Mn/Model Final Report Chapter 8: Model Results and Interpretation

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Appendices

Chapter 8

Model Results and Interpretations

By Elizabeth Hobbs, Craig M. Johnson, Guy E. Gibbon, Carol Sersland, Mark Ellis, and Tatiana Nawrocki

Statewide Survey Impelmentation Model Map

Chapter 8 Table of Contents
8.1   Introduction
8.2 Model Description
         8.2.1 Environmental Context
         8.2.2 Types of Models
8.3   Model Evaluation
8.4   Model Interpretation
         8.4.1 Presentation of Interpretations
         8.4.2 Previously Identified Variables
8.5   Model Comparison
         8.5.1 Subsection Group Approach
         8.5.2 Site Catchment Analysis
         8.5.3 Cultural Context and Site Location
         8.5.4 SHPO Intuitive Model
8.6   Model Results
         8.6.1 Phase 1 Results
         8.6.2 Phase 2 Results
         8.6.3 Phase 3 Results
8.7   Agassiz Lowlands
8.8   Anoka Sand Plain
8.9   Aspen Parklands
8.10 Big Woods
8.11 Blufflands
8.12 Border Lakes
8.13 Chippewa Plains
8.14 Coteau Moraines / Inner Coteau
8.15 Glacial Lake Superior Plain/Northshore highlands/ Nashwauk Uplands
8.16 Hardwood Hills
8.17 Laurentian Highlands
8.18 Littlefork-Vermilion Uplands
8.19 Mille Lacs Uplands
8.20 Minnesota River Prairie
8.21 Oak Savanna
8.22 Pine Moraines & Outwash Plains
8.23 Red River Prairie
8.24 Rochester Plateau
8.25 St. Croix Moraines and Outwash Plains (Twin Cities Highlands)
8.26 St. Louis Moraines/ Tamarack Lowlands
8.27 Conclusion
        References

8.6 MODEL RESULTS

8.6.1 Phase 1 Results

In Phase 1 of the project, models for sites excluding single artifacts were developed only for the 29 counties for which "probabilistic" surveys were available (Figure 4.5). These were grouped into five archaeological resource regions (Section 4.6.1) for modeling. Since it was not possible to acquire and convert data for all of these counties in time to meet modeling deadlines, some of the counties were not modeled or were modeled only for one region when they otherwise would have been modeled for two regions. The regions necessarily had incomplete and sometimes discontinuous coverage.

Models were built using only sites from "probabilistic" surveys, excluding single artifacts. All other sites in the counties modeled were used to test the models. Negative survey locations represented non-sites. Modeling methods for this initial phase of the project are discussed in Section 7.3.

Some of these regions were too large and contained too much environmental variability to model well using such small site numbers and environmental data from distant and disjunct areas. For example, when models developed for Nicollet County were applied to all counties in the Prairie Lakes Region, they performed well for counties near Nicollet County but not as well for distant counties. In the Central Lakes Coniferous Region, models performed better for centrally located counties that had more data and less well for counties on the margins of the region, which had fewer sites.

Because of bias in the locations of "probabilistic" surveys (see Chapter 5), there was not a wide range of environmental difference between sites and non-sites. This weakens the models in two ways. First, it reduces the ability of the statistical analysis to distinguish between sites and non-sites. Second, it fails to represent all possible environmental settings, providing potentially fallacious predictions for unsampled landscapes.

In general, site numbers used to build the models were extremely low - only sites from "probabilistic" surveys and then only from some of the counties in each region. Within the modeled areas, only 576 sites were available that met the criteria. However, there is no apparent relationship between the performance of the models and the number of sites used to build them (Table 8.6.1). Site numbers were not, in fact, significantly lower than those used to build individual Phase 2 models excluding single artifacts (Table 8.6.2).

Table 8.6.1. Evaluation of Basic Phase 1 Models, Percent Known Sites (excluding single artifacts) in Each Site Potential Class.

Modeling Region	# Sites Modeled	% Low	% Medium	% High	% High /Medium	Gain
Nicollet County (pilot)	31	0	14	86	100	0.34
Prairie Lakes	190	11	18	71	89	0.26
Southeast Riverine	87	8	13	79	92	0.29
Southwest Riverine	41	8	17	75	92	0.29
Central Lakes Deciduous	227	14	27	58	85	0.22
Central Lakes Coniferous	147	2	13	85	98	0.33
Average	96	7	17	76	93	0.29

Phase 1 models were run using logistic regression in GRID, not S-Plus. This undoubtedly produced weaker models than Phases 2 and 3 for two reasons. First, because there is no stepwise function in GRID for selecting the best model variables, only a limited number of variable combinations could be tried. There is no guarantee that any of these models represents the absolute best set of variables from those available. Second, variable coefficients are rounded in GRID, sometimes to zero for small coefficients. As we found out in Phase 2, small differences in coefficients and attributing zero values to variables with small coefficients can make a considerable difference in model performance.

All Phase 1 models had approximately 33 percent of the landscape classified in each of the low, medium, and high site potential zones (Figure 8.4a). Regional models varied primarily in how many sites were predicted to be in the high site potential zone. These models had gain statistics ranging from 0.22 to 0.34 (Table 8.6.1). Gain statistic values are low because the high and medium probability areas were, by definition, 66 percent of the landscape. The strongest model was developed for a small, homogeneous area (Nicollet County.) The weakest model was for the Central Lakes Deciduous Region (Figure 2.2), where the area modeled was large and the data discontinuous.

