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

By Carol Goland, 1993.

Chapter 9 - Field Scattering as Risk Management in Cuyo Cuyo

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Based on a small sample of visits to fields during which I timed travel and recorded paths, I estimate that the average walking speed in Cuyo Cuyo is 4 km/hr. Obviously this figure will vary: going upslope and carrying a heavy load, pace will slacken considerably, while on level ground or going downslope travel may quicken. This approximation is within the range of other published figures (see Durnin and Passmore 1967; Thomas 1973). Durnin and Passmore estimate that walking on level ground at 4 km/hr men expend an average of 3.4 kcal/min, while women expend 2.6 kcal/min. The average of these two figures, 3 kcal/min, is the starting point for the estimate derived here. I assume that men and women make comparable numbers of trips to the fields.

Energy expenditure in walking increases with slope gradient. Durnin and Passmore (1967: Table 3.9) report changes in energy costs at gradients of 0, 10% and 20%. From level ground to 10% slope (with no load) energy expenditure increases by 80.6%; from a 10% to 20% slope the increase is less dramatic, 43.1%. Thus, as gradient increases caloric expenditure rises dramatically at first, then at a lesser rate.

In Cuyo Cuyo slopes are steep, up to 45%. But the paths and routes actually traveled are gentler. They follow contours and are selected precisely to reduce slope gradient traversed. In travelling to Awi Awi, Puna Aylleños ascend a short distance over steep slopes within the community (perhaps 10% gradient for 200 meters) to merge with a major path. They then travel the remaining distance of approximately 5 km over a gently undulating path. In similar fashion, Ura Aylleños must ascend as they return from distant fields located downvalley from the community. They follow the road. Once they have traversed the distance from field to road (again, a rather trivial distance relative to the total route traveled), the path home climbs and undulates gently, with few steep segments.

I have chosen 5% as a representative slope gradient for movement between home and field in Cuyo Cuyo. Interpolating between values provided by Durnin and Passmore (1967: Table 3.9), the original value of 3 kcal/min on level ground is augmented by a factor of 40% to produce a new estimate of energetic expenditure of 4.2 kcal/min (for travel at 4 km/hr over a 5% slope, with no load).

The next adjustment reflects load. The load carried to fields varies significantly over the course of the agricultural cycle. Seed and fertilizer must be transported at planting time;⁶ nothing but lightweight tools and perhaps a lunch need be carried for visits to fields for weeding. At harvest time considerable quantities of produce must be transported back home.⁷ Given the high level of variance, I have selected an average figure of a 10 kg load by which to increment energetic costs in travel. This approximation is meant to provide an average value for all trips to fields: in some, actual load will have been greater, in others, less.

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Durnin and Passmore (1967: Table 3.9) indicate that increasing load from 0 to 10 kg results in an increase of energetic expenditure between 6.5% (on level ground) and 20.3% (on slopes of 20% and greater). The average increase for the three gradients they document is 13.7%. Augmenting the previous estimate for Cuyo Cuyo travel (4.2 kcal/min) by this amount results in a new sum of 4.8 kcal/min. Rounding up, I arrive at a final figure for movement between home and fields of 5.0 kcal/min. This estimate is similar to Thomas' (1973) independent figure for energy expenditure in walking in Nuñoa. He calculates that men spend between 3.3 and 4.6 kcal/min walking, 5.0 kcal/min walking to and from fields, and between 4.5 and 6.0 kcal/min transporting materials (dung, seed, harvest) between fields and home (Thomas 1973: Tables 17 and 18).

Because travel between home and fields is measured in distances, the value of 5.0 kcal/min must be converted to a cost per unit distance traveled. Walking at a rate of 4 km/hr, Cuyo Cuyeños travel 67 meters per minute. At 5.0 kcal per minute this amounts to 75 kcal/km.

The final step is to calculate the number of visits made to fields during the course of the agricultural cycle. This information was routinely collected for each field; the number of person-trips was easily totaled. This figure, multiplied by the round-trip distance, provides the total number of kilometers walked to and from each field. Multiplying this by energy cost results in an estimate of the total caloric expenditure spent in travel to scattered fields.

