The Little Tennessee River flows from its headwaters in the Blue Ridge Physiographic Province of northern Georgia to its mouth on the Tennessee River. Most of the study region lies along the lower Little Tennessee and Tellico Rivers in the Ridge and Valley Physiographic Province of East Tennessee. Several archaeological endeavors have documented the geographic characteristics (Cridlebaugh 1984:9-14; Kimball 1985:88-120; Davis et al. 1982:8-36) and cultural sequence (Kimball 1985: and Davis et al. 1982:333-411) of the Valley. Applying the model to this setting requires calibrating population and soil productivity in terms of this information.
The region's late prehistoric/early historic period has been divided into four sequential manifestations: Martin Farm (A.D. 900 to 1000), Hiwassee Island (A.D. 1000 to 1300), Dallas and Mouse Creek (A.D. 1300 to 1600?), and Overhill Cherokee (A.D. 1700? to 1819) following, in part, Lewis and Kneberg (1946) and Kimball (1985). In this study these periods will be designated Mississippian I-IV, respectively, on the basis of ceramic continuity (Kimball and Baden 1985).
Regional Mississippian research has primarily been restricted to salvage operations resulting from Tennessee Valley Authority reservoir construction (1934 to 1979). These include the Norris (Webb 1938), Chickamauga (Lewis and Kneberg 1941, 1946), Chilhowee, and Tellico Reservoir projects. Reports produced by the Tellico Archaeological
Project (1967 to 1982) serve as the modern basis for understanding the Mississippian sequence in the study region. Particular emphasis is placed on the excavations at the sites of Bat Creek (Schroedl 1975), Toqua (Polhemus 1984), Citico (Salo 1969; Chapman 1979), and Martin Farm (Schroedl et al. 1985). The unexcavated site of Great Tellico (40MR12), located on the upper Tellico River, also served as a major Mississippian center. In addition, because the Valley was the homeland of the Overhill Cherokees (A.D. 1700? to 1836), the historically recognized (Timberlake 1927) towns of Chota/Tanasee (Schroedl 1986, edited), Tomotley (Baden 1983; Guthe and Bistline 1978), Citico (Chapman 1979), and Mialoquo (Russ and Chapman 1983) play an important role in understanding the region's late Mississippian Period. The most significant Mississippian and Cherokee sites are shown in Figures 10 and 11.
Environmental data pertinent to quantifying the area's soil productivity are available in the soil survey reports for Blount (United States Department of Agriculture 1953), Loudon (United States Department of Agriculture 1961), and Monroe (United States Department of Agriculture 1981) counties. Interpretation of resource utilization patterns depend on the results of two research projects which examine the region's cultural sequence: Cridlebaugh's (1984) palynological/paleobotanical study and the 1982 probabilistic survey of cultural resources (Davis et al. 1982; Baden 1985). Combined, the available data for this region are highly suitable for testing the applicability of the preceding model.
Figure 10. Distribution of Mississippian sites along the Little Tennessee River Valley
Figure 11. Distribution of historic Cherokee (Mississippian IV) sites along the Little Tennessee River Valley
The Mississippian Sequence
The Emergent phase of East Tennessee Mississippian, Mississippian I, is characterized by small settlements appearing ca. A.D. 900. Some villages included the construction of substructure mounds [such as the one found at Martin Farm (40MR20)] (Schroedl et al. 1985:462). The overall settlement distribution appears to have been dispersed along first terrace (T1) surfaces [i.e. floodplain surfaces abandoned by the Little Tennessee River between 3500 and 4000 years ago (Delcourt 1980)].
Mississippian II sites appear ca. A.D. 1000 and consist of more centralized and complex villages such as those at Bat Creek (40LD24) and Martin Farm. Site selection shifted to second terraces (T2), possibly due to increased flooding of T1 elevations or, alternatively, selective use of the lower terrace for agriculture (Schroedl et al. 1985:466). The villages appear, based on evidence from Bat Creek, to have represented brief, intensive occupations without subsequent Mississippian III development (Schroedl 1975:278-279).
The Mississippian III period (Dallas) is most prevalent at Toqua (40MR6), Citico (40MR7), and Great Tellico beginning around A.D. 1300. This was the period of organizational climax growing out of an elaborate Mississippian II base in East Tennessee. Toqua served as a major center during the period with one of two substructure mounds dating to A.D. 1208 _ 133 years (middle Mississippian II; C14 corrected) (Baden 1980). Archaeomagnetic dating documents the primary occupation occurred between A.D. 1370 and 1470 (Baden 1980).