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8.6.2 Phase 2 Results

Phase 2 models were developed for all 87 counties, divided into 15 modeling regions based on archaeological resource regions (Section 4.6.2). Modeling methods are discussed in Section 7.3. Several variations of site probability models were developed. Basic models refer to those developed using variables that were available statewide. Enhanced models also included variables that were available for only limited parts of the state. Basic and enhanced models were developed for two populations of known sites, one excluding only single artifacts and the other excluding both single artifacts and lithic scatters. A total of 1,815 sites were available statewide that met all modeling criteria and excluded single artifacts. When lithic scatters were removed, this reduced the statewide dataset by 43 percent to 1,048.

The best Phase 2 basic models are summarized in Tables 8.6.2 and 8.6.3. The composite of models excluding only single artifacts is illustrated in Figure 8.4b. A goal set at the beginning of this phase of the project was to develop models with 85 percent of the known sites predicted in 33 percent of the area modeled. That would be the equivalent of a gain statistic of 0.61. Seventy-three percent of the models developed with only single artifacts excluded and 36 percent of those with lithic scatters also excluded met or exceeded this goal. Models excluding only single artifacts produced gains statistics ranging from 0.28 to 0.89, with an average gain of 0.68 (Table 8.6.2). Models excluding both single artifacts and lithic scatters had gains from 0.12 to 0.94, with an average gain of 0.61 (Table 8.6.3).

These results indicate that models excluding only single artifacts performed, on average, much better than models excluding single artifacts and lithic scatters. However, results varied between regions. While gain statistics for some regions may decline from incorporating lithic scatters as part of the database, this loss is less than 0.10 in all but two regions (Table 8.6.4). However, the increased gain from including lithic scatters is less than 0.10 in only one region. On the average, the gain statistic increases by 0.11 from including lithic scatters in the database. Whether the improvement is attributable to the particular information contained in the lithic scatter locations or simply due to the increase in the number of sites modeled could be debated. The Lake Superior model would not run at all when removing lithic scatters reduced the database from eight sites to three. Certainly the inclination is to have more confidence in models built with large numbers of sites. However, all of the site populations modeled in Phase 2 are smaller than ideal for multivariate analysis. The inclusion of lithic scatters could improve models in cases where lithic scatters have similar environmental settings as other modeled sites by enhancing the detectable pattern. On the other hand, if lithic scatters are found in different environmental settings, or if there is no pattern to where they are found, they could degrade model performance by muddling the "pattern." Consequently, it is important to remember that the detectable pattern from such small site populations, no matter how distinct, may not be representative of the entire universe of sites, most of which have not yet been found. Even relatively modest changes in the number and characteristics of the site population may exert a strong influence on model results. Only very large site populations from a random sample of all landscapes in a region will produce a representative database for modeling.

Table 8.6.2. Best Phase 2 Basic Models (excluding single artifacts).

Modeling Region	# Sites Modeled	% Area High/ Medium	% Sites Predicted	Gain
Southwest Riverine	41	35	86	0.59
Prairie Lakes East	77	25	64	0.61
Prairie Lakes North	120	20	71	0.71
Prairie Lakes South	209	20	77	0.74
Southeast Riverine East	58	34	72	0.53
Southeast Riverine West	63	63	87	0.28
Central Lakes Deciduous East	278	18	82	0.78
Central Lakes Deciduous South	199	24	81	0.70
Central Lakes Deciduous West	165	18	81	0.78
Central Lakes Coniferous South and East	119	15	78	0.81
Central Lakes Coniferous Central, North, and West	236	19	77	0.75
Red River Valley	80	19	79	0.76
Northern Bog	8	33	59	0.44
Border Lakes	154	10	81	0.88
Lake Superior	8	8	74	0.89
Average	121	24	77	0.68

Table 8.6.3. Best Phase 2 Basic Models (excluding single artifacts and lithic scatters).

Modeling Region	# Sites Modeled	% Area High/ Medium	% Sites Predicted	Gain
Southwest Riverine	11	80	91	0.12
Prairie Lakes East	29	30	56	0.46
Prairie Lakes North	74	49	66	0.26
Prairie Lakes South	91	40	82	0.51
Southeast Riverine East	38	17	62	0.73
Southeast Riverine West	54	48	81	0.41
Central Lakes Deciduous East	196	10	76	0.87
Central Lakes Deciduous South	105	34	80	0.58
Central Lakes Deciduous West	103	19	81	0.77
Central Lakes Coniferous South and East	5	22	43	0.49
Central Lakes Coniferous Central, North, and West	171	43	84	0.49
Red River Valley	44	15	78	0.81
Northern Bog	6	44	81	0.46
Border Lakes	118	5	78	0.94
Lake Superior	3	NA	NA	NA
Average	70	35	80	0.61

Table 8.6.4. Comparison of Phase 2 Models With and Without Lithic Scatters.

