Posts Tagged ‘high-level theory’

A Very Preliminary Interpretation of Mound Size Variability

May 11, 2013

Monumental architecture, by virtue of its scale, implies something about the organizational capabilities of the groups that produced it. The previous analysis of burial mound size further implies something about the variation in those capabilities. I explore some of those implications at greater length here.

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The following thoughts should be considered preliminary. The original goal of this particular analysis was very modest, concerned with establishing a reliable measure of monument scale or prominence. My hope was that mound volume had stayed reasonably constant despite the effects of weathering and other processes. The analysis was being done as part of a project regarding monument function and social organization. While the analysis showed that many mounds lost volume as a result of modern plowing, it also showed that the volume of plowed mounds and whole mounds varied in very similar fashion. Variation in mound volume can be modeled with the exponential distribution. I did not expect this result at the outset.

I have often regarded mounds as potentially reflecting the “strength” of the groups that built them. Group strength might be a function of many different factors, such as group size, the productivity of the territory that the group occupies, the group’s organizational capabilities and the size of the social network upon which the group could call. Groups that scored higher on these variables should have been capable of building larger mounds. Groups that scored lower on these variables should have been limited to building smaller mounds. A large list of qualities could thus contribute to group strength and to burial mound size. I assumed that each factor would have a small additive effect on strength. Consequently, I supposed that variation in group strength and mound size should take the form of a normal distribution.

Clearly, this intuition was wrong. Upon further reflection, I think that I’ve underestimated the contribution of social networks. Their contribution is probably not minor. Ethnographic studies of leadership in small-scale societies illustrate the hard work and emphasis that group leaders often put on the maintenance of their networks. The effect of each additional ally is probably not merely additive, since each ally that gets incorporated has the potential to contribute their own unique allies to the network. Modern studies of social networks indicate that variability among individuals in network size has a heavy-tailed distribution, where most individuals have a relatively small network and a few individuals have very large networks. The mound data is suggestive of similar processes at play.

Before getting too carried away, let me emphasize again that this interpretation is very preliminary. It is, nevertheless, consistent with other archeological evidence for the operation of long-distance exchange networks at the time. The results also illustrate the potential value of this form of statistical modeling. The type of probability model which can be fit to the data — whether normal, exponential, or some other model — reflect the type of processes which operated in the past. The modeling thus constrains the set of possible interpretations that should be considered.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2013.

Identifying and Explaining Intensification in Prehistoric Fishing Practices XII: Specific Hypotheses to Explain Variation in Net-Use

November 28, 2009

The previous post in this series presented some high-level theory that might account for variation in fishing intensification and, thus, net use. This theory will now be tailored for my study area to generate some specific expectations. As noted elsewhere, I will not be dwelling on the details of the site and study area except as necessary to explain how I arrived at particular predictions.

The archeological assemblages that I have been analyzing derive from a single shell midden site. The analyzed deposit ranges from 15 to 55 centimeters below the ground surface. The site was excavated in five-centimeter arbitrary levels. I have treated each arbitrary level as a distinct analytic unit, which seems reasonable as spatial analysis of radiocarbon dates and other chronologically-diagnostic artifacts show very little vertical mixing or movement of artifacts. Poor environmental conditions appear to have occurred during the time period in which three levels–located between 35 and 50 centimeters below the ground surface–were deposited.

The period is characterized by widespread drought. These conditions disrupted settlement at many other sites. My site is one of the few sites in the region to have been continuously occupied during the period. The site lies near the mouth of a creek, an important source of fresh water.

Marine productivity may also have declined during the period of poor environmental conditions. Paleoenvironmental data regarding ocean conditions are complex and not entirely consistent. Proxy data derived directly from archaeological sites within the region, however, shows that sea surface temperatures during the period of drought were unusually high. These conditions may have affected the distribution and abundance of fish.