Table 9.12 illustrates these calculations for Family P. For each field, total one-way distance between home and field is presented. The number of person-trips (each way) is multiplied by the one-way distance. In the final column this total distance traveled is multiplied by .075, the energetic cost (kcal/m) of travel.

CALCULATION OF NEW NET YIELDS

Travel to fields reduces net yield by the energy expended. Since 1 kilo of potatoes produces 1000 kcal, travel energy expenditure (kcal) need only be divided by 1000 to calculate its potato (kg) equivalent. Mathematically:

K = [(V x D) x 0.075]/1000

Where K = Kcal equivalent of travel to field, in kg of

potatoes

V = Number of trips made to field

D = Distance to field

The value of 0.075 is the caloric expenditure for each meter traveled.

Table 9.13 shows these data in detail for Family F. This family planted six potato fields in 1986-87. Two were located in the estancia, near to the home; four were located at distances between 7.3 and 8 kilometers from the home. The first column of the table indicates the caloric cost of travel (based on distance and number of person-trips); the second column shows the energetic equivalent in kilos of potatoes. Column 3 indicates the original net yield (gross yield minus seed input); the fourth column shows the net yield adjusted for additional costs of travel. The next two columns indicate the yield per hectare for each field, as originally calculated, and based on the adjustment made for travel. The final column shows the net yield per hectare adjusted for travel as a percentage of the original (unadjusted) yield.

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The original (unadjusted) yield/ha (Y_u) is given by:

Y_u = (T/A) x 10000

and adjusted yield per hectare (Y_a) is given by:

Y_a = [(T-K)/A] x 10000

Where Y_u = Unadjusted yield/ha

Y_a = Adjusted yield/ha

T = Total net production (harvest - seed)

A = Area of Field

K = Kcal equivalent of travel to field (in kg

potatoes of production)

For the two fields located in the estancia (F-17 and F-18), travel costs are minimal, less than a kilo of potatoes. This represents 1% or less of the original net production. For more distant fields the costs of travel are greater. Energy expended in travel amounts to between 9% and 19% of net production. The most distant field (F-16) also happens to be a field with relatively low yield per hectare. Energy expended in travel to this field is equivalent to over 55 kilos of potatoes. The travel-adjusted yield is equivalent to only 81% of the value of the original. For distant fields the costs of travel can rapidly decrement the true value of the yield, especially if that yield was low. The average reduction in net production for individual fields for Family F is 9%.

Table 9.14 summarizes information on adjusted net yields for all fields of each household. This table indicates the number of fields planted by each family, and the maximum and minimum reduction in yield calculated for individual fields. The final column indicates the average reduction for all fields. This number represents an average for the landholding of the family. Below, this figure will be calculated in a different way, based on aggregate yields and travel costs.

Overall, travel costs reduce net yield on individual fields by nearly identical proportions (10.88% in Puna Ayllu, and 10.04% for Ura Ayllu). Strikingly, my observations produce the same figure estimated by McCloskey (10%) to represent the reduction in net yield due to travel for medieval agriculture in the English Midlands. Among individual families, the highest average reduction is experienced by Family S (39%), perhaps not surprising given their disastrously low yields to begin with. Conversely, Family P experiences only a 2% net reduction in yields due to travel costs. The small value for Family P is largely due to their high potato yields during 1986-87, which minimized the impact of travel costs. The yields of individual fields of the majority of families are reduced on the order of 7% to 14%.

REDUCTION IN YIELD DUE TO TRAVEL

Travel to the full set of dispersed fields maintained by a household is the cost of field scattering. The next question concerns travel costs when different numbers of plots are cultivated. This requires some hypothetical calculations like those used to estimate variance given various degrees of consolidation. We now know several important pieces of information: (1) the caloric cost of travel to each individual field; (2) the reduction in net yield this produces for each field; and (3) the yield reduction average by family and community. The next step is to consider how yields would be affected by travel costs if families were to

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consolidate landholdings, and to compare this to the actual effect of aggregate travel costs on the pooled yields of their scattered fields.