Late in the period, probably during the fifteenth century A.D., a more dispersed, remnant settlement pattern developed which we call Mouse
Creek (after the type site 40RH41 in the Chickamauga reservoir) (see Lewis and Kneberg 1941:7-11; Garrow 1974). Concentrated in the Ridge and Valley Province of northern Georgia and southeastern Tennessee, this developmental phase shares several material and structural similarities with Dallas and Overhill sites. Limited exposure of a possible square townhouse at Tomotley (40MR5) (Baden 1983:129) in close proximity to late Dallas features (Guthe and Bistline 1978:42-43) demonstrates the existence of this phase in the study area (cf. Lewis and Kneberg 1941:7). However, with this exception, obvious Mouse Creek contexts are not recognizable in the Valley. The lack of a clearcut transition between elaborated Mississippian and historical Cherokee has led many to presume an occupational hiatus occurred during the seventeenth century A.D. (see Schroedl 1986).
By 1720 early military and economic surveys of the region began to produce an Anglo-American record of the Cherokee occupation. Census data generated in 1721 (Fernow 1890:273-275) give us the first quantitative measure of aboriginal occupation in the area. Such data continued to be produced until the final Cherokee removal in 1836.
Generalized site distribution early in the eighteenth century consisted of a limited number of villages (Chota, Tanasee, Toqua, and Great Tellico/Chatuga). By A.D. 1750 military disruptions forced Cherokee refugees from the Lower (South Carolina), Middle (mountains of North Carolina), and Valley (Valley River, North Carolina) Cherokee towns to seek refuge in the Overhill country (Baden 1983:20). This resulted in the village pattern witnessed by Timberlake (1927) in 1762 (Figure 12). This settlement system was destroyed by Revolutionary
Figure 12. Lieutenant Henry Timberlake's 1762 map of the Overhill Cherokee villages
forces in 1776 when the pro-British inhabitants were driven south to the Chickamauga area. Subsequent aboriginal occupation of the Valley was limited to a few reservations and four small, more traditional settlements (Citico, Chilhowee, Great Tellico, and Tallassee) until final Cherokee removal in 1836 (Riggs 1987).
We have hypothesized several utilization characteristics for the Mississippian Period. Early maize consumption was limited to approximately one third of the total caloric intake. Later, production levels increased the dependance to almost 75%. This expanded consumption is correlated with improved productivity as 12/14 row races were replaced by 8/10 row types. The increase is also a reflection of an expanding population's impact on less stable wild resources. Because traditional resources are subject to cyclical yield fluctuations, horticultural substitutes offered an increase in expected productivity. To use these hypotheses effectively, our model requires verification of their validity under East Tennessee conditions.
The task of quantifying horticultural utilization by Mississippian groups is a difficult one to undertake. Until recently, paleobotanical recovery and analysis were biased in favor of those situations where preservation conditions were ideal. Today, techniques and sampling schemes have been developed that enhance the systematic recovery of plant remains (Watson 1976). Unfortunately, most of the more critical excavations in the study area predate widespread use of these tech
niques. This limits our validation to a search for contradictory evidence.
In the Little Tennessee River Valley, there is no ethnobotanical evidence to support heavy aboriginal use of 12/14 row varieties (Chapman and Shea 1981). Throughout the period of maize horticulture, the most abundant forms were the 8/10 row specimens. This extends back to the Middle Woodland Period as revealed in Middle Tennessee's Owl Hollow phase sites where 10 row race(s) were recovered (Crites 1978:82-83). The smaller rowed varieties similarly predominate the record of early maize in East Tennessee (Chapman and Shea 1981:72; Schroedl et al. 1985:456). This runs counter to our expectation, based on Cutler's (1956) data, that older forms will tend to display higher row numbers. On the other hand, looking at the end of the Mississippian period (Kline and Crites 1979; Schroedl and Shea 1986:520), the absence of many-rowed types confirms our belief that the more advanced southern dent varieties did not become prevalent at any time in the precolonial period. Production would not appear to be limited by any obvious varietal component. Therefore, maximum potential yield can be assumed to be constant (18.8 quintals/ha) over the period.
As noted in Chapter III, skeletal analyses document that maize was not an important caloric source prior to A.D. 1000. Early (Mississippian I) dependence on maize was on the order of 35% increasing to over 70% of the diet late (Mississippian III) in the sequence (Lynott et al. 1986:61). Archaeological investigations from East Tennessee have failed to detect such an increase between Mississippian I and II (Schroedl et al. 1985:456). This is based on the lack of a significant
change in the abundance of maize remains from one period to another at Martin Farm. Over the entire Mississippian era, however, such a trend has been interpreted from the collective botanical evidence (Chapman and Shea 1981:72).