Modeled Region	Difference in number of sites modeled (number of lithic scatters)	Lithic scatters as percentage of all sites excluding single artifacts	Gain excluding single artifacts minus gain also excluding lithic scatters
Southwest Riverine	30	73	0.47
Prairie Lakes East	48	62	0.15
Prairie Lakes North	46	38	0.45
Prairie Lakes South	118	56	0.23
Southeast Riverine East	20	34	-0.20
Southeast Riverine West	113	68	-0.13
Central Lakes Deciduous East	82	29	-0.09
Central Lakes Deciduous South	94	47	0.12
Central Lakes Deciduous West	62	38	0.01
Central Lakes Coniferous South and East	114	96	0.32
Central Lakes Coniferous Central, North, and West	65	28	0.26
Red River Valley	36	45	-0.05
Northern Bog	2	25	-0.02
Border Lakes	36	23	-0.06
Lake Superior	5	63	N.A.
Mean	58	48	0.11

8.6.2.1 Improvement over Phase 1 models

To measure the improvement of Phase 2 models over Phase 1 models, the Phase 1 models were extended to other counties in the Phase 2 model subregions of which they are a part (Table 8.6.5). For this analysis, Phase 1 models were classified into three probability classes following the same procedures used in the Phase 2 modeling (Section 7.5.1.2).

In these fourteen subregions, the gain statistic improved an average of 0.29 from Phase 1 to Phase 2. This improvement is attributable to several factors. Most important, the variable selection procedure in S-Plus allows consideration of all the variables in the dataset at once. Most Phase 1 models were developed using only logistic regression in GRID, which takes only a small number of variables at once. For those models, variables had to be grouped subjectively for evaluation. The only model from Phase 1 that performs better for a subregion than the Phase 2 model was in Central Lakes Coniferous South. This is the only Phase 1 model that was developed using variable selection in S-Plus. Additional factors contributing to model improvement are the increase in the number of sites available for modeling, the addition of vegetation data from Marschner, and the modeling of subregions, which in some regions reduces the environmental diversity being considered.

Table 8.6.5. Evaluation of Best Phase 1 Model vs. Best Phase 2 Basic Model (excluding single artifacts).

Modeling Region	Phase 1 Model			Phase 2 Model
	% Area H/M	% Sites Predicted	Gain	% Area H/M	% Sites Predicted	Gain
Southwest Riverine	45	83	0.46	35	86	0.59
Prairie Lakes East	60	82	0.27	25	64	0.61
Prairie Lakes North	63	84	0.25	20	71	0.71
Prairie Lakes South	59	85	0.31	20	77	0.74
Prairie Lakes East	52	83	0.38	34	72	0.53
Southeast Riverine West	67	86	0.22	63	87	0.28
Central Lakes Deciduous East	67	86	0.22	18	82	0.78
Central Lakes Deciduous South	47	73	0.36	24	81	0.70
Central Lakes Deciduous West	76	87	0.13	18	81	0.78
Central Lakes Coniferous West	41	83	0.51	18	76	0.76
Central Lakes Coniferous East	77	89	0.51	15	82	0.82
Central Lakes Coniferous North	39	85	0.54	19	84	0.77
Central Lakes Coniferous South	35	91	0.62	15	25	0.40
Central Lakes Coniferous West	49	85	0.42	19	63	0.70
Average	55.5	84	0.37	24.5	74	0.66

H/M = High/Medium

8.6.2.2 Contributions of Individual Variables

With square root, sine, and cosine transformations included, a total of 120 basic variables were evaluated in each Phase 2 model run (Table 8.6.6). Two additional variables (distance to nearest bedrock outcrop and the square root of the same) were evaluated in the two Southeast Riverine subregions. Considerable redundancy was contributed to the data by slightly different versions of some environmental characteristics (i.e. distance to lakes, distance to large lakes, distance to permanent lakes) and by transformations (square root, sine, cosine) of most variables.

The variable probabilities reported by S-Plus are the best measure for comparison of the performance of individual variables (Section 8.3). Of the 122 variables evaluated in 30 models, all but 13 were assigned a probability greater than zero in at least one model (Table 8.6.6). Fifty-six variables had a maximum probability of 100 in at least one of the thirty runs. Thirteen more had maximum probabilities greater than 80. The cumulative probability is provided in Table 8.6.6 as a measure for ranking variables on a statewide basis. This value was obtained by multiplying the number of model runs in which each variable is not zero by the mean probability for that variable. The results were then analyzed to determine which variables performed best.

Several things are apparent from this analysis. First, transformed variables are better predictors than their untransformed counterparts. Second, distances to large, permanent or perennial water bodies are more consistently useful measures than many of the other distance to water variables. Third, any kind of water or wetland may provide protection from fire and other related resources, such as wood for fuel.

The prominent role of topographic variables suggests they are more universal, applying to a broad range of archaeological regions. It could be that since there are fewer of these landscape variables, there is less repetition or redundancy in what they are measuring versus a much larger suite of water-related variables considered for model construction. Moreover, subtle variations in topography may serve as surrogates for other factors, such as landscape scale vegetation patterns, soil drainage, or visibility, which are not adequately represented in the database. The importance and meaning of these and other variables can only be evaluated with further analysis.

Table 8.6.6. Performance of All Phase 2 Basic Variables in 30 Model Runs.

Columns indicate the number of models in which each variable had probability greater than zero, the maximum probability recorded, and the cumulative probability.