A variety of social and economic responses to the challenges of the period of poor environmental conditions have been documented. Economic specialization in artifact production emerged at my site and across the region. Local manufacturers produced trade goods. In exchange for these goods, these specialists presumably received food and other items that could not be produced locally as easily. Fishers at my site may have responded by changing their fishing strategies. The number of fish caught by the site’s inhabitants seems to peak during the interval of poor environmental conditions before declining.

This observation is consistent with other faunal analyses of the site’s deposits, but it could be attributable to a number of different factors. The peak in density of fish remains could be due to an increase in population at the site during the period of poor environmental conditions. The site may have served as a refuge for groups from elsewhere in this period, since fresh water was more readily available at the site. The increase in the density of fish remains could reflect a more widespread emphasis on fishing by the site’s inhabitants as other foods normally taken by them became less abundant. It could be attributable to increased economic specialization. Fish may have subsidized on-site specialized artifact production. Workers at the site may have specialized in both artifact production and fish procurement, as the local inhabitants had comparative advantages in these activities and exchanged their wares and fish for other goods. The greater density of fish could also be due to some quirk of cultural transmission, as fishers made choices about the appropriate gear to use and effort to undertake based on the work being done by their neighbors. A more detailed examination of the data will allow these possibilities to be distinguished.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2009.

Identifying and Explaining Intensification in Prehistoric Fishing Practices XI: High-level Theories for the Explanation of Variation in Net Use

November 1, 2009

The ten previous posts in this series developed the middle-level theory needed to quantify the intensification of fishing. This theory linked archaeological data to interpretations of past human behavior. Fishing effort intensifies as fishers rely more extensively on nets to catch fish. Net use can be identified and distinguished from the use of other gear as a distinctive mode within a size-frequency distribution of fish bone size. To explain variation in fishing practices, high-level theory must be developed. For this theory, I turn to some formal economic models.

Formal economic theory provides expectations for the relationships among fish size, net use, and environmental conditions. Many different kinds of formal economic theory exist, and some of this diversity will be explored in the following paragraphs. I begin with a discussion of a technological intensification model. This model is both simple and directly relevant for understanding the decisions made by fishers faced with a choice of gear to use.

Recall that nets are more expensive to produce compared to other types of fishing gear. These fixed costs affect the circumstances under which different gear was employed. This insight can be formalized in a model for technological intensification, following Bettinger et al. (2006: 541). Let:

mi = the hours required to manufacture a particular gear type, i, such as nets or spears;

fi(mi) = the return for using the ith gear type (in kcal or some other currency) as a function of gear manufacturing time; and

p = the hours spent procuring fish.

Assume that nets are more expensive to produce than another type of gear (i.e., mnets > mother) and that nets provide a greater return [fnets(mnets)> fother(mother)]. Nets would never be adopted if they were both more expensive and had a lower return rate. Under these assumptions, fishers will adopt nets when:

\frac{f_{nets}(m_{nets})}{m_{nets}+p} > \frac{f_{other}(m_{other})}{m_{other}+p}

The foregoing equation can be used to derive the length of time that fishers would have to be engaged in procurement for nets to produce better returns than another gear type. This threshold is given by the following equation:

p=\frac {[f_{other}(m_{other}) \cdot m_{nets}]-[f_{nets}(m_{nets}) \cdot m_{other}]}{f_{nets}(m_{nets})-f_{other}(m_{other})}

Some useful insights can be derived from the model. Because nets are expensive to make or acquire, they have to be used extensively in order for the benefits to outweigh the costs. Fishers should prefer to use nets once some threshold level of fishing effort has been reached. The model can not, however, explain why fishers might choose to fish extensively. Declining environmental conditions would seem a plausible reason to redouble fishing efforts. Despite the plausibility of this intuition, any drop in environmental productivity that affects the return rates of different gear types to the same extent does not alter the threshold value of fishing effort. Any constant that changes the value of return rates equally can be divided out of the model. The model was not intended to evaluate the effects of such factors on investment in technology.