Our application should reproduce this change with a concomitant adjustment in field size and an increased sensitivity to decreasing annual yields. Lacking contrary evidence, we can use (3.10) to estimate the time-dependent, optimal production needs (quintals per person) for the Mississippian Period. Field sizes would be based on expected yields and required need. With a mean non-depleted yield of 9.99 quintals/ha, a requirement of 0.88 quintals/person could be met by planting 0.09 ha/person. Likewise, 0.16 ha/person would supply 1.63 quintals/person. When failure is defined by a yield in quintals/person below the minimum required, the uselife of a field will be directly related to its size per person. Obviously, small fields will tend to fail sooner while not using as much of the total land reservoir. Because we do not know how large the fields were per person, the size parameter must be defined as a bounded value, [0.1,0.4] ha/person. The boundaries are defined by minimum need and maximum area capable of being cultivated per person. Although this may seem imprecise, we will show that field size does not significantly alter the expected time of total failure by more than three generations.
The palynological evidence gathered from cores taken from Black Pond and Tuskegee Pond (Cridlebaugh 1984) reveals several important facts concerning maize production in the Little Tennessee River Valley. Maize pollen was consistently recovered from levels dating back to the
Middle Woodland. Sharp increases in the pollen spectrum occurred ca. 900 B.P., 700 B.P., and 350 B.P. (A.D. 1050, 1250, and 1600, respectively). A major decline was observed at approximately 450 B.P. (A.D. 1500) (Cridlebaugh 1984:68). Charcoal peaks are correlated with maize production and interpreted to be the result of clearing practices (Cridlebaugh 1984:133-134). A decrease in this charcoal influx from 470 to 360 B.P. (A.D. 1480 to 1590) is assumed to be an indication of a settlement decline. Additionally, because Tuskegee Pond is situated on a third river terrace, we know that upper terraces were used for agricultural purposes as early as the Middle Woodland. Fluctuations in the pollen spectrum may provide us with the only evidence of settlement adjustments as independently predicted by the basic model.
An analysis (Baden 1982,1985) of data from the 1982 probabilistic survey provides another interpretation of Mississippian land use. Using probability models of site location, it is possible to locate areas of increased Mississippian activity over that of the previous Woodland Period. The heaviest concentration lies in the Tomotley Bottoms area between the mouths of Tellico River and Citico Creek. It is in this area that sites like Toqua, Tomotley, Chota, Citico, and Martin Farm flourished. A secondary area of habitation lies along Tellico River and extends to the site of Great Tellico/Chatuga. As will be discussed later, these locations are correlated with Statler-Staser-Transylvania soil associations which constitute the richest agricultural soils of the Valley. These small arable sections will be shown incapable of longterm support of Mississippian development.
These observations are not sufficient for us to make specific statements on the importance of maize in the study area or identify the races grown. However, we can say that there was an increase in utilization based on the observed increase in material deposition during the period and note that the higher row numbered varieties do not contribute more than a trace amount to the botanical assemblages. We can also identify periods of decreased utilization of at least part of the Valley and use these dates as benchmarks to compare with our model's predictions. Our isolation of heavily utilized areas provides useful correlations with soil types which are needed to quantify expected yields for the period.
Estimating population parameters from archaeological evidence is at best difficult. Of the principal excavated sites, only Toqua produced sufficient evidence to warrant serious demographic estimation. From both village and mound contexts, 439 burials were recovered (Parham 1984:392). Following the standard stationary population assumptions, life table approximations projected a life expectancy of 16.1 years (Parham 1984:422). Estimates of village size were made for a presumed range of 2500 to 5000 possible burials (deaths) at the site during the primary 300 years of Mississippian use. Using the methods described by Ubelaker (1974:66) and Acsadi and Nemeskeri (1970), these constant population values fell between 134 and 299 individuals.
An intersite osteobiography of late Mississippian phase sites (Boyd 1984:92) presented constant village size calculations of 890 for Ledford
Island (40BY16) and 193 for Rymer (40BY15). Both sites represent Mouse Creek phase occupations (ca. A.D. 1500) in the Chickamauga Reservoir area. The estimated numbers of burials at each of these sites are 3962 and 811, respectively.
