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

time (Table 7.1). Importantly, because the regression of time versus depth of deposits including all data from 22,000-8,000 cal BP may not be a reliable predictor (due to the low r2 value), all following analyses utilize only data from pre-8650 for all variables.

Population Growth Rates The ability to measure population growth rates over long time periods allows us to understand human behavior better as well as the major transitions in our evolutionary history. While we will never know exactly how many people are represented in each 50-year period, I posit that we can produce an overall model of population growth based on these particular proxies.

** Figure 7.15 shows all of the proxies of patterned population proxies through time.**

Each variable has been scaled to the percentage for each 50-year increment in order to have a directly scaled comparison. The overall trend in Figure 7.15 demonstrates an increase in all of the population proxies through time until 8700 cal BP. By taking all of these variables we can add all of their percentage values for each 50-year increment and calculate the percent change or growth rate from one period to the next by (Time1 × Time 2 ) / 50, obtaining growth rates from one period to the next. The result is depicted in Figure 7.16.

** Figure 7.16 demonstrates the positive and negative growth rates for each 50year increment through the sequence of 8,650-22,000 calibrated years ago.**

There are several interesting patterns within the graph. First, note that the growth rates were very small throughout the Epipaleolithic, probably mimicking essentially zero-growth rates. This is emphasized by similar frequency and scaled negative growth rates with their positive counter part growth rates.

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159 160 Figure 7.16. Changing growth rates through the sequence. Note that the dashed line tracks the growth rates and the significant increase during times of population growth after the first well documented case of intensive food storage.

regarding the potentially deleterious effects that deeply stratified Early Natufian sites may impose on the model, it is clear that growth rates in the Early Natufian were on the order of the rest of the Epipaleolithic despite the early increase in this variable.

This may help clarify some of the arguments regarding population growth during the Early Natufian (Goring-Morris and Belfer-Cohen 1998; Boyd 2006; Henry 1989) for this model indicates that their populations likely remained on the same order of magnitude as other Epipaleolithic populations.

Another interesting pattern that occurs during the Epipaleolithic including the Natufian is the seemingly minor impact that technological inventions had on increasing population growth rates. Through the model presented in Chapter Four, I argued that a significant increase in population growth would not occur until all of the fundamental elements were in place including storage technology. The logic is that food storage provides a stabilized diet of foods associated with increased fertility.

The model presented in Figure 7.16 suggests that there is significant credibility to the hypothesis that these early inventions of technology that aided in harvesting and processing efficiency did not overly influence population growth.

Perhaps the most significant contribution of the model is the suggestion that the first population growth rate event that is higher than those of the Epipaleolithic, occurs in the Early Neolithic during the Pre-Pottery Neolithic A (Figure 7.16). This event is congruent with the first evidence of intensive storage in the form of grain

suggests a strong correlation between food storage and population increase.

Interestingly, each sharp increase in population growth rates only occurs during one 50-year interval. The same is true for negative growth rates, hinting that population increases and decreases happened over short periods of time (cf. Rollefson and Pine n.d.). Also note that the negative growth rates follow a pattern similar to positive growth rates in terms of scale and frequency. That is, once populations start grew at a high rate, negative growth rates also occur more dramatically. This may indicate stressful periods, where shortfalls in crop failure may have had more catastrophic effects on population size as noted in Chapter Four under delayed-return food economies. Alternatively, short-term positive growth rates may sometimes be indicative of the addition of resource bases that may raised some theoretical carrying capacity and, at the same time, influenced fertility. This may be evidenced by the occurrence of domesticated animals when we see a likely in situ domestication of goats at ‘Ain Ghazal during the MPPNB (Savard et al. 2006) and the dairy products that they would have provided also associated with increasing fertility.

While most of the other spikes in population growth seem to have strong correlates with the addition of resource bases, the final and largest growth rate spike during the LPPNB between 8950-9000 cal BP is probably associated with the mass movement of people from the sites in the west to inhabit villages east the Jordan Valley (Kuijt and Goring-Morris 2002; Rollefson 2004). This too appears that it was a very rapid shift that occured in less than ca. 50 years.

transition to agriculture likely never exceeded 2 percent per year, arguably a very conservative estimate. Support for this view are the similar findings that BocquetAppel (2002:647) suggests for the NDT in Europe. The model also suggests that the largest growth of human population likely occurred in the Late Pre-Pottery Neolithic B with other significant growth events in the Middle Pre-Pottery Neolithic B and in the Pre-Pottery Neolithic A.

Simulating the Effects of Taphonomic Bias Through a simple simulation model, we can compare these results with the expected destruction of sites promoted by Surovell and Brantingham (2007). We can demonstrate this model very easily through a simple decaying exponential function;

however, what their model fails to specifically address is the relationship between the frequency of sites that were added in relation to the number that were destroyed. The following exercise provides an example where we can control the rate of sites being added and subtracted from the archaeological record through an easily explainable analogy. This simulation produces a plot comparable to Figure 7.16 and the behavior of the data based on different rates of adding and subtracting archaeological sites from the record. This approach allows further justification for the conclusion that the dataset utilized here may not be significantly affected by taphonomic bias.

