Basal diameter (2014 BD)

The variance analysis (ANOVA) for the 2014 basal diameter showed significant effects of P and the P*K interaction (Table 2). This was confirmed by the Tukey test (α =0.05), which, in addition, indicated that the application of N and K caused no significant effects (Figure 1). The above leads to the conclusion that the P is a nutrient that determines the growth of the species in the study area (^{Garrison-Jhonston et al., 2005}).

For a nutrient, equal letters signify statistically equal means.

Figure 1 Tukey tests (α =0.05) for 2014 basal diameter and total height in the Pinus cooperi Blanco fertilization experiment in Molinillos, Durango, Dgo. 

2014 Total Height (TH 2014)

In the case of the total height of 2014, the analysis showed that the tested factors produce no significant effects (Table 3, Figure 1). This may be due to a high variability of the height of the seedlings between experimental units, which in turn were a result of the system of reproduction of the species in the nursery (from seeds), since the germplasm used in the local nurseries generally lacks a strict quality control (^{Gülcü and Bilir, 2017}). Even when there were no significant effects, the Tukey test for the variable total height 2014 exhibited a trend which indicates (Figure 1) that the average dose of N generated the greatest height, i.e., that N is a deficient nutrient, at least partially in this area, as the height of seedlings responded favorably, though not significantly, to its application.

Dry weight of 100 needles (DW 100)

The dry weight of 100 needles (DW 100) was not significantly affected by the application of fertilizers, except in the case of K (Table 4). An increase in the weight of the needles was expected with the application of some of the fertilization treatments, because a tree with an adequate nutrition tends to grow more quickly than those trees that are deficient in nutrients. In such case, the increase in the growth is reflected mainly in the basal diameter and total height or in the diameter at breast height, although, in general, there is an increase in the size of the needles (^{Weetman, 1989}).

The Tukey test (α=0.05) indicates that the doses of N and P did not have a significant effect on the dry weight of 100 needles (Figure 2). On the other hand, there were differences between doses zero and one of K; of these, the first proved to be the better, i.e. the application of potassium had a negative impact on the growth of needles. This means that potassium is a nutrient found in sufficient quantities in the study site, and its application probably generates an imbalance (excess) with respect to the most deficient nutrients (^{López-López and Alvarado-López, 2010}).

For a nutrient, equal letters signify statistically equal means.

Figure 2 Tukey test (α =0.05) for the DW of 100 needles in the Pinus cooperi Blanco chemical fertilization experiment in Molinillos, Durango, Dgo. 

Increments in basal diameter (IBD) and total height (ITH)

The analysis for the increment in basal diameter between the assessment dates (2012-2014) showed significant effects of the tested nutrients on this variable, especially of N and the N*P and P*K interactions (Table 5). N promoted significant differences in the IBDs between levels zero and one. P had no significant effect on any of the three tested levels; this was also the case with K (Figure 3), which probably had a negative effect on the increment in the basal diameter.

For a nutrient, equal letters signify statistically equal means.

Figure 3 Tukey tests (α =0.05) for the increments registered between 2012 and 2014, in the Pinus cooperi Blanco fertilization experiment in Molinillos, Durango, Dgo.  

The increment in total height did not significantly differ between the tested factors (nutrients), except in their interactions (Table 6). Only N with dose one exceeded the zero level. The height of the trees is largely variable, and this feature may have been the reason for the confused effects between of the tested treatments. ^{López-López and Flores-Nieves (2016)} reported similar results with regard to the increment in height.

Foliar analyses

Most of the applied treatments (except three of them) generated a lower dry weight of needles than the control (Figure 4). This highlights the importance of carefully defining the fertilization nutrients and doses before applying them, since not all treatments generate positive results (^{Sumner, 1977}; ^{Moreno et al., 2002}).

Figure 4 Timmer diagram for the analysis of N in the Pinus cooperi Blanco chemical fertilization experiment in Molinillos, Durango, Dgo. 

The critical concentrations in Pinus cooperi are unknown, but Figure 4 shows higher concentrations of N (which in the control treatment are approximately 1.7 %) than the mean concentrations in nursery-grown conifers (0.87 %), according to the data presented by ^{Hernández and Torres (2009)}. This is the case even when the nutrient concentrations in the tissues of the nursery-grown plants are higher than those of individuals grown in the final sites, due to the intensive management provided in the nursery.

This means that N is probably not a deficient nutrient in the study area, or that its deficiency is rather slight. It is worth noting that even with the application of N, its concentrations in the foliage remained at levels similar to or lower than those of the control plants. The above indicates that there was loss of soil N, possibly due to vaporization or leaching. The nitrogen fertilizing material utilized was urea, which in the soil is converted into ammonium —a radical prone to vaporization (^{Binkley, 1993}; ^{Schlesinger, 1997}). As for phosphorus (Figure 5), leaf concentrations in most of the treatments were lower (0.096 %) than the average critical concentrations registered by ^{Hernández and Torres (2009)} for nursery-grown Mexican conifers (0.16 %).

Figure 5 Timmer diagram for the analysis of P in the chemical fertilization experiment of Pinus cooperi Blanco in Molinillos, Durango, Dgo. 

Therefore, the P is a nutrient that determines growth in the study site. This matches the positive effect described for the application of P on basal diameter grwth. Consistent with this finding, all treatments that produced higher dry weights of needles than those of the control saplings included a dosis of P (Figure 5), which, according to ^{López-López and Alvarado-López (2010)}, corresponds to Timmer’s vectors (^{Timmer and Stone, 1978} ) such as +,+,+, or +,-,+. ^{López-López and Alvarado-López (2010)} point out that this type of vectors is indicative of deficiency of the nutrient before its application.

However, the concentrations of K were lower (<0.2237 %) than the mean concentrations of K in the foliage of conifers (0.55 %) (^{Hernández and Torres, 2009}). In general, leaf concentrations of K in the present experiment was increased by applying this nutrient (Figure 6). This implies that K is not limiting the growth and that there is another factor that favors an effect of K concentration in the foliage (^{López-López and Alvarado-López, 2010}). This diagnose agrees with the significant negative impact of K on the dry weight of 100 needles (Figure 2).

Figure 6 Timmer diagram for the analysis of K in the Pinus cooperi Blanco chemical fertilization experiment in Molinillos, Durango, Dgo. 

The fact that K, still present in low concentrations in the foliage, had no positive effects on growth when applied means that the nutrient status of the trees must be based on a comprehensive analysis of several nutrients. An individual analysis of the concentrations of K in the foliage of Pinus cooperi would have led to the conclusion that it is deficient in the study site, and that its application would result in increment in growth; however, due to the presence of another deficiency, probably more severe than that of K, probably that of P, such a recommendation would be incorrect.

According to the results of this research, the application of a high dose of P, an intermediate dose of N and a low dose of potassium K can be recommended for the study site. This strategy would amend the most limiting nutrient deficiency (P), increase the availability of the slightly deficient nutrient (N) and increase the availability of the least deficient one (K), while the application of P alone might cause both N and K to become deficient, according to Liebig’s law of the minimum.