In order to incorporate stable population parameters (3.2) into such an exercise, the formula:
can be used to estimate the starting population needed to produce T burials after t years where the death rate is d and the net growth rate is r. Using the data in Table 1 (p. 39), a stable population with a GRR(23) of 3.0 and a r of 0.003 will have a death rate of 0.051. Under such conditions a P0 of 101 at Toqua would produce 2500 deaths in 300 years and a final ulation of 248 people. This is a reasonable estimate, given the argument that the reciprocal of the mean age at death (16.1 years) is either a measure of the birth rate for a stable population (Sattenspiel and Harpending 1983:493) or the death rate for a stationary population. Toqua's death rate would fall in the range of 0.059 (implying a P0 of 87.09 for r = 0.003).
Both approaches assume continuous site occupation for the period. If the village is intermittently abandoned, as the Kinkaid example implied, the relationship between total burials and population size is invalidated. In such a case the interval, t, is discontinuous and site specific. To be valid, the number of burials must be calculated in terms of the entire settlement area. If it can be shown that continuous
occupation is highly unlikely, we would need to reconsider many of our assumptions about "contemporary" sites.
We can, therefore, simplify our analysis by presenting the population parameters for the study region as an aggregate rather than a sum of individual values for each specific site. During the early contact period, Cherokee villages tend to have less than 200 residents. This is supported by the 1721 census listed in Table 5 (Fernow 1890). The average village size was 196.9 with a range of 62 to 622. A similar tabulation by Haan (1981:353) produces an average village size of 186.8 for 60 Cherokee towns in 1720. Using the data in Table 5 we can estimate the relationship between the numbers of men (m) and the total village size (V ) as :
This allows us to estimate the 1762 population of the nine principal Overhill villages to be 2417 based on Timberlake's census of 809 warriors (see Figure 12, p.91). From a similar setting, Schoolcraft's (1847:32-33) data on Iroquois reservations (Table 6) allow us to estimate the average aboriginal family size to be 5.3 with an average aboriginal growth rate for one year of 0.006. All of these values are within the expected range for Mississippian populations given the arguments in the preceding chapters. This is true despite the fact that historical data encompass the effects of decimating diseases introduced by western colonists (Dobyns 1983:8-32). It is difficult to assess to what extent historical accounts reflect reduced population sizes. Size estimates of Florida's Timucan population, generated from early Spanish recollections (Dobyns 1983:186-205),
have exceeded 130,000. If depopulation trends followed Dobyns' (1983:29) proposed 94.9% reduction rate between A.D. 1515 and 1625 (something unsupported paleodemographically), the Mississippian population of the Valley would have climaxed at 47,151 individuals late in Mississippian III given the "surviving" 2400 inhabitants in 1762. Such estimates are probably extreme and fail to recognize that archaeological and historical records are not capable of extrapolating total settlement size from site specific observations (see Zambardino 1980 for a critiqueof using such data). Although a village like Estatoe (Table 5) may have 622 inhabitants, others may be substantially smaller and more dispersed across the catchment area. Also, one village of 600 that periodically moves will produce several archaeological sites each apparently capable of supporting 600 people.
Population estimates should be framed in terms of socio-political and technological levels of organization and applied to catchment regions rather than individual sites. Following observations involving implications from basic information theory (Forge 1972:374; Johnson 1978, 1982; Root 1983), socio-political control is limited by the ability of a society's hierarchical structure to maintain accurate and efficient information flow. For the contact period this would be around 200 people per village aggregate and probably no more than a dozen villages per political unit (i.e. the Overhill, Middle, Lower, and Valley towns). The Little Tennessee Valley supported approximately 2400 people in nine villages in 1762. This would mean a population density 2of 0.006 per ha (1.62 per mi ) was maintained over the three county area, at least for a short time. Obviously the hunting range for these
villages extended great distances beyond this arbitrary area. But, because agricultural catchment tends to lie within a two mile radius from each village (Chisholm 1962:66), density defined in terms of the study area would seem appropriate.
Calculations by Parham and Boyd confirm probable village sizes of about 200 for sites like Toqua, with major centers having up to 1000 inhabitants. With primary (though not necessarily contemporaneous) Mississippian III settlements at Toqua, Bussel Island, Citico, and Great Tellico a minimum Dallas population of 800 people might be expected for the Little Tennessee Valley. Similarly, the Mississippian II villages were probably fewer in number with concentrations at Toqua and Bat Creek. Mississippian I sites predate heavy dependence on agriculture. As hunter/gatherers they probably consisted of small, dispersed settlements.
