# «By Nathan B. Goodale A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY WASHINGTON STATE ...»

model for the southern Levantine Neolithic and Epipaleolithic, I examined patterns in the variables of site size and depth of deposits dating from 8000-20,000 calibrated years ago. Best-fit exponential decay models were found for all variables. The exponential decay models are determined by finding a 1/λ value. 1/λ controls the rate of exponential decay in the model and can be thought of as the constant rate of site destruction of one site a year, regardless of the number of sites added each year. By presenting the patterns of site size and depth of deposits with a best fit 1/λ value, we can estimate how significantly processes of taphonomic bias may be influencing the dataset.

** Figure 7.1.**

1/λ values for depth o deposits. RED = all data, GREEN = only pre-8650 data, BLUE = only pre-10,500 data.

bias will influence the frequency of both sites occupied and 14C dates to pattern in an exponential manner. However, they do not postulate how taphonomy may potentially influence site size and depth of deposits. Arguably, if we make the assumption that we have a reliable representation of the largest/smallest sites and the deepest/shallowest sites, we may suggest that these two variables (site size and depth of deposits) may not be largely affected by taphonomy. In this case, if taphonomy is not highly influencing the patterns, we would expect the curves for the frequency 14C dates and frequency of sites occupied to be less steep than those of depth of deposits and site size.

As indicated in Figures 7.1-7.4, this pattern of exponential decay is found within these data. Although the curves are shallower for the frequency of 14C dates and the frequency of sites occupied, the variables suggested by Surovell and Brantingham (2007) can be greatly influenced by tamphonomic destruction. These interesting patterns may suggest that the data used here are not significantly impacted by taphonomic bias.

Due to the somewhat tentative nature of this conclusion, a simulated model is provided at the end of this chapter to compare this frequency data to simulated data that is representative of archaeological sites appearing and disappearing at different rates through time. The simulation further demonstrates that the data pattern in a consistent manner with little influence of taphonomic bias. Next however, we move

population proxies.

** Figure 7.2.**

1/λ values for site size. RED = all data, GREEN = only pre-8650 data, BLUE = only pre-10,500 data.

** Figure 7.3.**

1/λ values for number of sites occupied. RED = all data, GREEN = only pre-8650 data, BLUE = only pre-10,500 data.

Cross-correlation Analysis: The Best Fit This section presents the results of the cross-correlation analysis which enables a graphical representation of both when and how well each population proxy correlates with the others. This allows a comparison of which variables may match up most closely with each other, providing a topographic landscape of the entire time from 22,000-8,000 cal BP. This analysis is important because if each variable is a viable proxy for population growth, each of them should monitor and track the phenomenon in a similar manner.

Cross-correlation analysis provides an additional tool for examining datasets that should be following the same phenomenon in similar manners. More

phenomenon in relationship to all of the other variables. In this analysis, the data were scaled to the percent of the data occurring in each 50-year increment. In other words, as indicated in Appendix B, the 50-year increment of 9900-9950 cal BP contains a total of 47.195 meters of deposits which is.0146 percent of the total. This was done in order to compare different measures on the same scale such as site size in hectares to depth of deposits in meters.

In Figures 7.5 – 7.10, each dataset is cross correlated with all of the others.

Depicted in each figure is the raw data shift as well as the final cross-correlation. In the final cross-correlation we see 1) where the peaks, or best fits, occur and 2) how far each dataset has to be shifted in order to produce the best fit cross-correlation.

The hypothesis states that the better the cross-correlation between two variables, the sharper and better defined the peak and where the peak forms is expressed in how many years the data have to be shifted in order to achieve the best fit. If the variables are proxies of population growth, they should require relatively little shifting while forming well defined peaks, the idea being that as proxies of population growth, all variables should correlate more or less with each other.

Depth of deposits to Frequency of Occupied Sites The cross-correlation between the total depth of deposits versus the frequency of occupied sites demonstrates a very good correlation with zero shift and a well defined peak (Figure 7.5). This suggests that the total depth of deposits and the

phenomenon in a very similar manner.

** Figure 7.5.**

Cross-correlation of depth of deposits versus frequency of occupied sites from 22,000 to 8,000 calibrated years ago. Blue = Depth of Deposits and Red = Frequency of Sites Occupied.

Frequency of Sites Occupied to the Frequency of 14C Dates

growth appear to track the phenomenon of population growth in a similar manner.

147 Figure 7.6. Cross-correlation of frequency of occupied sites versus frequency of 14C dates from 22,000 to 8,000 calibrated years ago. Blue = Frequency of 14C Dates and Red = Frequency of Sites Occupied.

Site Size to the Frequency of Sites Occupied The cross-correlation between site size and the frequency of sites occupied is also a good correlation (Figure 7.7). This is highlighted by a defined peak (although not as well defined as those above) and a minimal shift of 100 years. This amount of shift in an archaeological sense is probably inconsequential in terms of how well each line of evidence is monitoring population growth.

Site Size to Frequency of 14C Dates The cross-correlation between site size and the frequency of 14C dates is also moderate to good (Figure 7.8). There is a well formed peak but to obtain this, a shift of 250 years is required. While this shift is greater than all of the others presented thus far, my overall interpretation of this is that on an archaeological time scale, a shift of 250 years is fairly inconsequential. Thus, I would argue that these two variables are monitoring and tracking population growth fairly consistently in comparison to each other.