BASIC VARIABLE	Number of Models	Maximum Probability	Cumulative Probability

Elevation	8	100	676.16
On alluvium	1	0.8	0.8
Prevailing orientation	2	87.5	186.2
On colluvium	0		0
Distance to well-drained soils	1	60.9	60.9
Square root of distance to well-drained soils	2	4.7	13.8
Distance to edge of nearest large lake	5	100	492.5
Square root of distance to edge of nearest large lake	10	100	859
Distance to edge of nearest large area of organic soils	3	97.9	153
Square root of distance to edge of nearest large area of organic soils	4	100	257.6
Distance to edge of nearest large wetland	5	96.6	213
Square root of distance to edge of nearest large wetland	5	100	311.5
Distance to edge of nearest lake, wetland, or area of organic soils	3	22.8	34.2
Square root of distance to edge of nearest lake, wetland, or area of organic soils	4	59.2	98
Distance to edge of nearest lake, wetland, area of organic soils, or stream	4	100	146
Square root of distance to edge of nearest lake, wetland, area of organic soils, or stream	1	18.1	18.1
Distance to edge of nearest lake	5	78.6	132.5
Square root of distance to edge of nearest lake	5	93.1	233.5
Distance to edge of nearest marsh	3	20.1	34.8
Square root of distance to edge of nearest marsh	2	9.3	13.2
Distance to edge of nearest large river	3	38.7	56.7
Square rot of distance to edge of nearest large river	2	100	200
Distance to edge of nearest area of organic soils	5	100	426
Square root of distance to edge of nearest area of organic soils	5	100	297.5
Distance to edge of nearest permanent lake	9	100	594
Square root of distance to edge of nearest permanent lake	9	100	603.9
Distance to edge of nearest perennial river or stream	5	100	317.5
Square root of distance to edge of nearest perennial river or stream	9	100	856.8
Distance to edge of nearest river or stream	3	100	135.9
Square root of distance to edge of nearest river or stream	0		0
Distance to edge of nearest swamp	1	2.9	2.9
Square root of distance to edge of nearest swamp	4	100	233.6
Distance to edge of nearest wetland	4	79.7	95.2
Square root of distance to edge of nearest wetland	3	9.4	21.6
Depth to bedrock	3	94.5	184.5
Distance to nearest intermittent stream	3	100	138.6
Square root of distance to nearest intermittent stream	4	100	244.8
Direction to nearest permanent water	2	66.6	69
Sine of direction to nearest permanent water	1	39.3	39.3
Cosine of direction to nearest permanent water	1	28	28
Direction to nearest water	1	33.2	33.2
Sine of direction to nearest water	1	48.2	48.2
Cosine of direction to nearest water	2	24.8	27.8
Direction to nearest water or wetland	6	100	532.8
Sine of direction to nearest water or wetland	8	100	703.2
Cosine of direction to nearest water or wetland	2	100	200
Distance to bedrock outcrops	1	13.7	13.7
Square root of distance to bedrock outcrops	1	3.5	3.5
Distance to aspen-birch	2	100	200
Square root of distance to aspen-birch	3	100	293.4
Distance to birch	2	1.5	1.9
Square root of distance to birch	1	100	100
Distance to brushland	1	100	100
Square root of distance to brushland	0		0
Distance to Big Woods	2	91.8	103.6
Square root of distance to Big Woods	2	11.8	23.6
Distance to conifers	0		0
Square root of distance to conifers	3	100	215.4
Distance to cranberry	2	100	101.6
Square root of distance to cranberry	2	41.5	45
Distance to hardwoods	6	100	361.8
Square root of distance to hardwoods	5	100	149.5
Distance to Kentucky coffee tree	2	43.7	53.8
Square root of distance to Kentucky coffee tree	1	9.1	9.1
Distance to glacial lake sediments	8	100	286.4
Square root of distance to glacial lake sediments	5	100	356
Distance to sugar maple	5	100	324.5
Square root of distance to sugar maple	5	100	185
Distance to mixed hardwoods and conifers	3	99.4	116.1
Square root of distance to mixed hardwoods and conifers	3	100	204.3
Distance to oak woodland	0		0
Square root of distance to oak woodland	1	100	100
Distance to pine barrens or flats	4	100	258.4
Square root of distance to pine barrens or flats	1	4.7	4.7
Distance to pine groves	1	4.3	4.3
Square root of distance to pine groves	2	7.9	10.6
Distance to prairie	2	11.2	20.4
Square root of distance to prairie	4	100	296
Distance to river bottom forest	7	100	510.3
Square root of distance to river bottom forest	4	100	293.6
Distance to woodland	0		0
Square root of distance to woodland	1	2.8	2.8
Distance to nearest perennial stream	2	100	103.4
Square root of distance to nearest perennial stream	4	100	335.6
Soil drainage	0		0
Height above surroundings	7	100	511
Square root of height above surroundings	10	100	812
Distance to nearest lake or wetland inlet/outlet	1	3.5	3.5
Square root of distance to nearest lake or wetland inlet/outlet	2	11.6	13.6
Solar insolation	0		0
Distance to nearest lake inlet/outlet	2	11.8	17.6
Square root of distance to nearest lake inlet/outlet	1	81.9	81.9
On glacial lake sediment	1	37.6	37.6
Size of nearest lake	2	95.8	101.4
Square root of size of nearest lake	2	94.5	131.8
Distance to nearest permanent lake inlet/outlet	3	100	237.3
Square root of distance to nearest permanent lake inlet/outlet	6	100	531.6
On mine pits or dumps	0		0
Vegetation diversity within 0.5 km	2	82.5	93.4
Vegetation diversity within 1 km	3	100	223.8
On peat	0		0
Distance to nearest confluence between perennial streams and large rivers	2	100	104.4
Size of nearest permanent lake	4	100	244
Square root of size of nearest permanent lake	4	64.1	217.6
Relative elevation	7	100	403.9
Square root of relative elevation	12	100	538.8
Surface roughness	6	100	532.8
Distance to nearest confluence between perennial or intermittent streams and large rivers	3	94.9	122.7
Square root of distance to nearest confluence between perennial or intermittent streams and large rivers	3	100	294.9
Susceptibility to sedimentation	0		0
Slope	5	100	444.5
Square root of slope	3	95.4	157.2
Distance to nearest confluence between streams of different classes	2	6.6	12.6
Square root of distance to nearest confluence between streams of different classes	0		0
On a river terrace	3	100	186.9
Vertical distance to water	2	100	105.6
Vertical distance to permanent water	4	100	144.4
Susceptibility to erosion by water	0		0
Distance to nearest wetland inlet/outlet	3	41.5	45.6
Square root of distance to nearest wetland inlet/outlet	1	5.7	5.7
Distance to nearest permanent wetland inlet/outlet	5	100	252
Square root of distance to nearest permanent wetland inlet/outlet	3	10.7	23.4

