Cultivating Diversity: Field Scattering as Agricultural Risk Management in Cuyo Cuyo, Department of Puno, Peru

By Carol Goland, 1993.

Chapter 8 - Agricultural Yield and Variability

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The multivariate regression models for potato yields provide better results than the univariate models. The model presented here is the result of a series of modeling procedures. My goal was to locate the model which could explain the highest proportion of variance in potato yields (adjusted R² value) without unacceptable levels of collinearity (tolerance values greater than 0.80). The potato yield data was analyzed in the aggregate, with the following cases excluded: (1) polycropped fields (n=2); (2) fields with seed densities judged to be erroneous (n=29; less than 500 kg/ha or greater than 5500 kg/ha); and (3) fields which failed completely (n=9). Because the final model selected the labor variable, only fields from the second year of the study were included.

Polycropped fields were excluded in potato yield regressions (as well as for the other crops analyzed) for the following reason: since labor and fertilizer data were reported for the total field, it was impossible to determine how much of each of these inputs was allocated to the individual crops. Although it might have been possible to assume an allocation based on seed ratios (and thus, the assumed proportion of the field occupied by each crop), I elected to use the more conservative approach of analyzing only monocrops. For potatoes, only two fields were polycropped.

Fields which failed completely were excluded from the analysis of potato yields only after comparing the results of each modeling procedure with and without them. The model differed little whether these fields were included or not. Based on families' comments, it is clear that potato fields fail for a variety of reasons: an extreme attack of late blight, damage caused by animals, and destruction of fields by landslides are among the problems cited. In total, nine potato fields failed completely, six in the first year of the study, and three in the second.

Several regression methods were used, among them forced inclusion of all variables and stepwise regression, both forward and backward. The final models resulting from the stepwise procedures were quite consistent in adjusted R² values, variables selected for inclusion, and partial coefficients of the variables. The best model is shown in Table 8.15 (See also Figure 8.2). The selected variables explain 29.5% of the variance in potato yields. The amount of preparation and weeding labor, quantity of fertilizer inputs, and nearness are statistically significant predictors of potato yields. Every additional day of labor increased per hectare yield by 6.8 kg/ha, while each unit increase in the NPK index increased yield by over 5.5 kg/ha. Estancia fields produced 2062 kg/ha more than fields located farther from the communities. Compared to labor and fertilizer, the impact of nearness is weaker, with a standardized regression coefficient only about half (0.19) that of the other variables.

Because this model selected the labor variable, hence data only for the second year of the study, the sample is stratified by year. I attempted to find the best model for fields from the first year of the study, in the absence of data on labor. Examination of residual plots indicated that the model was mis-specified (the residuals exhibited high degrees of non-normality). No adjustment of independent variables improved this situation. It seems reasonable to assume that the mis-specification results precisely from the absence of labor data. This observation underscores the importance of the field preparation and weeding variables for understanding variance in potato yields.

In summary, the independent variables which together account for the greatest amount of the variance in potato yields are labor inputs (preparation and weeding), fertilizer inputs (measured with the NPK index), and nearness (of home and field). The importance of proper seed bed preparation for potatoes is well known (Beukema and van der Zaag 1979; Cortbaoui 1981). The goal of preparation is to provide a seed bed without compacted soil layers and

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clods, so that there will be (1) sufficient oxygen for the developing plant, and (2) appropriate soil moisture. The potato is sensitive to both insufficient and excessive water (Haverkort 1982). Because the root system of potatoes is weak, hard soil layers inhibit rooting, make the crop more vulnerable to drought stress, and ultimately reduce yields. In regions with abundant rainfall (such as Cuyo Cuyo, especially during the two study years) drought may not be a frequent stress, but inadequate soil preparation can also cause problems after heavy rainfalls. In this case the danger is that compaction causes the soil to remain saturated for too long a period following a heavy downpour, so that the roots begin to die and tubers rot. The most important aspect of proper seed bed preparation is probably its effect on soil moisture properties during the pre-emergence stage of potato growth. Preparation also affects soil temperature; together with planting depth, temperature is an important determinant of success and rate of emergence (Hay and Walker 1989).

Ridging during the growing season allows potatoes to be planted at fairly shallow depths. Nearer the surface, soil temperatures are higher. This promotes more rapid emergence. But if tubers are planted too close to the surface they become susceptible to direct light (which will turn them green), insect damage, very high temperatures (leading to secondary growths and tuber deformation), and soil drying. In an environment such as Cuyo Cuyo, the best strategy is to plant shallow to promote rapid emergence, and then following emergence, to build up the ridges around the tubers. Ridge building is concomitant with weeding.