Depth of Deposits to the Frequency of 14C Dates The cross-correlation between the total depth of deposits and the frequency of 14 C dates demonstrates a good cross-correlation with a well defined peak. but a shift of 900 years is required before the best fit occurs (Figure 7.9). A potential explanation for this result is the nature of the settlement strategies specifically during the Early Natufian. As noted in Chapter Five, Early Natufian settlements are commonly in caves where depth of deposits will become deeper due to the horizontal restriction that the caves impose. Thus, we expect that depth may be the hardest variable to cross correlate with the others. However, because site size is restricted during this

final section, other variables such as site size should circumvent any deleterious effects that depth of deposits impose on the model. Thus I argue that while depth of deposits is not well correlated most likely due to this change in settlement patterns, it is still an important parameter for modeling population growth.

** Figure 7.9.**

Cross-correlation of depth of deposits versus frequency of 14C dates from 22,000 to 8,000 calibrated years ago. Blue = Depth of Deposits and Red = Frequency of 14C Dates.

Depth of Deposits to Site Size The cross-correlation between depth of deposits with site size is similar to that of depth of deposits to the frequency of 14C dates with a fairly well defined peak but a required shift of 1650 years (Figure 7.10). For the reasons noted above associated

consistent cross-correlation should circumvent most deleterious effects of depth of deposits on the overall model of population growth.

** Figure 7.10.**

Cross-correlation of depth of deposits versus site size from 22,000 to 8,000 calibrated years ago. Blue = Depth of Deposits and Red = Site Size.

Overall Trends in the Cross-correlation The purpose of the cross-correlation analysis is to utilize a technique designed to measure how well certain related variables reflect a single phenomenon in comparison to each other. Most of the measures fit well with each other with little to minimal shifting required that develop well defined peaks. However, depth of deposits compared to site size and 14C date frequency were the weakest measures. I

Early Natufian settlement patterns. Interestingly, the Early Natufian period is regarded to be on the order of about 1700 years (Table 5.1). As an amazing coincidence or something that can substantiate my argument, the biggest shift that has to be made is 1650 years for the correlation between depth of deposits and site size (the two variables largely affected by the intensive use of caves during the Early Natufian). As a result, with the good cross-correlation between the other variables, they should combine to minimize deleterious effects on the model caused by the variable “depth of deposits.” Furthermore, because “depth of deposits” is likely showing this change in settlement during the Early Natufian, I believe that it is an important parameter to keep in the model. This may also help to answer the long standing question if population grew during the Early Natufian.

Regression Analysis: Population Growth through Time The goal of this section is to provide a more robust statistical evaluation of the data that I have argued thus far are 1) not overly influenced by taphonomic bias and

2) appear to be monitoring and tracking the same phenomenon (population growth) in a consistent manner. To achieve statistical verification, a series of regression analyses is used to examine the overall significance of the model and also how reliably each of the population proxy variables is predicted by the dependent variable – time. All analyses utilized the raw data transformed for normality with Log10.

outcome of one dependent variable through a series of predictors or independent variables. In this case the dependent variable is time and the predictor variables are the frequency of 14C dates, the frequency of sites occupied, depth of deposits, and site size. The results indicate that the overall model is statistically significant and positively correlated (f=254.95; df=4; p =.0001; r2=.7870). The high r2 value also indicates that together, the variables are reliable predictors of time.

Simple linear regression analysis is a common parametric statistical test utilized to examine patterns in archaeological data. Specifically, I use regression analysis here to examine the dependent variable – time as calibrated radiocarbon years BP - with the population proxy variables including: depth of deposits, frequency of 14C dates, frequency of sites occupied, and the total site size occurring in each 50-year increment. By running pair-wise regression tests we gain a more detailed understanding of each datasets relationship with time and thus, population growth.

Regression analysis was conducted using SAS v.8 statistical software with the proc reg function. For each case, the regression analysis was run twice with time as the dependent variable. The first run included all of the data compiled from 22,000 to 8,000 calibrated years BP. Due to a substantial decrease in available data representative of population at the end of the Late Pre-Pottery Neolithic B (LPPNB), the second regression analysis was conducted with only data pre-8650, as this is the date regularly regarded as the end of the LPPNB (Kuijt and Goring-Morris 2002)

** Figure 7.11.**

Linear regression of depth of deposits to time (calibrated BP).

Regression line in RED reflects that of all data and regression line in BLUE reflects that of only data pre-8650. Data points in RED are those dating to post-8650 cal BP.

155 Figure 7.12. Linear regression of the frequency of 14C dates to time (calibrated BP).

Regression line in RED reflects that of all data and regression line in BLUE reflects that of only data pre-8650. Data points in RED are those dating to post-8650 cal BP.

** Figure 7.13.**

Linear regression of the frequency sites occupied to time (calibrated BP). Regression line in RED reflects that of all data and regression line in BLUE reflects that of only data pre-8650. Data points in RED are those dating to post-8650 cal BP.

156 Figure 7.14. Linear regression of site size to time (calibrated BP). Regression line in RED reflects all data and regression line in BLUE reflects that of only data pre-8650.

Data points in RED are those dating to post-8650 cal BP.

Results depict an overall trend that each variable positively and significantly increased through time (likely indicating that population increased through time);

however, there are different levels of prediction indicated by the r2 values (Table 7.1 and Figures 7.11-7.14).

Having argued that taphonomic biases have not significantly influenced the data of the southern Levant used here (and verified by computer simulation later), we can assume each variable with both significant p values as well as high r2 values (ca.

.60 but the higher the better) is a reliable predictor of population growth through time. Thus, as each variable examined here has both significant p values as well as r2 values.60, (excluding time versus depth of deposits all inclusive data r2.4921)