lowest value (101.6 kg ha^-1). The dose of phosphorus and compost of worm was constantly examined, and the level of nitrogen (9, 1, 5) was varied to confirm the dose of N. According to ^{Schultz-Schaeffer et al. (1989)}; ^{Ramírez et al. (2011)}, the N is a limiting element for the growth of a crop, in addition, as the environment is more favorable, a larger amount of the N dose should be applied and the amaranth grain yield increased, where yields higher are associated with NPK formulas 80-60-40 and 80-30-40.

The yield per plant had a similar behavior and was significant in the same treatment 5, showing effect in 64.63 g of grain, also exceeded the rest of the treatments and above the control with difference of 29.84 g. However, it is of specific importance to observe responses for the variable RP in treatment 8 with the dose 80-40-00-2 kg ha^-1 of N and 40 of phosphorus with two t ha^-1 of compost of worm compost (Table 3). In which the RP is attributed to the compost when the level of N and P is left constant, with a difference of 3.97 g. Similar results show ^{Ramírez et al. (2011)} and ^{Myers (1998)} for temporary conditions with chemical fertilizer. According to ^{Sánchez et al. (2015)}, the incorporation of manure and organic residues reduces the fertilization dose.

Regarding the CV of each of the studied variables, it is observed that they are lower for AP of 0.35, RM² of 14.48 and RP of 8.2 (Table 3). While the DMS is 0.23, 37.8 and 24.38, respectively.

The distribution of the PA with respect to the different treatments evaluated in the analysis of variance, expressed statistically significant differences (Tukey, p≤ 0.05). A more extensive appreciation of the response to NPK doses plus compost is shown in Figure 1. The fertilization rate 80-40-00 kg ha^-1 of N-P-K plus three tonnes of compost ha^-1 underestimates the value of 1.52 m in TR 14.

Figure 1 Mean height of amaranth plants obtained with different doses of N-P-K and compost in the years 2014 and 2015. Vertical bars represent the confidence interval ± of test mean Tukey (p≤ 0.05). 

When treatment 40-00-00 kg ha^-1 of N-P-K plus one ton of compost ha^-1 overestimated the 1.83 m height value in TR 11 (Figure 1), the plant only needed 1 t ha^-1 of worm compost to increase 0.31 m in height, lowering the level of N, P and compost of worm. These results contrast with those reported by ^{Pospisil et al. (2006)}, who mention that fertilization has no significant effect on the height of amaranth plant. When a correlation test was carried out, it was found that at a higher number of plants per experimental unit, plant height decreased (Figure 2), which coincides with that reported by Glimplinguer et al. (2008) who indicate that the height of plant diminishes with the increase in the density of plants. In contrast, ^{Torres et al. (2006)}; ^{Ramírez et al. (2011)} found that the height of A. hypochondriacus increases with plant density.

Figure 2 Correlation between number of plants and height of amaranth plants. The correlation is significant at the 0.05 level, according to the Pearson coefficient. 

Statistically significant differences (Tukey, p≤ 0.05) were found in yield per m² and yield per plant. The fertilization formula was 80-20-00 kg ha^-1 of N-P-K plus one ton of compost ha^-1 with the highest grain yield in both variables (Figure 3 and 4). In relation to the doses of N, these results are similar to those reported by ^{Ojo et al. (2007)} who mention that under optimal conditions the optimum N doses should be in the range of 60 to 80 kg ha^-1. However, ^{Myers (1998)}, in an experiment conducted in Missouri, USA, evaluated doses of 0 to 180 kg N ha^-1 and found a higher yield at the highest dose. On the other hand, ^{Makus (1991)} evaluated doses of 0, 60, 120 and 240 kg N ha^-1 and found no statistical differences in yield.

Figure 3 Average yield of amaranth obtained in 1 m2 with different doses of N-P-K and compost in years 2014 and 2015. Vertical bars represent the confidence interval ± of test mean Tukey (p≤ 0.05). 

Figure 4 Average yield of amaranth per plant obtained with different doses of N-P-K and composite in years 2014 and 2015. Vertical bars represent the confidence interval ± of test mean Tukey (p≤ 0.05). 

The highest yield per m² (201.81 g), with the dose 80-20-00 kg of N-P-K ha^-1 plus one ton of compost ha^-1, is equivalent to 2 018.1 kg ha^-1, which is considerably higher than (^{SIAP, 2014}), the yield of 1 016 kg ha^-1 obtained with the control treatment and the yield of 1 668.73 kg ha^-1, obtained with doses of 80-60-40 in localities of San Miguel of Milagro, Tlaxcala and Montecillo, State of Mexico (^{Ramírez et al., 2011}).

A negative correlation was observed between the number of plants and yield per plant (Figure 5); which means that a greater number of plants is not determinant in the yield per plant. This agrees with what ^{Ramírez et al. (2011)} who reported that the lowest number of plants ha^-1 increased yield of amaranth seed. This indicates that the average grain yield and grain yield per plant were affected by the height (Table 3) and the number of plants in negative mode (Figure 2 and 3), according to the dose of organic-mineral fertilization (Table 3) that required the cultivation of amaranth during the two years of study.

Figure 5 Correlation between number of plants and yield of amaranth per plant. The correlation is significant at the 0.05 level, according to the Pearson coefficient. 

De acuerdo con ^{López et al. (1996)} en el caso de trigo, incrementos de N fertilizante por un periodo de tres años, disminuyó significativamente el promedio del peso de grano, debido a dos años secos y por otros factores presentes en el suelo. No obstante, ^{Díaz et al. (2004)}; ^{Torres et al. (2006)}; ^{Arellano y Galicia (2007)} encontraron que a mayor densidad de plantas, mayor fue el rendimiento de grano, además, estudiaron el N y la variedad.

It seems to be that the tendency towards more grain yield and number of plants suggests the use of new varieties that consider stem size, number of plant with spike and density of plants. However, some of these factors do not appear to be associated with increased yield (^{Wang et al., 2002}). This part, agrees with the results obtained in his study by ^{Henderson et al. (2000)} pointing out, plant density does not have a significant effect on yield of amaranth grain. However, yields can be increased with organic-mineral fertilization in the amaranth region and good management of soil conditions.

Conclusions

With the organic-mineral fertilization formula 80-20-00 kg ha^-1 of N-P-K plus one ton of compost ha ^-1 it is possible to significantly increase yield of amaranth grain locally. However, the high negative correlation found between the number of plants and the yield suggests trials with levels in plant density, according to the characteristics of the traditional system of direct seeding 3 and 5 plants per plot, which explains higher plant densities (150 000 and 200 000 plants ha^-1) to those reported by other researchers (100 000 plants ha^-1).

These results show that in order to improve the yields of the producers it is necessary to specify the dose and the density of plants in other soil management conditions in the study region; and adequate organic-mineral fertilization in the amaranth root zone. In spite of the results obtained, it is important to test different organic products under similar conditions or in other soils of the region.