Contributions of Trygg Variables

Variables derived from Trygg maps were not strong contributors to the 18 Trygg enhanced models run in Phase 2 (Table 8.6.7). For those that did make significant contributions to models (probabilities greater than 50), four are vegetation variables redundant with information derived from Marschner, although from a higher resolution source scale. Only two significant variables, distance to Native American cultural features and square root of distance to junctures of roads and trails with water and wetlands can be derived only from Trygg map data. Results may be different, however, when Trygg maps can be made available in digital format for the entire state. Both continuous coverage and the opportunity to test all of the variables throughout the state could produce better results.

Table 8.6.7. Performance of All Trygg Variables in 18 Phase 2 Model Runs.

Number of models each variable had probability greater than zero, maximum probability recorded, cumulative probability.

BASIC VARIABLE	Number of Models	Maximum Probability	Cumulative Probability
Distance from grassland (prairie or meadow)	1	88	88
Square root of distance from grassland	1	2.6	2.6
Distance to Native American cultural features	2	100	106.4
Square root of distance to Native American cultural features	0
Distance to roads and trails	0
Square root of distance to roads and trails	0
Distance from wooded land (except swamp)	2	100	117.4
Square root of distance from wooded land	3	100	111.4
Distance to junctures of roads and trails with water and wetland resources	0
Square root of distance to junctures of roads and trails with water and wetlands	1	100	100
Vegetation diversity within 510 meters	1	51.9	51.9
Vegetation diversity within 990 meters	0
Distance to wild rice sites	0
Square root of distance to wild rice sites	0
Distance to beaver sites	0
Square root of distance to beaver sites	0

Contributions of High Resolution Soils Variables

Variables derived from high resolution soils data (digital county soil surveys) were used to enhance 14 Phase 2 model runs. Only three of these variables (mean soil reaction [pH] for the surface layer, square root of distance to edge of nearest hydric soils, square root of distance to edge of nearest large area of hydric soils) showed promise (Table 8.6.8). Like Trygg variables, soil variables may perform better when more extensive and continuous coverage is available. Improvements in the spatial accuracy of many of the digital soils surveys may also help.

Table 8.6.8. Performance of All High Resolution Soils Variables in 14 Phase 2 Model Runs.

Number of models each variable had probability greater than zero, maximum probability recorded, cumulative probability.

SOILS VARIABLE	Number of Models	Maximum Probability	Cumulative Probability
Suitability of soil for archaeological sites, based on soil texture classes	0
Mean depth to the lower boundary of the surface layer	0
Mean value for clay content of the surface layer	1	2.4	2.4
Mean value for the available water capacity for the surface layer	2	6.5	7.6
Mean value for organic matter content of the surface layer	1	1.6	1.6
Mean soil reaction (pH) for the surface layer	2	100	200
Mean permeability rate of the surface layer	2	2.9	5.7
Distance to edge of nearest hydric soils	0
Square root of distance to edge of nearest hydric soils	1	69.5	69.5
Distance to edge of nearest large area of hydric soils	3	42.9	49.6
Square root of distance to edge of nearest large area of hydric soils	4	100	114.6
Distance to edge of nearest water (lakes, wetlands, or hydric soils)	0
Square root of distance to edge of nearest water (lakes, wetlands, or hydric soils)	0
Distance to edge of nearest water (lakes, wetlands, hydric soils, or streams)	0
Square root of distance to edge of nearest water (lakes, wetlands, hydric soils, or streams)	0

The Sparse Population Problem

Once the models have been classified into 20, then three, probability classes, the raw model values are disguised. When the regression equation is applied to a region, it produces a value for each cell, which is the estimated probability of a site occurring in that cell. This value can range from zero to one. The ranges and means of these values vary from region to region (Table 8.6.9).

Table 8.6.9. Raw Model Values for Models Excluding Single Artifacts for Phase 2 Models.

Subregion	Minimum	Mean	Maximum	Std. Dev.
1 Southwest Riverine	0.000	0.116	0.999	0.144
2e Prairie Lakes East	0.000	0.064	0.985	0.111
2n Prairie Lakes North	0.000	0.283	1.000	0.258
2s Prairie Lakes South	0.000	0.445	1.000	0.276
3e Southeast Riverine East	0.000	0.480	0.945	0.253
3w Southeast Riverine West	0.003	0.812	1.000	0.122
4e Central Lakes Deciduous East	0.000	0.032	0.999	0.085
4s Central Lakes Deciduous South	0.001	0.216	0.999	0.221
4w Central Lakes Deciduous West	0.000	0.023	0.998	0.060
5e Central Lakes Coniferous East	0.000	0.216	1.000	0.251
5s Central Lakes Coniferous South	0.000	0.154	0.996	0.212
5c Central Lakes Coniferous Central	0.000	0.167	1.000	0.240
5n Central Lakes Coniferous North	0.000	0.065	0.993	0.144
5w Central Lakes Coniferous West	0.000	0.111	0.999	0.168
6n Red River Valley North	0.000	0.160	0.999	0.176
6s Red River Valley South	0.002	0.237	1.000	0.249
7e Northern Bog East	0.009	0.448	0.745	0.226
7w Northern Bog West	0.001	0.392	0.745	0.241
8 Border Lakes	0.000	0.089	1.000	0.185
9n Lake Superior North	0.001	0.258	0.937	0.280
9s Lake Superior South	0.000	0.138	0.937	0.223