In my analysis of potato yields, fertilizer inputs were found to be equally as important as labor inputs. Sufficient nitrogen is critical for vegetative growth, phosphorus is essential for root growth and seed formation, and potassium is needed for starch formation in the tubers (Vander Zaag 1981). In Chapter 7, I suggested that the limiting nutrient to potato production in Cuyo Cuyo is likely to be phosphorus, due especially to the low pH values for soils there. I offered a tentative hypothesis that fertilization regimes are geared toward providing an adequate supply of this nutrient. Because compound fertilizers (both commercial and locally produced) are used almost exclusively in Cuyo Cuyo, nitrogen and potassium additives are automatically increased along with phosphorus. In fact, nitrogen levels may actually be excessive in Cuyo Cuyo, especially in Puna Ayllu where average nitrogen inputs are greater than 400 kg/ha. High nitrogen levels delay crop maturation. If harvested before mature, dry matter content will be reduced (Beukema and van der Zaag 1979). This potential detriment to crop growth may be offset by the advantage of increased phosphorus. Potato yields are highly responsive to additional phosphorus, and for phosphorus-fixing soils (presumably, the soils of Cuyo Cuyo) applications higher than 100 kg/ha are recommended (ibid).

The association between nearness (estancia), and high labor and fertilizer inputs is interesting, but it is difficult if not impossible to identify causality. On the one hand, the estancia fields may receive higher inputs precisely because they are near, and thus travel and transport costs are reduced. If this is true, then distance is the primary factor determining yields. On the other hand, it could also be the case that estancia fields produce the greatest and most secure yields--not because of high inputs but because of intrinsic qualities of microclimate and edaphic conditions--and so are given preferential treatment because such inputs represent a more certain return on time and materials.

Analysis of Variance in Oca Yields

Table 8.16 presents descriptive statistics for the variables examined in the analysis of oca yields. Table 8.17 presents the correlation coefficients for each of the independent variables with yield. Correlations for each of the individual sample years as well as those for

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the aggregate sample are shown. Between years, the independent variables which are significantly correlated with yield are different. In 1985-86, the only variable which is significantly correlated with yield is rotation year. Fields planted in oca in the third year of the rotation (i.e., the Cuti Oca Manda in the estancia) produced significantly less than fields planted in the second year of rotation (either in the estancia or in Awi Awi). The correlations are quite distinct in the following year. Among the continuous independent variables, there is a significant positive correlation between seed density and yield, and a significant negative correlation between altitude and yield. Among the control variables, there is a significant positive correlation between Ura Ayllu fields and yield, and estancia fields and yield, and a significant negative correlation between Awi Awi location and yield. There is some redundancy in these correlations. The negative correlation between altitude and yield, and Awi Awi and yield (and the positive correlation between estancia and yield), largely indicate the same thing: the higher altitude Awi Awi fields produced, on average, less than the estancia fields. The correlation between date of planting and yield should be interpreted carefully: it may be mediated by location (Awi Awi), and thus elevation, factors. Awi Awi fields are planted later and produce less than the estancia fields.

MULTIPLE REGRESSIONS OF OCA YIELDS

Compared to the results for potatoes, the analyses of oca yields are considerably less straightforward. The complicating factor, from an analytical standpoint, is the large number of failed and marginally productive fields. When all fields are included in the regression model, the model performs exceptionally poorly. This is to be expected, given the subjective evaluations by Cuyo Cuyo farmers of the poor oca harvest during both years of the study, owing to disease. While generally widespread, disease was not uniform; a few fields escaped its ravages. Thus, stochastic factors outside the control of farmers reduced yields considerably.

As long as failed fields are included in the analysis, it is impossible to identify a model that can predict oca yields. This in itself is important, since it underscores the fact that fields fail for reasons outside the control of farmers. On the other hand, it is not informative if we are concerned with understanding the systematic factors which do account for variance in yields. To facilitate that goal, I limit the following analysis to those fields that did not fail.

The results of the best model for oca yields are presented in Table 8.18 (see also Figure 8.3). The oca yields were analyzed in the aggregate (communities and years), with the following exclusions: (1) polycropped fields (n=29); (2) fields with seed densities judged to be erroneous (n=12; less than 500 kg/ha or greater than 5500 kg/ha); and (3) fields which failed completely (n=14). Examination of residual plots from the initial analysis indicated moderate heteroscedasticity (unequal variance in the error term). To remedy this, several transformations of dependent and independent variables were attempted, as was a weighted least squares regression model (Berry and Feldman 1985; Lewis-Beck 1980; Neter et al. 1985). The best model used a weighted least squares procedure, with the reciprocal of seed/ha as the weight.