If we use a conservative r value of 0.003 and a P of 200, the 0expected population of the Valley in 800 years (A.D. 900 to 1700) would be 2205. This is conveniently close to the estimated 1762 Cherokee population without allowance for disease effects. But could such a low density support the development of stratified socio-political organizations during this period? The literature is unclear on the minimum population size required to encourage and pay for the development of Mississippian traits such as substructure mounds, apparent elite and artisan classes, and an inter-village political network. Considering these factors, we might suppose that population densities during Mississippian I-III were higher than those of the historical period. If this were the case, our estimate of P might have to exceed 1000. 0
Because we lack specific lower threshold limits, we will analyze the model for ranges of P and r values. In choosing this course we 0partially reject the need for site specific estimates in favor of bounded ranges of possibilities. The model's responses are then probable expectations of what should occur within the context of our overall demographic assumptions.
Until now we have assumed a constant maximum potential yield per unit area. This value has been shown to be approximately 18.8 quintals/ha. In reality this parameter will vary with soil type across a study area. Modern maximum yields and other soil characteristics for Monroe, Blount, and Loudon counties have been documented by soil conservationists (United States Department of Agriculture 1953, 1961, 1981). Using these observations it is possible to select those soils conducive to aboriginal use and predict the yield potential for each. Although soil characteristics have changed since the Mississippian occupational period, modern measurements should be sufficiently proportional to their prehistoric values to allow us to use them to scale our model's parameters to fit the East Tennessee situation.
Not all soils would have been suitable for primitive hoe agriculture. Soil characteristics of slope, depth, drainage, and tendency to erode combine to form a capability grouping useful in determining limitations for modern land development (United States Department of Agriculture 1981:62-63). This index refers to soils as Class I (no limitations) through Class VIII (extreme limitations on crop produc-
tion). Specific limitations are also coded using designations like IIe to indicate susceptibility to erosion and IIw to indicate a tendency to flood. Under minimal technologies, only Class I and some II, IIe, and IIw soils could be expected to be used by Mississippian cultures. All others would require extensive management practices, by today's standards, in order to produce marketable crops. Capability groupings are readily available for Monroe and Loudon county soils. Blount designations are lacking and require estimation based on cross-correlations with soil types from the adjacent counties. The 40 soils selected on the basis of capability grouping and potential yield are listed in Table 7. These are the soils most likely to be used by Mississippian farmers.
To estimate yield under aboriginal conditions, maximum, modern maize yields were equated with our expected prehistoric yield of 18.8 quintals/ha. These values are 72.19, 48.96, and 62.77 quintals/ha for Monroe, Blount, and Loudon counties, respectively. The relatively low yields for Blount County are a reflection of the 1950's agricultural technology. Today we would expect the measures to be proportionally higher and in line with the figures quoted for the other counties. If we multiply each soil type's modern yield estimate, as given in the soil reports, by the appropriate 18.8/(modern maximum) value we will have estimates of the aboriginal yields of each soil type. These are listed in Table 7 along with the surface area represented by each type. The product of each type's maximum yield and surface area is the maximum potential harvest for that type. The sum of these harvests divided by the total field area (29185.4 ha) for the study area is the weighted average maximum potential yield for the Valley. This is calculated to
be 17.06 quintals/ha and represents the standardized yield estimate for the 40 soil types. All yield equations (3.7-3.9) can be rescaled by 17.06/18.8 to adjust to these region specific potentials. It is possible that those soils subject to flooding and erosion may not have been usable by prehistoric populations. If this were the case, only Class I soils would have been used. This would result in 19559.2 ha of arable land and a valley-wide average yield of 17.35 quintals/ha. Because the average maximum yields are approximately equal, we can simplify our calculations by assigning their average (17.2 quintals/ha) as the overall Valley yield potential. The total arable land ranges between 19559.2 and 29185.4 ha. As a shorthand notation, we will refer to these sizes as L and H, respectively. By comparison, the more extensive Moundville settlement system along Alabama's Black Warrior River appears to have been supported by only 11,095 ha of arable land (Peebles 1978:407).
Applying the Model
The application of the model involves two steps. The first consists of defining the interacting variables in terms of the physical and behavioral restraints pertinent to an East Tennessee setting. As discussed above, most of these parameters will be expressed as bounded ranges rather than single values. This continuum of initialization conditions will still be useful in providing the output that constitutes the second step of generating model responses to these parameters.