Travel Costs to Consolidated Fields

To understand how net yield would change if families cultivated consolidated fields, we begin by imagining that each family had only one plot of land, equal in size to the sum of their actual potato landholdings. The fields of Family A illustrate this. Family A cultivated five potato fields (actually six, but one is excluded from this analysis due to missing data). We want to know what travel costs they would have experienced if all of their potato land had been located in any one of the five spots where they grew potatoes, rather than scattered about.

To compute these hypothetical values, imagine that this field received the same inputs as those of all of Family A's potato fields in the aggregate. The size of this field is equal to the sum of Family A's potato land (1574 sq m); it is located at the average distance of all of their potato fields (2504 m); and is planted with the same amount of potato seed as the total for all (244 kg). We must also determine the number of trips to this field. This is done by: (1) identifying the field visited most during the agricultural season; (2) calculating its area as a percentage of all potato fields; and (3) using this factor to augment the actual number of trips made to it (to account for the larger area of this hypothetical field). This value lies between the total number of trips made to all fields, and the average number of trips made.⁸ For Family A, the number of trips is set at 170.

To calculate the yield that would be experienced on the hypothetical consolidated fields, we examine the production:seed ratio for each of Family A's fields (Table 9.15). On each of the five fields, the ratio of production to seed was between 1.51 and 4.09. This value is used to compute a yield for each of the hypothetical consolidated fields (total seed input x this ratio for each actual field). Seed input, distance, number of trips (thus the potato kilogram equivalent to travel costs), and area remain the same for each field for this calculation. What will vary is the ratio of gross yield to seed, mimicking the conditions of production actually experienced at each plot, holding all other variables constant. From Table 9.15, we see that yield based on net production (harvest minus seed input) ranges from a low of 2342 kg/ha to a high of 6342 kg/ha, with an average value of 4696 kg/ha. When travel costs are subtracted from net yield prior to calculating yield per hectare, the yields range from a low of 2139 kg/ha to a high of 6139 kg/ha, with an average value of 4493 kg/ha. The average reduction in yield due to travel costs is 4.9%. Formally, the unadjusted yield/ha for a consolidated field (Y_cu) is:

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Y_cu = [(r x S s)/S A] x 10000

and the adjusted yield/ha on a consolidated field (Y_ca) is:

Y_ca = [((r x S s)-K)/S A] x 10000

Where Y_ca = Consolidated unadjusted yield/ha

Y_cu = Consolidated adjusted yield/ha

r = Ratio of harvest:seed

S s = Area of Field

K = Kcal equivalent of travel costs (in kg of

potatoes)

S A = Sum of field areas

Summary information for all families is presented in Table 9.16.

Travel Costs to Scattered Fields

The next step is to calculate the reduction in yield due to travel when a family plants scattered fields, as happens in reality. This computation is straightforward. First we need the original net production calculated from all fields combined (i.e., gross production minus total seed inputs). For Family A, total gross production equaled 715 kg. Subtracting seed (244 kg), 471 kg of potato remain (Table 9.17). Dividing by the total area cropped (1574 sq m), we arrive at an aggregate unadjusted yield per hectare for scattered fields (Y_su) of 2992 kg. To visit all of their fields during the agricultural season this family expended a total of 65,259 kcal, or the equivalent of 65.2 kg of potatoes. We decrement net yield by this amount, producing an adjusted net of 405.8 kg. Given the total area planted, this results in an aggregate adjusted yield for scattered fields (Y_sa) of 2578 kg/ha.

Formally, these values are given by:

Y_su = (S T/S A) x 10000

and

Y_sa = [(S T-S K)/sA] x 10000

Where Y_su = Scattered field aggregate, unadjusted yield/ha

Y_sa = Scattered field aggregate, adjusted yield/ha

T = Total net production (harvest - seed)

A = Area of Field

K = Kcal equivalent of travel to field (in kg

potatoes of production)

On a hypothetical consolidated field, travel reduced the yield of Family A by an average of 4.9% (Table 9.16). In contrast, actual travel to their scattered fields reduced yield by 13.9%. Summary information for all families is presented in Table 9.17.