The model also assumes that the costs of finding, chasing, and processing fish are constant across gear types (Bettinger et al. 2006: 541), so it does not explicitly include them. Like return rates, the values of these variables are likely to be affected by environmental changes. The technological investment model can be revised slightly to show the effect of search and pursuit costs.

The revision will allow variability in the abundance of fish to be evaluated. To extend the model, let:

o = the hours spent searching and pursuing prey.

Note that in this revision, like in the original technological intensification model, the hours spent searching and pursuing do not vary among technologies.

With this addition to the original model, the condition under which fishers would adopt nets is:

\frac{f_{nets}(m_{nets})}{m_{nets}+p+o} > \frac{f_{other}(m_{other})}{m_{other}+p+o}

The threshold number of hours spent in procurement at which the return rate of nets is the same as another gear type is thus given by:

p=\frac {[f_{other}(m_{other}) \cdot (m_{nets}+o)]-[f_{nets}(m_{nets}) \cdot (m_{other}+o)]}{f_{nets}(m_{nets})-f_{other}(m_{other})}

The revised model does not have qualitatively different implications for the adoption of different gear types. The revised model does show that an increase in the hours spent searching for fish would reduce the time at which nets would be preferred relative to another gear type, given the assumption that nets have a higher return rate. An environmental change that altered the abundance of fish, increasing search times, could lead to greater use of nets.

Poor conditions may have other observable effects on archeological fish assemblages. Fish size may be sensitive to climate and to predation. The prey choice model speaks to the relationship between fish size and fishing practices. This model may therefore provide a better context for understanding net use.

Prey choice models show that foragers who seek to optimize their returns should preferentially take certain kinds of prey. All other things being equal, fishers using hook-and-line or spears should focus their efforts on prey that is large, readily caught, and easily processed. Such prey provides a greater return for the effort expended. Archaeological applications of prey choice models typically assume that larger prey is preferred to smaller prey. In these applications, the cost of handling and processing larger prey is presumed to not be commensurately bigger as well. When large prey is abundant, fishers will forgo opportunities to catch other types of fish. Fishers will become less selective, however, as the density of preferred prey decreases.

Thus, fishers should target large fish, unless such fish become scarce due to overexploitation, reduction in favorable habitat, poor marine productivity, or other circumstances. Fishers will still take large fish whenever they are available, even as those fish become less abundant. They should just be more willing to take smaller fish in the face of scarcity. Mean caudal vertebra height among fish caught by hook or by spear may thus serve as an index of environmental conditions. Fish size should also be correlated with other environmental indices.

The discussion of the prey choice and technological intensification models can now be integrated to provide additional predictions. Net use provides better returns than other gear only if fishing effort exceeds a threshold number of hours, in order to offset the high costs of making those nets. The threshold number of hours is the same for all fishers, so these fishers should respond identically when faced with changes in search costs or gear production costs. Shifts in environmental conditions that decrease fish abundance and increase search costs will lower the threshold number of hours for all fishers. The frequency of net use may only change (but change rapidly) once environmental perturbations have altered this threshold value sufficiently. Using mean fish size among hook- and spear-caught fish as an index of environmental conditions, net use may only change once mean fish size has reached certain levels. Net use may predominate when mean fish size reaches a particularly low value, and it may be rare when mean fish size attains a particularly high value.

In practice, however, individuals may vary in return rates and in their opportunity costs to using various types of gear. Children, for example, may be better suited for simple hook-and-line fishing than for the production and use of large nets. This variability may engender a more gradual response among fishers to changing conditions. Some fishers may be quite sensitive to environmental changes and quickly switch to nets, while other individuals may not be so sensitive. Mean fish size among hook- and spear-caught fish, again serving as an index of environmental conditions, may therefore be negatively correlated with net use, provided that the assumptions of these models hold true.