The selected variables account for 18% of the variance. Seed/ha and date of planting are statistically significant predictors of oca yield. Each additional unit of seed increased yield by 2.5 kg/ha, while each additional day of delay in planting reduced yield by almost 111 kg/ha.

As noted above, the correlation among Awi Awi fields, altitude, and planting date suggests that the significance of the independent variable for planting date should be interpreted with caution. It is interesting that seed density shows a strong linear relation with

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oca yields (unlike the case for potatoes, where it is curvilinear). In my discussion of potato yields, I suggested that the apparent over-seeding might be an adjustment to the potential worst-case scenario. If the minimum goal is to recuperate seed investment and maintain seed stores, then high seed densities could be a strategy to ensure this. The case of oca fields presents a contrast: the relationship between seed/ha and yield rise monotonically throughout the range of seeding density. There is no point at which yield begins to drop off. This relationship is precisely what we might expect when seed density is high and production poor. If production had been good, by my hypothesis a curvilinear relationship might have been evident. Competition between plants may not be a serious detriment to yield when the crop becomes naturally thinned due to factors such as low emergence rates and disease. This generally supports the comments made with respect to potato yields and seeding density.

Analysis of Variance in Habas Yields

Table 8.19 presents descriptive statistics for the variables used in the analysis of habas yields. Table 8.20 presents the correlation coefficients for each of the independent variables with yield. Correlations for each of the individual sample years as well as those for the aggregate sample are shown. The correlations for the individual sample years are quite different. For the 1985-86 data, altitude and the control variables for failure and community are significant, while in the following year seed/ha, weeding, NPK input, and control variables for use of fertilizer and failure are significant. In neither year are date of planting or rotation year significantly correlated with yield, and in the aggregate sample, calendar year is not significantly correlated with yield.

These figures require some cautious interpretation, given problems in the data described previously. Harvest data for Ura Ayllu's 1985-86 habas crop is missing in most cases. Comparison across years may be confounded by the proportional over-representation of Puna Ayllu in the sample from the first study year. For example, the significant correlation of altitude and yield in 1985-86, but not in the following year, may indicate actual changes in the condition of crop growth between the two years. The much more likely explanation, however, is the paucity of data points for Ura Ayllu habas yields in 1985-86. Failed fields are over-represented, so that the mean net production (n=5) was actually negative. Thus, since Puna Ayllu's fields are higher in elevation, this statistic says no more than that Puna Ayllu's production was greater than the meager and unrepresentative result for Ura Ayllu for that year. Within Puna Ayllu alone, the correlation between yield and altitude is not significant.

MULTIPLE REGRESSIONS OF HABAS YIELDS

The results of the best model for habas yields are presented in Table 8.21 (see also Figure 8.4). The habas yields were analyzed excluding the following cases: (1) polycropped fields (n=11); (2) fields with seed densities judged to be erroneous (n=17; less than 100 kg/ha or more than 1500 kg/ha); and (3) failed fields (n=19). The analysis was run with failed fields included and then excluded; the model performed poorly in the former case, an indication that the reasons fields fail completely cannot be specified by the independent variables included in the model.

The selected variables account for 26.4% of the variance in habas yields. Seed/ha, and the use of fertilizer (scored as present or absent) are statistically important predictors of habas yields. Each additional unit of seed/ha increased yield by nearly 2 kg/ha, while the use of fertilizer increased yields by 1038 kg/ha. This value represents the increment difference accruing to those fields which were fertilized, versus the excluded (non-fertilized) cases.

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Consideration of the importance of seed density in this crop is important, especially given my interpretation of potatoes and oca. Like potatoes, the habas crop was said to have performed exceptionally well, especially in the second year of the study. But unlike potatoes, yield appears to increase linearly with greater seed density. There are several possible explanations for this. First, habas may not respond to over-seeding in the same way that I suggested for potatoes and ocas. In these data, the average seed/ha is 347 kg (with range 102 - 1415 kg/ha). The average seeding rate for commercially grown Vicia faba is in the range of 175 - 325 kg/ha (Walton 1988: Table 8-1). Seed density for habas in Cuyo Cuyo does appear to be on the high end of the range. Second, and key, is that competition between individual plants of habas is not as great as that for tubers. Broad beans (habas) have been shown to respond favorably to increased plant population (Ishag 1973; Sinha 1977). The primary reason for this is the morphology of the plant itself. Relative to other food legumes (and the tuber crops) branching of habas is limited. The plant is erect and carries its pods directly on the main axis. In other food legumes, when plant densities are increased, the number of branches is reduced. Thus, in crops such as pigeon peas and chickpeas, since it is the late order branches which bear pods, the net effect of this crowding is a reduction in yield. In contrast, since habas carry their pods on main shoot and primary axis, population pressure does not affect pod development (Sinha 1977: 22-23). This may explain the linear relationship between seed and yield in the Cuyo Cuyo habas data.

