Accumulation of Stochastic Copying Errors, Akumulation ov Stokastic Coppying Errrors, Akoomulajon ov Stokasic Coppyng Errrers

The Accumulation of Stochastic Copying Errors Causes Drift in Culturally Transmitted Technologies: Quantifying Clovis Evolutionary Dynamics. Hamilton and Buchanan, 2009.
This paper looks at the application of Eerkens and Lipo’s (2005) model on determining causes of copying errors that result in variation in material culture, and how different forms of cultural transmission or social learning affect the amount of variation. Eerkens and Lipo’s model basically seeks to predict the amount of variation given different factors and circumstances. Unlike Eerken’s and Lipo (2005) however, the Hamilton and Buchanan seek to determine not only frequency of variation but also its distribution through measuring the mean, variance, skewness and kurtosis.
Hamilton and Buchanan adapt Eerkens and Lipo’s model to analyze the variation found within Clovis point sizes, to determine if this variation is stochastic (random) or deterministic (result of biased selection). They also argue that this model can be used to track the movement of people across space and time, due to the drift effect of variation in Clovis point size.
Hamilton and Buchanan are particularly interested in drift “which is caused by population fluctuations and subsequent founder effects. A second source of drift is the accumulation of neutral, unbiased, but proportional copying errors through time.” (Hamilton and Buchanan 2009, page 55).
Hamilton and Buchanan term the first model the ACE, accumulated copying error model, which determines variation as a result of the accumulation of stochastic, imperceptible errors during transmission events. Thus the ACE is unbiased vertical transmission from a master to an apprentice. The Weber fraction explains that when humans try to make a copy of something without measuring it directly, their copy will vary by up to 5%. This difference becomes a source of variation which becomes compounded as copies of the copy (and so on) are produced with up to 5% copying errors at each generation.
From the ACE model, Hamilton and Buchanan develop the BACE model, which stands for biased accumulated copying error model. The BACE is similar to the ACE except cultural transmission in this case is biased.
Hamilton and Buchanan go on to create complex equations and simulations to test their models and the results of copying errors. First they test the ACE model, unbiased stochastic copying errors. Their simulation shows negative drift of the mean over time. Next, Hamilton and Buchanan test the BACE model, which is the biased accumulation of copying errors. They identify multiple sources of biased transmission. One of these is conformism where “each individual within a population chooses either to copy the most frequent variant, often given by the population mean […] a process akin to stabilizing cultural selection, […]or follow the rules of vertical transmission” (page 58). Another source of biased transmission is prestige bias, “where prestigious individuals influence social learning [because] each individual within a population chooses either to copy a prestigious individual […] or follow the rules of vertical transmission” (page 58). Here, prestigious individuals are skilled flintknappers from whom beginners would rather learn from. Like conformists, prestigious individuals and their followers are most likely to produce projectile points close to the mean variant. Both are analytically equivalent because the bias is towards the average variant, thus under biased accumulation of copying errors variation should be overall reduced. However copying errors still occur and result in negative drift of the mean. Thus it is predicted that projectile points should decrease over time at a slower rate than unbiased ACE.
The authors propose a case study on Clovis projectile points. The authors look at 232 points from 26 sites across North America. These sites are either caches, camps or kill sites. Also look at radiocarbon dates to determine time scale. This data shows their hypotheses to be true. They are as follows:
Hypothesis 1: frequency of distribution is lognormal as predicted by the ACE and BACE models.
Hypothesis 2: mean size of Clovis points decreases over time, as a function of distance from origin. Site type and raw material are non-significant factors.
Hypothesis 3: size of decrease in size caused by stochastic cultural transmission should be about 5%, as predicted by the Weber Fraction. Copying error accounts for about a quarter of the variation found in Clovis points.
Hypothesis 4: Variation should remain constant over time, suggesting variance is “bounded by transmission bias as predicted by the BACE model” (page 65). This highlights the relevance of biased cultural transmission is social learning.
Since the case study fits within the authors’ models and prediction, they argue it is strong support in favour of their hypotheses. Thus point sizes may be used as a tool for interpreting Clovis populations. They argue that the movement of people across North America can thus be found by analyzing average point size. Specifically the authors argue that by analyzing variations they can determine that Clovis populations were stable and spread rapidly while maintaining long distance social networks.
Furthermore, the authors conclude that the decrease in Clovis point size over time is a result of accumulated copying errors, and not a deterministic selection for smaller points. In other words, points got smaller because of errors in copying and not because smaller points were actually better for hunting due to ecological changes. That is not to say selection never occurred, but rather it simply wasn’t the main cause of the drift in mean size. Variance may have been reduced due to both conformist and prestige bias, due to the fact that the mean was probably the optimal form.
One interesting fact about this paper is that although the authors cite Eerkens and Lipo for the weber fraction figure, Eerkens and Weber say it is a 3% error while Hamilton and Buchanan say it is “up to 5%”, but never discuss where this difference comes from.
Despite this, the authors successfully applied Eerken and Lipo’s previous model, and expanded it. Use of these models in analyzing variation among artifacts can be very useful to archaeologists in interpreting hunter-gatherers behaviour. Use of these models can identify where variation is significant or not, and whether it is linked to particular types of cultural transmission. Furthermore, archaeologists may be able to interpret movement of populations over time. There are without a doubt other factors not accounted for by these models, including social relationships, skill level, etc etc, yet I think the models remain valid.
Clearly, research in evolutionary archaeology can result in new ways of interpreting data.