Pretend you are at the carnival or country fair. The life sized doll of Richard Simmons has caught your eye, and the only way to win it is to pop balloons stapled to a board by throwing darts at them. You’ve bought the Super-Mega-Family packet of tickets, so you can throw as many darts as you’d like at the board. The objective of the game is to pop all of the balloons, where the balloons are analogous to archaeological sites and the board analogous to some defined geographic area. Your aim is random and you consistently hit the board somewhere, but other than that, the darts go all over. At first you break balloons quite often, but later fewer and fewer dart-throws break balloons, and the last several seem to take forever to pop. The reason for this is simple: with random throws, you’re more likely to break a balloon when there are lots of balloons to break; later on, when there are fewer balloons left on the board, breaking one by chance takes longer. In fact, the probability to break a balloon on any particular throw, because you can’t aim any better than to hit the board, is simply the area covered by unpopped balloons, divided by the total area of the board. In other words, as archaeological sites become less and less frequent due to their age, the less probable it will be to destroy those few remaining sites defined

**as:**

where areasite is the area covered by a single archaeological site (d), and b is the frequency of sites in the defined geographic area. The rate of the site destruction (that

increase with time. Also, P(destroy) is positive; I simply choose the proportionality constant k to be positive, so that there must be a negative sign out in front. Rewriting Equation (7.2) to include Equation (7.11) gives

where the constant areasite =areageography has been absorbed into the constant k, because the product of a bunch of constants is still a constant. Equation (7.3) is the simplest non-boring differential equation imaginable. It says that how fast something changes (b here, the number of sites left to destroy) is proportional to how much of that something is present. It’s commonly referred to as the heat equation, because it describes how fast (for example) a cup of coffee will cool down. It can be solved by integrating both sides, or by remembering that the exponential function has the interesting property that its slope is proportional to its value at all points. In other words, the solution to Equation (3) is

** Figure 7.17.**

A typical exponential decay curve. In this case, the curve’s equation is −7 Note that the curve starts at 100; and after any given interval of length 1, the 100e 10 t

It is relatively easy to simulate the dart-throwing and the expected outcome.

The board chosen for the simulation has 8 rows of 7 sections where each section is divided up into 9 squares and any or all of the squares starts out with a balloon stapled to it. The computer then throws darts randomly at the board, hitting somewhere in the 8 × 7 × 9 = 504 squares, and keeps track of whether it hits a balloon

simulation for a given board continues until all of the balloons are popped. Figures 7.18, 7.19, and 7.20 show three simulations with different starting numbers of balloons. We can imagine these boards with balloons as defined geographic space with some N number of sites.

By having the computer keep track of how many balloons were on the board at each step, we can see the rate of balloon pop. Of course, the starting number is set by the analyst, but after that, the randomness of the dart throws means that the number of balloons is only described approximately by Equation (7.4). Sometimes, the numbers deviate wildly from what is predicted on the average. Figure 7.21 illustrates the results of a number of dart games, with different numbers of starting balloons. Even though it seems that the games with larger numbers of balloons are more accurately predicted by Equation (7.4), this is only because the scales on the plots have been changed to show the full results. If one looks at the tails of the records in Figure 7.21b and 7.21c, they are just as jagged and unpredictable as the records in Figure 7.21a. In fact, this is guaranteed by the nature of the process we are dealing with: the balloons on the board do not have any knowledge of what number of darts have been thrown at them, nor whether their neighbors have been popped or not. This means that we can take the case of the boards which start with 504 balloons, throw darts, and wait until there are only 56 balloons left, and then count those as though we have just started throwing darts at the boards. The entire game has

to look, on average, just like any other portion.

** Figure 7.18.**

The board at different steps in the simulation. Black squares represent balloons left on the board. The simulation starts with 54 balloons on the board.

** Figure 7.19.**

The board at different steps in the simulation. The simulation starts with 216 balloons on the board.

** Figure 7.20.**

The board at different steps in the simulation. The simulation starts with the board fully covered: 504 balloons are on the board.

This simulation is very similar to that provided by Surovell and Brantingham (2007) for the destruction of archaeological sites and decaying exponential expectations. The limiting factor to this is the absence for considering the rate of

operator adding balloons to the board when you were not looking. In our real example of measuring population growth rates during the NDT, the “sneaky operators” are the people of the past, consistently (but not necessarily constantly) adding new sites to the record. Here is a simulation to account for this problem.

** Figure 7.21.**

The total number of balloons left on the board, after a number of throws.

The different subfigures show results for boards starting with 56, 226, and 504 balloons, respectively.

Suppose that the operator of the dart boards is sneaky, and every once in a while, if your back is turned, he quickly staples a new balloon to the board. This modifies the rate of the balloon disappearance, and the original differential equation,

**Equation (3), gets an added term:**

where a is the rate at which the operator sneaks new balloons onto the board or in our case study, the rate at which people are adding sites. Perhaps it is once every throw (if you’re very distracted—in this case, you don’t have a hope of winning), or perhaps it is only once every 100 throws. The solution to this equation is nearly as simple as the original. It is

dependent term). The only term which changes with time is the one containing t, this one goes to zero as t → ∞ but the population never quite reaches zero. It

once in a while. When the probability of the operator adding a balloon equals the probability of you popping one, then the population of balloons reaches a static value.

Figure 7.22 contains several curves showing what should happen if the operator adds