Comparisons of these values provide a rough indication of the relative probability of finding sites within subregions. Mean values, for models excluding single artifacts, range from 0.023 in Central Lakes Deciduous West to 0.812 in Southeast Riverine West. This high value is an outlier and may indicate problems with the model. For models excluding both single artifacts and lithic scatters, means ranged from 0.051 in Central Lakes Coniferous South to 0.599 in Central Lakes Deciduous South (Table 8.6.10). These values should be interpreted with caution. They may reflect the amount of survey that has occurred in these regions, as well as the potential for sites. For less surveyed regions, values may be lower than would be the case based on true site potential. On the other hand, the biased nature of survey locations may result in values higher than true site potential.

Table 8.6.10. Raw Model Values for Models Excluding Single Artifacts and Lithic Scatters for Phase 2 Models.

Subregion	Minimum	Mean	Maximum	Std. Dev.
1 Southwest Riverine	0.003	0.076	0.487	0.069
2e Prairie Lakes East	0.000	0.061	0.508	0.109
2n Prairie Lakes North	0.000	0.243	1.000	0.356
3e Southeast Riverine East	0.014	0.322	0.913	0.258
3w Southeast Riverine West	0.006	0.284	0.982	0.245
4e Central Lakes Deciduous East	0.000	0.081	1.000	0.167
4s Central Lakes Deciduous South	0.000	0.599	1.000	0.309
4w Central Lakes Deciduous West	0.000	0.081	1.000	0.156
5e Central Lakes Coniferous East	0.001	0.074	1.000	0.220
5s Central Lakes Coniferous South	0.001	0.051	1.000	0.184
5c Central Lakes Coniferous Central	0.000	0.333	1.000	0.292
5n Central Lakes Coniferous North	0.000	0.224	1.000	0.247
5w Central Lakes Coniferous West	0.000	0.242	1.000	0.285
6n Red River Valley North	0.000	0.222	0.996	0.245
6s Red River Valley South	0.000	0.396	0.999	0.286
7e Northern Bog East	0.153	0.352	0.997	0.231
7w Northern Bog West	0.177	0.371	0.998	0.237
8 Big Lake	0.000	0.113	1.000	0.239

Comparing model probabilities with data from random surveys, it would appear that the models overestimate site potential. Three random surveys were conducted for this project in the summer of 1996. The Wright County survey found sites on seven percent of the locations surveyed. The model for Central Lakes Deciduous South estimates a mean probability of 0.216, or 22 percent. The Cass County survey had a two percent success rate, which the model for Central Lakes Coniferous Central predicts 0.167 or 17 percent. The Wabasha County survey had the greatest success with sites on 22 percent of the locations surveyed. However, the models for the Southeast Riverine Region predict 0.480 (48 percent and 0.812 (81 percent). Aside from the possible effect of survey bias, this apparent discrepancy can be at least partially explained by unmet potential. In other words, there are more suitable habitats for sites than there are sites. The population density of Minnesota was quite low in the precontact period. Therefore, all suitable locations were not occupied. Consequently, not all places that are equally well-suited for sites contain archaeological properties.

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8.6.3 Phase 3 Results – Statewide Models

This section summarizes the Phase 3 models on a statewide basis. Except for the last model discussed (Section 8.6.3.4), all of the models discussed here are simply composites of the regional models. Section 8.6.4 provides detailed evaluations of the models for each Phase 3 modeling region.

8.6.3.1 Site Probability Model

The site probability models developed in Phase 3 are the counterparts of models developed in Phases 1 and 2. They predict the potential for finding precontact archaeological resources across the state. Figure 8.5 provides a composite map of these 20 models, showing the statewide pattern of site potential from the best Phase 3 models.

The average model predicts 86.8 percent of modeled sites in 25 percent of the region's land area. The average gain statistic is 0.68, and the average Kappa (stability value) is 0.54 (Table 8.6.11). These values reflect averages from 20 regions of different sizes, however. When the composite model is evaluated, 86 percent of all modeled sites in the state, excluding single artifacts, are predicted in high and medium probability zones that constitute only 22.82 percent of the state's area. This produces an overall gain statistic of 0.73. This composite model well exceeds the project's goals of predicting 85 percent of known sites in 33 percent of the land area (for a gain statistic of 0.61). However, because composites of the preliminary models were not developed, no Kappa statistic was calculated statewide. The composite model performed well in 2001, when it was tested with 977 sites that were not available when the models were developed. The statewide model predicted 76.6 percent of the new sites, producing a gain statistic of 0.72 for the test population. For the combined training and testing populations, the model predicted 85.5 percent of known sites and produced a gain statistic of 0.73.