Discussion

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If Cuyo Cuyo households planted but a single consolidated field, the reduction in net yield they experienced as a result of travel costs would be less than 4% on average. In contrast, by planting scattered fields, the increment in travel expenditure increases the loss of yield to 7% on average. (This number, based on aggregate household yields, seed, and travel is slightly less than the 10% calculated above as the average of individual fields.)

For scattered fields, the average reduction in yield in Ura Ayllu is 7.1%; in Puna Ayllu this value is nearly identical (7.6%). In contrast, the reduction in yield on consolidated fields for the two communities differs. In Ura Ayllu this average is 2.7%; in Puna Ayllu it is 5.3%. The average for both communities is 3.9%. The much larger reduction estimated for Puna Ayllu families is clearly dominated by the circumstances of Family S (Table 9.16). This family began with extremely low net yields. Reducing net yield further by travel costs drove it to 0 in two out of five of the fields they planted. If Family S is excluded from the total, the average yield reduction for Puna Ayllu is nearly identical to that for Ura Ayllu, 2.48%. Among individual households, these figures vary widely. Yields for Family A, for example, are reduced by nearly 14% on scattered fields versus less than 5% on a hypothetical consolidated field. Family P, in contrast, loses only 3% of net yield in scattering, and would suffer less than a 0.5% loss in yield if they were to consolidate fields.

For one family, consolidation would actually result in a greater loss of net yield. Family Q experiences an estimated 4% loss of net yield for scattered fields compared to an estimate of 6% under consolidation. The reason for this can be understood by examining the actual distribution of their landholdings during 1986-87. This family planted eight potato fields. Two were located in the estancia, the remainder were located in the Awi Awi Valley. One of the two estancia fields was relatively large (over 0.10 hectare, or 50% of their total potato landholdings), and was the best yielding field among all eight. Had conditions at this best yielding field been experienced on a consolidated plot, the reduction in yield due to travel would have been 2% -- less than that calculated for scattered fields (3.8%). In this case, loss in yield calculated for scattered fields has been artificially dampened by the inclusion of one very large, very near, and very high-yielding field.

There does not appear to be a consistent relationship between the reduction in yield for scattered fields and the number of fields used. Families I and L, with the fewest number of fields (n = 4), are not those with the smallest reduction in yield due to scattering. At the other extreme, the families that actually cultivated the greatest number of fields (Families H, T and G with 14, 12, and 10 fields, respectively) are not among those with the greatest reduction in yield from scattering. Intervening variables--especially quality of harvest and distance--may be more influential. Low yield (quality) explains the extremely high cost of scattering calculated for Family S. By contrast, Family D experiences a reduction in yield from scattering of only 1.38%, despite cultivating seven fields. All of their potato fields are located in close proximity to the home.

SUMMARY: COSTS AND BENEFITS OF FIELD SCATTERING

Table 9.18 provides summary information for reduction in yield and probability of disaster for scattered (actual) and consolidated (hypothetical) fields. The probability of disaster for scattered fields for each family is given for the actual number of fields cultivated by them, while for consolidated fields it is equal to their probability of disaster for an n = 1. Table 9.18 also indicates the number of fields required for the probability of disaster to drop to 0.

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Probability of disaster figures are recalculated from Tables 9.10 and 9.11. They are based on net yields adjusted to reflect travel costs to dispersed fields.

Table 9.18 allows us to contrast the benefits of scattering (risk reduction) with its costs (reduction in net yield due to travel). Table 9.18 makes clear that although all families absorb a reduction in net yield due to scattering, not all are able to avoid disaster by a corresponding rise in minimum production above their critical threshold. These are the families with a 100% probability of disaster under scattering. Three of these families (C, L, and S) would experience disaster regardless of the number of plots planted. The other three (A, B, and J) would have had a better chance of avoiding disaster had they planted in only one field. However, to avoid disaster by planting in a single field, they would have had to know prior to planting which of their separate plots would achieve a yield sufficient to meet their needs (and, of course, been able to expand this land to a sufficient size).