Stability was initially defined as a measure of a system's maintainability in the presence of changing conditions. In particular, we
want to determine the conditions which might encourage the system's response to converge on non-maintainable situations given behavioral and physical restraints. These situations are, topologically speaking, critical points in the phase space of a Mississippian agricultural system. The primary response variable at these points is a measure of insufficient arable land to meet demand at some point in time, t. To simplify and place this discussion into the perspective of temporally defined archaeological phase-shifts, this variable is defined to be the time in years since t=0 required for the system conditions to reach some level of failure. Before developing a notation to simplify this discussion, the specific physical and behavioral restraints should be listed.
The model can be formulated in terms of the following restraints and rules:
A. Physical Restraints
become (E0 = 9.14 and s0 = 3.03) (substitute 2t for t to account for weedy plants) :
will abandon the Valley. If, after the recovery period (125 years), the population should need to return it will do so at the P(t+125) level.
To implement the dynamics of this model, a Pascal program (Appendix B) was developed. This algorithm, with relevant adjustments, served as the basis for the following observations. Unless otherwise noted, all output was the result of a single simulation using the same sequence of random [n(0,1)] deviates (Kolmogorov-Smirnov Z = 0.844, p = 0.416) to estimate annual yields (using 4.3 and 4.4). We will use the notation, (P0,r,fs,R), to represent the initialization parameters of starting population, population growth e, field size per person (* will denote an adjustable value), and total area of the land reservoir (L = 19559.2 and H = 29185.4 ha). Thus, a simulation using a starting population of 100, a growth rate of 0.003, 0.1 ha planted per person , and 19559.2 ha of land is denoted by:
As P0, r, fs, and the net value of R vary, does the system lose its ability to maintain itself in terms of supplying its population's harvest needs (Ct )? This is the basic question to be addressed by examining the response of the system to different sets of input parameters.
As stated, the system's response can be simplistically reduced to the maintenance of some potential function, V (see page 5). If dV/dx=0
then stability is defined. If, for some t, dV/dx is undefined the point, t, is considered a critical point. In a system's sense, this occurrence is termed a catastrophe and a discontinuous transition in the form of an archaeological phase shift will take place. There can be two kinds of "conflicts" that might induce such adjustments given a system trajectory that converges on a critical point. The first occurs when the population's need for land exceeds the finite amount of available land. Such an occurrence will be referred to as a fissioning point: the time, t, when P must be reduced sufficiently so as not to exceed the tnumber of people that can be ported. The second type of critical point occurs when no land remains in the land reservoir. In this case total soil depletion takes place and the system collapses (Valley abandonment). We can refer to these situations as system transition points and represent them as functions of the starting parameters. In both cases one or more of the initialization parameters must be adjusted in order to maintain acceptable levels of system production. The point (in years after t=0) of first fissioning can be denoted as:
Similarly, the critical point of first total soil depletion will be:
The values of Sf and Sd will be said to be undefined when, for a given set of parameters, either fissioning or total depletion does not occur. In stability terms, the initialization parameters fail to cause the system to converge on a critical point over the 800 year study period. In the case of an undefined Sf the system can be said to be relatively stable. In the absence of a real valued Sd , however, unstable periods
may occur. To analyze the model we will consider three classes of parameter values. From these special cases we will be able to extrapolate the dynamics of a Mississippian agricultural system.
In the first case r will be a positive value and fs will be fixed. This will be useful in demonstrating the affect of individual parameters on the values of Sf and Sd. In particular, we need to map the interaction of different values of P0 and r over an 800 year period and determine their influence on defining the duration of Sf and Sd.
The second type sets r equal to 0.0 for P0 set to the largest value producing an undefined response for Sf and Sd , respectively. In this situation we are able to examine the affect of zero-growth, carrying capacity arguments used by other researchers. It will be shown that these values are representative of all conditions producing undefined responses (i.e. where P0 is less than this maximum value). Therefore, we can define a small subset of all possible input parameters to summarize a precariously successful system.
The final situation will involve adjusting fs such that the size of the fields increases in response to current need and past production experience. This is a more realistic approach to defining fs where the parameter starts out small and increases in size according to the system's needs. By combining this approach with the zero growth P0 values, we can produce generalized models of system response under optimal, Mississippian conditions. This application best represents the probable trajectory of Mississippian systems. The output under these conditions will be used to correlate this model with the archaeological record.