To evaluate the degree of confidence in these models, one must consider a suite of factors (Table 8.6.11). The Gain Statistic may be the least reliable of these. A reliable model should both predict an adequate number of test sites (85 percent) in a relatively small area (33 percent of the landscape) and be at least somewhat stable (Kappa > 0.5). Models for only four of the 20 regions meet these criteria:

Agassiz Lowlands
Aspen Parklands
Border Lakes
Chippewa Plains

However, two of these regions, Agassiz Lowlands and Aspen Parklands, have very few surveyed places. In these cases, the site models may not adequately reflect the distribution of archaeological resources within the subsection.

There is no discernable pattern between the number of sites available for modeling and the overall quality of a model, as measured here. However, any statistical analysis should be improved by a larger sample size. Marginal results achieved by regions with the highest site numbers (Minnesota River Prairie, Big Woods) may have more to do with the nature of the data than with its quantity. Site location errors may be part of the problem, with enough sites erroneously located in unlikely places that it confuses the detectable pattern. For the same reason, model tests may be inaccurate, as site location errors are known to be present in the test data as well. Another possibility is that site function or temporal use may be confusing the analysis. With large samples, the likelihood of having a sizeable number of sites that are different in some way increases. An analysis of the characteristics of sites not predicted by the models may shed some light on this question.

Table 8.6.11. Site Probability Model Performance for All 20 Regions Modeled in Phase 3.

Modeled Region	Site Probability Models
Modeled Region	No. of Modeled Sites	Site Frequency 1	% area Hi/Med	% modeled sites predicted	Modeled Gain	Kappa	No. of Test Sites	% Test Sites Predicted	Test Gain	% Test and Modeled Sites Predicted	Combined Test and Model Gain
Agassiz Lowlands	53	0.00295	19.49	86.79	0.77543	0.55809	7	85.71	0.77258	86.67	0.77512
Anoka Sand Plain	337	0.06599	24.56	83.98	0.70755	0.49125	38	81.58	0.69891	83.73	0.70669
Aspen Parklands	59	0.00561	22.84	83.03	0.72492	0.68100	28	96.43	0.76316	87.36	0.73854
Big Woods	637	0.07934	33.93	86.18	0.60629	0.47874	69	76.81	0.55826	85.27	0.60209
Blufflands	554	0.11336	34.35	87.01	0.60522	0.52492	51	54.90	0.37432	84.30	0.59253
Border Lakes	960	0.10278	18.88	88.54	0.78676	0.67215	154	76.62	0.75358	86.89	0.78271
Chippewa Plains	513	0.06081	26.79	85.96	0.68834	0.62861	158	78.48	0.65864	84.20	0.68183
Coteau Moraines /Inner Coteau	350	0.03152	34.76	86.00	0.59577	0.49626	41	70.73	0.50855	84.40	0.58815
Glacial Lake Superior Plain/ North Shore Highlands/ Nashwauk Uplands	86	0.00825	22.65	84.9	0.73322	0.31592	26	80.76	0.71984	83.94	0.73016
Hardwood Hills	470	0.02394	19.2	85.53	0.77552	0.61453	54	81.48	0.76436	85.11	0.77441
Laurentian Highlands	120	0.06315	9.94	95	0.89537	0.15717	25	84	0.86921	93.10	0.89323
Littlefork-Vermilion Uplands	25	0.00438	18.32	92	0.80087	0.35445	22	63.63	0.71208	78.72	0.76728
Mille Lacs Uplands	437	0.02786	14.37	86.72	0.83429	0.57116	63	76.19	0.81139	85.40	0.8317
Minnesota River Prairie	969	0.03088	19.84	82.98	0.76091	0.58827	57	80.70	0.75421	82.85	0.76052
Oak Savanna	121	0.01761	20.55	91.73	0.77597	0.51064	12	50.00	0.58900	87.97	0.76640
Pine Moraines & Outwash Plains	474	0.03261	19.21	86.07	0.77681	0.78248	64	67.19	0.71409	83.83	0.77085
Red River Prairie	270	0.01469	29.9	84.82	0.64741	0.47199	58	87.93	0.65996	85.33	0.64959
Rochester Plateau	81	0.01524	51.47	85.18	0.39575	0.44729	1	100	0.48523	85.37	0.39709
St. Croix Moraines And Outwash Plains (Twin Cities Highlands)	126	0.05112	48.68	86.51	0.43729	0.99927	12	100	0.51318	87.68	0.44480
St. Louis Moraines/ Tamarack Lowlands	186	0.0165	9.76	87.64	0.88864	0.50751	33	66.67	0.85361	84.47	0.88445
AVERAGE BY REGION	341.45	0.03843	24.97	86.83	0.67678	0.542585	48.65	77.99	0.67733	85.33	0.70691
STATEWIDE EVALUATION	6828	0.03124	22.82	86.00	0.73465	NA	977	76.66	0.72304	85.56	0.73329

¹ Site frequency is the number of sites per square kilometer within a region.

Improvement over Phase 2

Because different regionalization schemes were used, Phase 2 and 3 models cannot be compared on a regional basis. This discussion is based on the average values for the models in each phase. Phase 3 models performed better than Phase 2 models by every measure except gain (Table 8.6.12). The emphasis in model reclassification in Phase 2 was to maximize gain (Section 7.5.1.2.4), while the emphasis in Phase 3 was to predict as close to 85 percent of known sites possible. With this methodological change, it was expected that Phase 3 models would classify more land areas high/medium potential. Despite this, Phase 3 models reduced the area slightly while increasing the percentage of sites predicted significantly. At the same time, Phase 3 models did not, on average, reduce the gain statistics.