I am unable to describe how, or how sharply, these production deficits were felt by these six families, nor how these households responded. I presume that these shortfalls in subsistence production were met initially by increased reliance on purchased foods. When the PSE data on household economics are analyzed, it will be possible to compare purchases made by these families to those with more adequate subsistence production.

Of the remaining thirteen families, all but one (Family O) would have experienced some probability of disaster on a consolidated field, but all reduced this probability to 0 through cultivation of several fields. Comparison of the actual number of fields cultivated, and the number of fields at which the probability of disaster reached 0 indicates that most planted somewhat more fields than was, strictly speaking, necessary to reduce their risk to 0. For example, Family G planted 10 potato fields that in the aggregate reduced their yield by 6.16% due to travel costs. Given the conditions actually experienced on these fields, only six were needed to reduce their probability of disaster to 0. Had they known in advance of planting the level of yield to be experienced on each, they could have planted only these six fields, and minimized their costs of travel. However, both the lack of prescience, and the inability to expand the area of a plot, make this impossible in the real world situation. The mean degree of over-scattering is actually quite small. Among these thirteen families, the average number of fields in "excess" of reducing the probability of disaster to 0 is 2.5. (compare columns 2 [actual number of fields] and 6 [number of fields when probability of disaster equals 0] in Table 9.18).

In all but one instance, each of the thirteen families could have increased net yield by planting in a single consolidated field rather than in scattered fields. However, in doing so, they would have dramatically increased the probability of disaster. Table 9.18 empirically demonstrates the logic of the safety-first model: lower average yields are accepted in order to avoid risk. For most families, the ability to avoid disaster by planting many fields offsets the rather small increments in travel costs as the number of fields increases.

With data collected over longer time periods, it would be possible to specify an optimum number of fields to plant in Cuyo Cuyo. This optimum would be the point at which subsistence needs can be assured, with the minimum loss of net yield due to travel costs to scattered fields. However, given the relatively small reductions in net yield observed here, it would appear that Cuyo Cuyo farmers can adopt a conservative posture, and slightly over-scatter (relative to a specified optimum) with little penalty.

But this year, by all accounts, was not typical; it produced a potato crop better than that usually obtained. Patterns of landholdings evolve over the course of a family cycle. They are guided by both the direct experience of household members, and received wisdom in the form of tradition. The landholdings of a family at any given time are also structured by access

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to land through inheritance and/or access to capital and opportunity to purchase it. To whatever degree families seek to maintain a distribution of land that is sufficient for mediating risk, ultimately, their ability to do so must be judged over longer periods of time. In 1986-87, most families planted a greater number of fields than was needed to reduce the probability of disaster to 0.

Loss in net yield from travel is minimized when yield is high. For instance, the failure of several fields planted by Family S increased the impact of travel costs above that experienced by any other household. By extension, the same could be expected for other households during less successful years of potato production in Cuyo Cuyo. Returning to Cuyo Cuyo in such a year, we might find the reduction in net yields to be greater and the probability of disaster increased. This also may help to explain in part the small degree of over-scattering observed in 1986-87 with respect to a risk minimization goal.

The best strategy open to Cuyo Cuyo farmers is to plant scattered fields. Dispersed plots reduce the probability of disaster because production among them is not strongly positively correlated. Although production on consolidated fields would minimize loss of net yield by minimizing travel costs, families would be exposed to intolerably high levels of risk. If the first goal in production is to avoid disaster, Cuyo Cuyo farmers achieve their aim admirably by cultivating a diverse set of agricultural plots. As well, to whatever degree the yield from fields can be increased by inputs of production factors under the control of households (fertilizers, labor, etc.) families should work their fields intensively. This has two important effects: first, it further reduces the probability of disaster by achieving high yields; second, it reduces the impact of travel on net yield