References:
Eerkens, JW; Lipo, CP. 2005. Cultural transmission, copying errors, and the generation of variation in material culture and the archaeological record. Journal of Anthropological Archaeology 24 316–334
Hamilton, MJ; Buchanan, B. 2009. The accumulation of stochastic copying errors causes drift in culturally transmitted technologies: Quantifying Clovis evolutionary dynamics. Journal of Anthropological Archaeology 28 55–69

Cultural Transmission, Copying Errors, and the Generation of Variation in Material Culture and the Archaeological Record. Eerkens and Lipo 2005.

In this paper, Eerkens and Lipo make a model to understand the means by which variation in material is produced. It is important to realize that here the authors are discussing variation among the same type of artifact, for example variability in thickness of the same type of ceramic pot or projectile point. They look specifically at copying errors as a source of variation, and how methods of cultural transmission either reduce, increase or maintain this variation. They have thus constructed simple models to quantify expected distribution of variation through time under different conditions. The authors claim their arguments can be extended to other aspects of human culture, although they never go into the meaning of this statement.

The authors discuss what produces variation. Although previous work has been done on the subject, it has focused on variation of types and not variation within types.

They begin by exploring cultural transmission, noting its difference with biological transmission, and thus the difficulties in tracking its complex processes.

According to the authors, variation can occur at different points in the creation of material culture in the archaeological record. There are: (1) transmission of instructions, (2) execution of instructions, (3) result of using different raw materials (Eerkens and Lipo 2005, page 319).
The authors propose a schematic for the generation of variation of material culture, which I have replicated here: (sorry about the bad reproduction, I had no choice but to up it up as an image)

The authors argue that the left and right column (stochastic and biased errors, respectively) create different kinds of variation patterns. Stochastic errors are compared to random mutations in genetic transmission, and therefore do not have a predetermined direction. This supposedly leads to smaller scale variation. On the other hand, biased errors, which are intentional, are greater and can be directional. This is because cognitive processes can “sort variation” (page 320). Thus when a hunter-gather wants to create a new form (ei: invent something new), it is not produced by random errors or from a blank slate, but with intentional modifications of a prior known (inherited) form that is believed to be an improvement.

However the authors are mostly concerned with the first column and variation as a result of stochastic copying error. They describe the Weber Fraction, a well known concept, which says due to the human threshold of perception; humans produce 3% error when copying something without being able to directly measure it. Thus we can expect a variation of 3% across a type of artifacts stemming from imperceptible human error. As the errors accumulate, they become perceptible over time, resulting in drift.

In their simulations, unbiased copying errors cause variation to be transmitted and increase over time, although the rate of increase slows down over time. They simulate biased transmission, notably conformist and prestige transmission. Conformist transmission means “individuals conform to the average value […] of the entire previous generation” (page 323). In conformist simulations, variance equilibrium is always eventually reached, although the time it takes to reach that equilibrium depends on the strength of conformity. Overall, this reduces the effect of drift. In prestigious bias, individuals are more likely to try to copy from prestigious flintknappers, which are assumed to produce variants closest to the mean. Thus, prestigious bias should reduce variance. However, prestigious individuals may not necessarily be producing traits that are closest to the means, and individuals may have to choose between multiple prestigious flintknappers, therefore drift is possible. Overall, biased transmission reduces variability caused by the accumulation of copying errors throughout time.

The authors then apply this model to two case studies. The first involves the basal width and thickness of Owens Valley projectile points. Since variation of basal width reduces over time, it suggests non-copying errors may be factors, in other words a biased transmission process may be operating. Thickness however, becomes increasingly variable throughout time, suggesting stochastic copying errors. The second case study involves Illinois Woodland Pot Sherds. Thickness remained constant over time, probably because thickness is important to the function of a vessel and thus non-functioning thicknesses would be weeded out. It would seem that a particular thickness was a trait that was selected for, thus drift was not caused by stochastic copying errors.

The authors admit in their conclusions that there are surely many other factors at play, including changes in settlement patterns, social organization, individual memory, concept of ideal form, etc. However copying error seems to be universal, and thus this paper provide us with a null hypothesis with which we can test data to determine the source of variance over time in the archaeological record.

I like that the authors created a null hypothesis. They build a model based on a universal human trait, and therefore can theoretically be used in any case study and is then very useful to archaeology.

I find it interesting that the trend of random error accumulating over time is the same as that in biological evolution with a rate of increase slowing down over time. The cause of this in biology is history; although here is always variation in traits of organisms, the extent of that variation depends on the organisms’ genetic history (Bell 2008). If this the same in cultural information, even though there are errors, a previous artifact from a long time ago is still remembered, even though it is not the one being copied? I think there are many implications of this that can be more thoroughly investigated.

Clearly, creating a theory of cultural evolution based on Darwinian evolution has many challenges, but as the authors have demonstrated, with more research in this area it is possible to build models appropriate for archaeology.

References:
Bell, Graham. (2008). Selection: The Mechanism of Evolution, 2nd edition. Oxford University Press.
Eerkens, JW; Lipo, CP. (2005). Cultural transmission, copying errors, and the generation of variation in material culture and the archaeological record. Journal of Anthropological Archaeology 24 316–334.