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

By Carol Goland, 1993.

Footnotes to Chapter 2

¹ An important distinction between such aptitudes and genetic change is that the former pertain to individuals, while the latter is a population-level concept.

² Some constant aspects of environment require buffering (i.e., perfectly steady subzero temperature) but not through the type of adaptive mechanisms capable of handling variability and risk that are examined here

³ From least to most severe, these responses include: (1) a shift from preferred to secondary foods; (2) implementation of conserving techniques in food preparation; (3) increasing secretiveness in meal preparation and consumption; (4) intensified craft production and trade with regions not as deeply affected; (5) alteration of normal standards of conduct (especially, theft of food from fields and granaries); (6) disaggregation of villages; and (7) abandonment of dependent family members.

⁴ Within communities or across regions, exchange may occur either between individuals or households each of whom specialize in production and trade for what they do not themselves produce. Strictly speaking, this form of exchange is not considered to be a buffering strategy.

⁵ The relationship between diversity and stability is debated by ecologists, who have encountered divergent results in empirical studies and theoretical modeling (Goodman 1975; Holling 1973; Orians 1975). Empirical studies have tended to support the notion that diversity enhances the stability of ecosystems, while mathematical models have produced the opposite result (May 1974; Orians 1975). Holling (1973) has attempted to circumvent some of these problems by introducing the concept of resilience to describe the ability of systems to absorb external perturbations and yet maintain relationships among variables (see also Orians 1975). Anthropologists have been less critical in their acceptance of the relationship between system diversity and stability or resilience (see Segraves 1974; Geertz 1963; Ames 1981; Simenstad et al. 1978).

⁶ Burling (1962) objects to the use of goals such as "utility" and "satisfaction" as concepts too broad to have explanatory value, while conceding the difficulty of specifying particular goals.

⁷ Terminology is not used consistently across authors and disciplines. In the discussions that follow, I have inserted the meanings given here wherever necessary to provide clarity of exposition. That is, risk is reserved for probability of loss, while variance is used as a statistical measure of dispersion. It is assumed that all individuals will attempt to avoid risk, but may show different sensitivities for variance. My paraphrasing of researcher's results may not match the original, given terminological differences.

⁸ An earlier model proposed by Stephens (1981), called the extreme variance rule, examined choice where mean was fixed and only variance was modified, as in the experiments of Caraco and others. The extreme variance rule can be subsumed as a special case of the Z-score model.

⁹ All models discussed here assume a normal distribution of food rewards.

¹⁰ Recent reinterpretations of Knight suggest that this classic distinction attributed to him constitutes a misreading of the original and that Knight, in fact, considered all agents to operate with subjective probabilities. Instead, the argument is made that Knight intended to use risk to signify situations in which insurance markets exist, and uncertainty for situations in which they are absent (LeRoy and Singell 1987).

¹¹ Methodologically, many of these investigations proceed by presenting subjects with a series of hypothetical lotteries or gambles where choices are distinguished by different probabilities of payoffs and frequency of gains and losses (usually one alternative has a certain reward). The payoff structure is then altered (e.g., returns from the certain alternative reduced or increased depending on the initial preference) (Dillon and Scandizzo 1978; Scandizzo and Dillon 1979). These data allow researchers to establish the subject's degree of risk avoidance or preference, given the amount of income reduction accepted (or gain necessary) in order to switch (or be indifferent) between the two alternatives.

Formally, this is specified by the risk premium (the reduction of income accepted in order to reduce the probability of loss) and the certainty equivalent (the amount of return on the risky choice necessary for the decision maker to show indifference between the two choices). The certainty equivalent is simply the expected return on the risky choice minus the individual's risk premium. For risk (variance) avoiders, the certainty equivalent is less than expected value; for risk (variance) preferring individuals, the inequality is reversed (Fleisher 1990; see also Hey 1979).

¹² The bibliography in Roumasset et al. (1979) may be consulted for a comprehensive listing. Young (1979) presents a tabled summary of empirical studies of risk preference among individual farmers, ranging from peasant subsistence farmers to commercial producers. Anderson and Dillon (1977) also contains useful annotated bibliographies.

¹³ Fragmentation has also been used in reference to size, to describe the subdivision of the landholding into successively smaller parcels (Farmer 1960). This is also termed "pulverization" (Clout 1971). Some authors do not separate size and spatial dispersion in their definition of fragmentation. This definition is usually accompanied by an implicit judgement of the economic irrationality of this practice. King (1977:10) identifies fragmentation as "the division of farm property into undersized units too small for rational exploitation."

¹⁴ The same logic could be applied to changing opportunity costs during the life cycle of a farm household. During the early stages of family development, there may be a high consumer to worker ratio, and labor shortages. The value of the time lost in travel to dispersed fields can be significant. As the family matures and the number of available workers increases, this (opportunity) cost of field dispersion may be reduced.

¹⁵ Note that the equation is not defined for N > 2 when R = -1. Mathematically, these values would result in an attempt to take the square root of a negative number, an impossibility. This follows from considering that in the situation where R = -1, N > 3 cannot exist, because it would be analogous to asserting that there are three opposites (measured along only one dimension). The same limitation trickles down to smaller values of negative R. For example when R = -.4, the largest possible value for N is 4. In other words, as N increases, it sets upper limits for negative values of R.

¹⁶ McCloskey's argument is based in part on the absence of alternative insurance measures. This claim has been challenged. Fenoaltea (1976) counters that scattering was a means to maximize productivity by optimizing self-employment, and that other means of buffering existed. In particular, he claims that storage was a more effective risk buffering strategy. Unfortunately, the evidence for storage is rather limited. A large part of his argument is based on the size and capacity of monastic storage buildings. This counterproposal assumes that labor was difficult to hire, an assumption McCloskey (1986) finds little support for. McCloskey (ibid.) also argues that the cost of storage as insurance was many times higher than that for scattering. Reviewing grain prices for the 13th and early 14th century, McCloskey calculates the cost of storage as 32% a year. This is three times higher than the loss calculated for scattering, and does not include physical losses due to rotting and pests.

¹⁷ McCloskey bases his estimate on the increase in rents on land following enclosure.