Peanut growth and final yield are closely associated to peanut's capacity to take advantage of environmental resources (e.g. radiation, water and nutrients). For this reason, the management of plant density is one of the most effective tools to obtain canopy and root systems that are efficient capturing resources. Therefore, plant density selection is an important component of agronomic management to maximize yield (Bell et al., 1991; Rasekh et al., 2010). Peanut yield response to variation in plant density has been extensively studied worldwide. Generally, under well-watered conditions, plant densities ranging from 4 to 10 plant/m² produce the greatest yield. Densities above this range did not increase pod yield, while densities below 4 plants/m² reduced pod yield (Bell et al., 1987). Then, at high plant densities peanut yield is relatively insensitive to plant population with a wide range in seeding rates usually producing the same yield (Bell et al., 1987; Bell and Wright, 1998; Tewolde et al., 2002). At the same time, these responses to density may vary according to the environmental conditions (mainly hydric and nutritional), genotype used (growth habit and branching pattern), sowing dates and the combination of all these factors.

The optimum plant density (OPD), which is the minimum density of plants required to obtain maximum yields (Lee et al., 2008), determined in one place might not be applicable in another environment (Rasekh et al., 2010). In the Argentine peanut growing region, Giayetto et al. (1998) noted that planting density and arrangement affect the peanut growth, most compact spacing produces more dry matter per surface and leaf area index. Pedelini (2016) stated that a low densities (<8 plants/m²) peanut never reaches the maximum possible yield. While high densities (>17 plants/m²) did not diminish yield, they increased seed cost. On the other hand, Cerioni (2012) determined that 9 plants/m row spaced 0.7 m could be considered a minimum density to reach acceptable yields.

Previous experiments conducted in Argentina with runner-type cultivars, the most common type in the area, indicated no differences in yield from 5.7 plants/m² (Pedelini et al., 1986), 7.5 plants/m² (Casini et al., 1999), 9 plants/m² (Casini et al., 2008; Cerioni et al., 2012), and that maximum yields were obtained between 13 to 23 plants/m² (Casini et al., 1999), 16 to 18 plants/m² (Casini and Sagadín, 1998), 17 to 23 plants/m² (Pedelini et al., 1986), 24 plants/m² (Cerioni et al., 2012), and 30 plants/m² (Giayetto et al., 1998).

There are different statistical models that can be used as tools in the analysis of crop response to changes in planting density (Bell et al., 1991; Bell and Wright, 1998), including quadratic, lineal-plateau, quadratic-plateau and spherical-plateau functions. Among those, the equation proposed by Mitscherlich (1909), can be used to describe mathematically the law of diminishing productivities. This law postulates that each increment of the limiting factor, in this case the number of plants per unit area, corresponds to decreasing yield increases, yield gain until reaching zero gain. After review different statistical models used in the literature (Lee et al., 2008), the Mitscherlich equation was determined to be the most appropriate. Obtaining a response model can be used to develop a tool to help in the choice of peanut sowing density. The objective of this study was (a) to adjust the Mitscherlich equation of diminishing productivities to the yield response of runner-type peanut cultivars to the density of plants established under different growing conditions in the peanut growing region of Córdoba, Argentina; and (b) to validate this adjustment through experimental tests designed for this purpose.

All the data sets obtained from the literature fit the Mitscherlich model with coefficients of determination (r2) that varied between 0.22 and 0.95 (Fig 1A). In each of these studies the optimum plant density (OPD) varied between 10.5 and 24.8 plants/m², 7.3 to 17.3 plants/m row in 0.7 m rows.

In contrast, when analyzing the overall model (Fig 1B), a good fit of a single equation of the Mitscherlich model was obtained (r2 = 0.65; P < 0.0001). In which, in addition, no differences were detected between the obtained individual location model with respect to a single curve (F test, P > 0.05), so the data adjusted to a single yield response model at density

Thus, the optimum density (OPD), for the set of data analyzed in this study, was determined at 16.8 plants/m², which is equivalent to about 11.7 plants/m row.

The predicted OPD agrees with the technical recommendations for the peanut growing region of Córdoba. Pedelini (2016) proposed target densities of 10 to 12 plants/m row (14.3 to 17.2 plants/m²) and Giayetto et al. (2006) recommend 11 to 13 plants/m row (15.7 to 18.6 plants/m²), both for runner-type peanut cultivars. The high degree of fitness to this asymptotic model of diminishing productivity reveals that there is high intraspecific competition preventing further yield increase (Bell et al., 1987; Tewolde et al., 2002).

In the field experiment, for the 2013/14 growing season, precipitation of 648 mm was recorded between Oct to April (peanut growing season); and in the treatment under irrigation 136 mm were added. However, for the 2014/15 growing season, rainfall was 814 mm for the same period. Temperatures and incident radiation during the crop cycle were similar to the historical average values for the area in both experimental seasons.

For 2013/14, the main differences in yield were due to water availability (P < 0.0001) and density (P = 0.0006), without interaction between these factors (P = 0.9051), thus the irrigation treatments (2013/14 Irr) and rain-fed (2013/14 R) were analyzed separately.

In all the evaluated scenarios, there was a significant decrease in yield with the lowest plant density (5 plants/m²) (P = 0.0477, P = 0.0203 and P = 0.0002 in the 2013/14 Irr, 2013/14 R and 2014 to 2015 seasons, respectively); but no differences were detected among the other evaluated densities (12 to 36 plants/m²) (Fig 2).

The highest pod yields occurred with the densities of 36 plants/m² in 2013/14 irrigate (5062 ± 274 kg/ha); 18 plants/m² in 2013/14 rain-fed (3965 ± 315 kg/ha), and 25 plants/m² in 2014/15 (6201 ± 670 kg/ha). The Mitscherlich model fit the data (r² > 0.83 and P < 0.05) in the three cases evaluated (Fig 3). The OPD (0.95 relative yield) calculated from it was 16.9, 16.9 and 14 plants/m² (11.8, 11.8 and 10 plants/m to 0.7m between rows) for 2013/14 Irr, 2013/14 R and 2014/15, respectively.

These curves do not differ (2013/14 Irr: P = 0.1029, 2013/14 R: P = 0.1042, 2014/15: P = 0.1300) when analyzing the set of information in all the peanut growing area of Córdoba, indicating that it is possible to use this one model for the wide range of environmental conditions analyzed in this work. Contrary to what is stated in the literature (Bell and Wright, 1998; Giayetto et al., 2006), no differences were noted according to the water condition to which the peanut crop was exposed (irrigation and rain-fed). As growth and branch development are mechanisms that allows peanut crop to compensate modifications in its structure (plant density and spatial arrangement), it is expected that water as well as nutritional deficiencies affect the crop response (Bell et al., 1987; Rasekh et al., 2010).

Future studies should evaluate the effect of unfavorable environmental conditions, such as late sowing dates that modify temperature and radiation to which the crop is exposed, or cause water and nutritional deficiencies, which modify growth and branch development on the crop responses to changes in plant density. This approach can be a valuable input, along with other variables to analyze, when choosing peanut sowing density. For this, a spreadsheet was developed based on the results of this work. It includes other variables such as physiological quality, size and price of the seeds, expected yield, and production cost, to estimate the economically optimum plant density (EOPD). This system is available online http://www.produccionvegetalunrc.org as a help tool in the decision-making process by the Argentinian technician or producer (Morla et al., 2017).