The values of Sf for fixed fs of 0.1, 0.2, 0.3, and 0.4 ha/person and 0.003 through 0.017 values of r are presented in Appendices C (R = 19559.2 ha) and D (R = 29185.4 ha). Similar projections for Sd are given in Appendices E and F. From these we can observe the trivial verification that successively larger P0's and r's produce successively smaller critical points (earlier conflicts) for a given fs. From a nontrivial perspective, we also sense that fs values have an impact on the system's response. For example, comparing Sf (400,0.003,0.1,L) with Sf (400,0.003,0.2,L) suggests that smaller fs values imply later Sf critical points. Yet, this only holds true for the upper portion of the fs = 0.1 matrices [see Sf(400,0.003,0.2,L) versus Sf(400,0.003,0.3,L)]. A look at the mean harvest, surplus, and duration of land use per field (response statistics) for common values of P0 and r suggests that the Sf values mask important measures of system "quality".
Increasing the fixed field size results in decreased harvest potential while improving surplus and field life expectancy. This interaction requires some elaboration.
Harvest potential is an a posterior function of time that is "locked" by our sequence of random deviates just as the real system's weather patterns are now locked historically. Surplus, on the other hand, is a culturally regulated response. It is dependent on the demand curve and the amount of land allocated to each individual. Although climatic potential cannot be influenced behaviorally, cultures can
minimize its environmental impact by making technical adjustments. The function, YF, gives us the minimum harvest required to sustain the needs of the population. We can observe the interaction of harvest potential and various behavioral choices, in the form of selecting fs, by plotting this minimum requirement curve against the simulated harvests for fs values of 0.1 and 0.4 ha/person (Figures 13 and 14).
The relatively high position of the minimum demand curve for 0.1 ha/person results in a significant number of crop failures (harvest points below the curve). After frequent crop failures we would expect the new fields to support higher yield potentials according to (4.1). This is reflected in Figure 13's wider dispersion of harvest values compared with that shown in Figure 14 for 0.4 ha/person. Although forced field abandonment tends to raise the yield potential (as seen in the higher mean harvest for 0.1 ha/person fields), in the face of increased demand, small f choices will fail to meet the population's srequirements. Figure 14 shows the flattening effect of larger field sizes on the minimum yield curve. We also see a tighter distribution of harvest values as a result of the extended planting duration brought about by, in a sense, over planting. Even in a bad year, if enough land is planted, sufficient harvest needs can be met. This will occur at the expense of increased labor costs.
What adaptive lessons can be learned from these observations? First, planting smaller fields, although desirable from a conservation and labor point of view, is not a productive solution for expanding agricultural societies. A gardening approach could not sustain the trends we see in Mississippian demand. Secondly, the use of larger
Figure 13. Minimum required harvest versus real harvests for fs of 0.1 ha/person
Figure 14. Minimum required harvest versus real harvests for fs of 0.4 ha/person
fields to compensate for this growing demand will, perhaps surprisingly, extend the use life of the land reservoir while producing higher surpluses at the expense of increased demands on labor. At some point, society may become unwilling to contribute to such a labor intensive system.
If there is an indication that Mississippian agricultural systems are unstable, it lies in the Sd values in Appendices E and F. Isolated, undefined values of Sd and nonlinear trends separating adjacent conditions for fixed fs indicate a highly variable response pattern. In many cases an undefined point like Sd(1000,0.008,0.4,L) reflects an illconditioned set of parameters causing repeated population fluctuations (see Figure 15). Slight shifts in Pt could change a system's trajectory from a maintainable trend to a more disastrous one rather quickly. Also, the repeated values of Sd for differing initialization parameters suggests the existence of attractive critical points. That is, common system conditions that inevitably develop from different trajectory paths. These are qualitative indications of instability.
Throughout this part of the examination, population growth has not demonstrated an impact. Indeed, the contribution of population pressure on determining the longevity of the system is only manifested when fields are abandoned and new land is needed at the fs rate. Yet, in situations where fissioning occurs, the fluctuations in Pt are important indicators of system stress. By mapping Pt over time we can quantify societal conflicts for growing (r > 0.0) populations. A system trajectory like that shown in Figure 15, where multiple fissioning is required to maintain the system, forces the parent society to develop
Figure 15. Pt for (1000,0.008,0.4,L)
stabilization protocols and colonization capabilities. The implication of these organizational structures on Mississippian settlement systems will be discussed in the next chapter, but it should be clear that system maintenance will involve more than just agrarian decisions. Stress management in the form of carrying capacity control will also be needed.
As discussed earlier, some have argued that r is sufficiently small so that Mississippian populations can be considered stationary. Although not supported here, adoption of this theory does offer a way to quantify sets of undefined responses. All so called zero-growth P0's, where r is set to 0.0, which fail to converge on a critical point under either Sf or Sd conditions will display exactly the same system responses (average harvest, surplus, and planting duration per field) for common associated values of fs . Through iteration we can determine the zero-growth limits for each value of fs . Figure 16 is a graph of these values for total land reservoirs of 19559.2 and 29185.4 ha. Table 8 lists the response statistics for a few of these P0 values and Table 9 provides these values for the total depletion situation.