The technological intensification and prey choice models employ a number of assumptions. The models assume, for example, that individuals possess perfect information about their environment and the return rates to fishing with various gear types. The models also assume that the relevant currency is the nutrients that the prey would provide upon consumption. To the extent that these models fail to fit particular real-world cases, other models that use different assumptions should be explored.

Suppose, for example, that fish are valuable to fishers as a good to be exchanged for other products. The value of fish would thus be a function of both their return rate and the demand for fish among consumers. To the extent that fishers have a comparative advantage in fish procurement and demand for fish is relatively strong, net fishing may be worthwhile even if it is costly. The high cost of fish procurement would be offset by the goods received in exchange under these circumstances.

Specialized fishing need not have developed for fishing to be affected by the emergence of exchange systems. Fishing and the specialized production of other goods could be alternative strategies for the acquisition of desirable products. Under this scenario, fishing poses an opportunity cost to other specialized production. Fishers may therefore be less inclined to spend large amounts of time fishing if they can more easily satisfy their needs through the production and exchange of other goods. While the microeconomic theory underlying both of these proposals is well-established, archeological evidence for the operation of such processes may be less obvious.

If fishing develops into a specialized activity, the total amount of fish caught ought to be positively correlated with other evidence for the volume of exchange. Net use may increase dramatically once some threshold volume of exchange has been reached, as the number of hours spent fishing increases to the point at which net use becomes viable. Alternatively, net use may increase more gradually as exchange grows in importance due to variability among fishers regarding the threshold value at which they would adopt nets.

If fishing is a lesser alternative to the specialized production of other goods, net use may be negatively correlated with evidence for the volume of exchange. Net use may then drop precipitously once a threshold volume of exchange has been attained. Of course, net use may decline more gradually due to the same variability among fishers regarding the threshold level of effort that has been discussed previously.

Like the technological intensification and prey choice models, these microeconomic models of net use assume that fishers have perfect information about return rates, environmental conditions, and demand for fish. Assumptions of this sort may be appropriate as an approximation for simple adaptive problems. Information may, however, be very difficult to gather or evaluate. Return rates for the use of different gear types and search costs may be difficult to estimate, for example. Experimental studies, ethnographic evidence, and theoretical considerations suggest that individuals acquire relatively few norms through their own trial-and-error.

Models of cultural transmission allow the effects of imperfect information to be incorporated. Individuals acquire much of their norms through a mechanism of cultural transmission that includes some type of imitation. Most fishers may prefer to take their cues about the type of gear to employ from someone else, like a particularly successful fisher. Transmission rules of this sort can lead to the spread of adaptive norms.

The utility of explicit models of cultural transmission often lies in their ability to account for cases where culture change appears maladaptive or unrelated to adaptation. Simpler economic models may provide an adequate account of shifts in adaptive norms when such changes have obvious adaptive consequences, as may be the case with many changes in subsistence. Models like the prey choice and technological intensification models usefully draw connections between key variables such as diet breadth and environmental conditions. They do not address the processes by which norms regarding subsistence behavior change. The details of these processes can be significant for understanding changes with less obvious adaptive consequences.

Cultural transmission models may therefore provide insight to cases where change in subsistence does not conform to the predictions of the prey choice or technological intensification models. In many cultural transmission models, random factors like sampling effects and imperfect copying work alongside more focused imitation processes to elevate (or decrease) the popularity of particular cultural traits. Individuals, for example, may select a subset of the available population before choosing the “best” model or set of models to copy. These random factors work most powerfully among small groups. Sampling effects within small groups can eventually cause a particular variant to predominate within the group. Such changes typically occur only after many false starts with substantial swings in the frequency of the trait within the population. The operation of sampling effects may thus be identifiable as a pattern of gradual change that does not closely correspond to other environmental or economic trends.

Other effects resulting from the mechanics of cultural transmission are possible. Cultural transmission processes may sometimes lead to the development of exaggerated cultural traits featured in prestige competition or to within-group homogeneity and among-group heterogeneity in certain characteristics. The applicability of alternative models depends on the details of a particular case.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2009.