For food legumes in general, experimental studies indicate that yield responds to inputs of phosphorus. The response to nitrogen applications is less clear. In some legumes, nitrogen fertilizer appears to depress nodulation and nitrogen fixation (Sprent and Minchin 1983). Moreover, the time of application seems to have an effect: in soybeans, post-flowering application of nitrogen increased yields, while peas are responsive to nitrogen added at the time of planting. But even within the same legume species, varietal differences in response to nitrogen have been noted. Broad beans do not respond to nitrogen fertilization at planting (Sprent and Minchin 1983), although under experimental conditions the highest yields for broad beans have been obtained only when nitrogen has been applied in substantial quantities (presumably in the post-flowering stage) (Sinha 1977). Little work has been done in the Andes on the agronomy and response of broad beans (an introduced crop). Instead, most experimental and crop improvement work has been focused on cultivars native to the region.

A number of habas fields failed completely. Among fields that produced something, but had a net yield of zero or less, the reasons cited for reduced yield tended to be disease or, less commonly, other factors. One family explained their diminished yields by suggesting that they had done the aporque on a bad day. In contrast, factors cited when gross yield was zero were more catastrophic: theft, damage from animals, burial by a landslide from road construction, etc.

In summary, the model which accounts for the highest proportion of variance in habas production includes seed inputs and the use of fertilizer (scored as present or absent). Unlike potatoes, habas do not seem to respond to labor or incremental changes in fertilizers. Like oca, habas yields also seem to respond linearly to increased seed inputs.

CONCLUSION: SOURCES OF VARIANCE IN CROP YIELDS

McCollum and Valverde (1968) analyzed the effect of fertilizer treatment on potato yields in the Peruvian highlands, incorporating data from four years (1961-1964) and five regions. They present several regression models. When the regression equation is computed for aggregate locations and years, they find that 33% of the variation in yields are accounted for by fertilizer treatment. When location and year are incorporated into the model, the

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proportion of explained variance increases to 47%. Based on the assumption that differences between locations and years reflect climatic differences, they examine three of the five regions alone. They find that for these more circumscribed areas, the proportion of explained variance ranges from 46% to 76%. They conclude that much of the variation in yield can be ascribed to year and location effects. "Microclimate is a factor of considerable importance throughout the sierra, and the wide variation in yields among locations suggests a marked climatic effect" (McCollum and Valverde 1968:11; see also Ryan and Perrin 1973).

The data on which McCollum and Valverde's results were based were produced in highly controlled contexts, with respect to labor, pest control, water management, etc.. It is therefore expected that the proportion of explained variance is greater in their model than in the models derived using the data from the fields of Cuyo Cuyo farmers. Despite this difference, for both the experimental data reported by McCollum and Valverde and the regression analyses of yields in Cuyo Cuyo, the same conclusion is apparent: large proportions of unexplained variance appear to be the result of marked and unpredictable effects of microecological variation (climatic and/or edaphic conditions, disease, etc.). Although the experimental data are available only for potatoes, I expect that the effect of microecological variation is equally great for other crops.

The analyses of Cuyo Cuyo yields suggest several important points. First, for each of the three crops examined, a portion of the variance in yield can be accounted for by production factors (seed density, labor, fertilizer inputs) and inherent qualities of the plot (i.e., distance, altitude, etc.). Second, the factors which best explain variance for each crop differ. For potatoes, the best model includes labor, fertilizer inputs, and distance from the community. For oca, the best model incorporates seed density and date of planting. For habas, the best model includes whether or not fertilizer was used and seeding density.

Despite the modest and revealing success of the regression models, much of the variance in yields cannot be accounted for by those factors incorporated into the regression models. These include seed density, labor and fertilizer inputs, altitude, date of planting, and community affiliation. What the models fail to account for is important. The variables not available for the model are the same factors that are beyond the control of Cuyo Cuyo farmers: patchy distributions of rainfall, uneven soil qualities, unpredictable pest infestations, diseases, theft, and insufficient labor to complete agricultural tasks at the optimal time. Intuitively, these are the factors that suggest the value of planting in several fields dispersed over the landscape. If Cuyo Cuyeños were to plant each crop in but a single locus, the probability of failure--either complete or partial, but devastating nonetheless--would be substantially greater than it is with dispersed plantings. In the following chapter, I explore this argument in greater detail.