Holding fs constant, all zero-growth P0 values below the maximums listed in Table 9 will yield constant response statistics over the 800 years of simulated system development. This result may not be evident from the model definition. Restated, all cultural systems that, regardless of their initialization parameters, respond to ecological pressure by reducing population levels will perform equally well independent of Pt for all t until a Sd critical point is reached. It therefore follows that the curves in Figure 16 loosely approximate the
Figure 16. Maximum zero-growth P0 values for various fs specifications and total land reservoir limits of 19559.2 and 29185.4 ha
carrying capacities of Mississippian populations in the study region for specific, constant fs choices. However, we would not expect societies to use fixed fs levels over an 800 year period while demand is allowed to increase exponentially. This brings us to the third and last method of applying our model.
It would seem reasonable to expect fs to grow in size as demand, Ct , increases. To simulate this, we can superimpose the rule that after each field failure, fs is adjusted in a way that extends the next field's planting duration based on the last field's mean harvest and Pt's current Ct requirements. As Ct rises so will the value of fs. We will further stipulate that fs will never decrease despite occasional short term peaks in harvest potential that might encourage such a reduction. Over time, fs will now be a nondecreasing function of harvest potential and Ct. Appendix G presents the resulting Sf values for both levels of R. Appendix H provides the Sd values. The maximum zero-growth P0 values for nonconverging responses are 4010 (Sf, R = 19559.2 ha) and 8224 (Sd, R = 19559.2 ha). For R = 29185.4 ha the maximum zero-growth P0's will be 5984 (Sf) and 7850 (Sd). The mean response statistics per field are:
with an overall mean fs of 0.255 ha/person.
Using (4010,0.0,*,L) (where * denotes an adjustable fs value) we scan plot shifts in f (Figure 17) and the minimum required yield against harvest (Figure 18) over the study period. The dynamics shown here, based on all the preceding data, are our best estimation of a successful
Figure 17. Adjusted fs values for (4010,0.0,*,L)
Figure 18. Minimum required harvest versus real harvests for (4010,0.0,*,L)
East Tennessee Mississippian agricultural system. We see a sharp increase in fs over the first century (Mississippian I) followed by small, gradual increases until A.D. 1200 (Mississippian II) at which time more frequent adjustments occur. By A.D. 1300 the sharpest increase in Ct sparks a rapid rise in fs and, with it, a concomitant increase in surplus potential. The critical transition points appear to coincide with major Mississippian phase changes. If the real system were to fail as a result of cultural inflexibility, it would most likely do so ca. A.D. 950, 1200, 1325, and 1550. If r >> 0, we would expect this process to be exacerbated. The results in Appendix H suggest that under such circumstances total system collapse might occur ca. A.D. 1187, 1327, 1394, 1585, and 1629. However, earlier fissioning would probably put extreme pressure on the society prior to complete collapse.
If we approximate the potential function as a mapping of the land reservoir over time (Figure 19) for (4010,0,*,L) we can more fully characterize the dynamics of this system. As an approximation of V, this curve indicates that, at best, the Mississippian Period will consist of two centuries of unstable conditions (A.D. 900-1000 and 1300 1400) separated by a long, stable phase. This pattern is a response to behavioral decisions being superimposed on a ecological system. Mississippian I can be characterized as a period of technological development when hunters became part-time farmers under a low demand situation. During Mississippian II fs reaches a proper balance with demand and a stable situation occurs. By A.D. 1300 demand starts to increase and, despite fs adjustments, the system is driven towards a possible collapse ca. A.D. 1400. By slightly increasing P0, t = 1000
Figure 19. Land reservoir levels for (4010,0.0,*,L)
and 1400 will become critical points, which coincide with the more general results in Appendix H.
From the standpoint of stability, Appendices E, F, and H strongly imply the existence of a finite set of such critical points under almost all probable initialization conditions. Figure 19 graphically represents the Mississippian Period as a continuum of stable and unstable phases which correlate with both palynological and chronometric data. More exacting specification of P0 and r, based on future analyses, would improve model accountability. Until such time, we are left with this attempt to demonstrate the range of growth limitations and the predisposition of such systems to require cultural adjustments at predictable points. A summary of the implications of this data on archaeological interpretations follows in Chapter V.