Improvements in model performance can be attributed to much larger populations of known sites for deriving models (Sections 7.3.5.2 and 7.5.1.3), refinements in the classification procedures (Section 7.5.1.3), and reducing the environmental variability with regions by using a different regionalization scheme (Section 4.6.3)

Phase 3 models (Figure 8.5) did not completely eliminate the edge effect between regions observed in the Phase 2 models (Section 4.6.2 and Figure 8.4). However, this effect is absent between some regions and inconspicuous between others, particularly when region boundaries follow hydrologic features. There seems to be a relationship to site numbers, as the effect is most conspicuous where regions with very low site numbers abut regions with higher site numbers (e.g. Aspen Parklands and Red River Prairie).

Table 8.6.12. Comparison of Phase 1, Phase 2 and Phase 3 Site Probability Models. Values are averages of those for the separate regional model evaluations based on combined training and test data.

Model statistic	Phase 1	Phase 2	Phase 3
Percent area in high/medium probability class	55.5	24	23
Percent sites predicted	84	77	85
Gain	0.37	0.68	0.71

Contributions of Individual Variables

Only 44 variables were used to build models in Phase 3, a considerable reduction from Phase 2 (Section 8.6.2.2). It should be noted again that, in Phase 3, all horizontal distance and size variables were transformed to square roots for modeling and should be compared to the results of the square root equivalents in Phase 2. Likewise, direction was converted to sine.

Of the 44 Phase 3 variables, only one (distance to bedrock used for tools) failed to contribute to any site probability model (Table 8.6.13). Clearly, these variables were a more effective set than that used in Phase 2, when 13 variables (11 percent) failed to contribute to any model. All remaining Phase 3 variables had a maximum probability of 100 in at least one model. On the average, each variable figured into six models. Prevailing orientation, relative elevation, and size of nearest permanent lake each contributed to fewer than three models. Distance to edge of nearest large lake, distance to edge of nearest perennial river or stream, distance to nearest lake, wetland, organic soil, or stream, and height above surroundings each contributed to more than ten models. These four variables also had the highest cumulative probabilities.

Cumulative probabilities are perhaps the best measure of the contribution of the variables to the overall modeling effort. The average cumulative probability for the Phase 3 model variables is 561. The variables with above average cumulative probabilities are evenly spread between three aspects of the environment:

surface hydrology (direction to nearest water or wetland; distance to edge of nearest swamp; distance to edge of nearest large lake; distance to edge of nearest perennial river or stream; distance to nearest lake, wetland, organic soil, or stream)
vegetation (distance to sugar maple, distance to hardwoods, distance to prairie, vegetation diversity within 1 km)
topography (surface roughness; vertical distance to permanent water; elevation; height above surroundings; distance to nearest minor ridge or divide).

These results stress the importance of several components of the environment that are significant to hunter/gatherers:

topographic position (elevation; height above surroundings; distance to nearest minor ridge or divide). This can mean a variety of things, depending on the context. Height above surroundings is the top ranked variable and could indicate locations on rises in a floodplain, tops of bluffs, or defensible positions with wide viewsheds. Distance to nearest minor ridge or divide, if values are low, may indicate higher positions with views or in close proximity to the divide, which may have been used as travel routes. If the same variable has high values, this may indicate locations in the valley floors.
proximity to water bodies in general (distance to nearest lake, wetland, organic soil, or stream). This is the second most significant variable in the Phase 3 models.
proximity to large permanent water features (distance to edge of nearest large lake; distance to edge of nearest perennial river or stream; vertical distance to permanent water).
location with respect to features that can serve as firebreaks (direction to nearest water or wetland, surface roughness)
proximity to shelter and firewood (distance to sugar maple, distance to hardwoods, distance to edge of nearest swamp). Even distance to prairie, which tends to have an inverse relationship with site location, is an indicator of the importance of shelter and firewood. The more mesic wooded environments may also provide some protection from fire, while prairies would not.
proximity to a wide range of ecological resources (vegetation diversity within 1 km). Each vegetation type provides a different set of plant and animal products that can be used for food, clothing, shelter, and for making domestic items like baskets. Having several vegetation types within easy access reduces the expenditure of energy required for acquiring these resources.

Table 8.6.13. Performance of All Phase 3 Variables in the Best Site Probability Models.

Number of models in which each variable occurred with probability greater than zero, maximum probability recorded, mean probability recorded, and cumulative probability.

Variable	# of Models	Max Prob	Mean Prob	Cumulative Prob
Direction to nearest water or wetland	8	100	95.9	767.4
Distance to aspen-birch	4	100	92.9	371.4
Distance to bedrock used for tools	0	0	0.0	0.0
Distance to Big Woods	4	100	98.0	391.8
Distance to brushlands	5	100	85.3	426.3
Distance to conifers	6	100	79.0	474.1
Distance to edge of nearest large wetland	6	100	91.9	551.6
Distance to edge of nearest area of organic soils	4	100	97.6	390.3
Distance to edge of nearest large lake	13	100	97.1	1262.4
Distance to edge of nearest perennial river or stream	13	100	98.6	1281.9
Distance to edge of nearest swamp	8	100	100.0	800.0
Distance to glacial lake sediment	4	100	96.7	386.7
Distance to hardwoods	7	100	93.1	651.4
Distance to mixed hardwoods and pine	4	100	98.0	391.8
Distance to nearest confluence between perennial or intermittent streams and large rivers	4	100	87.4	349.7
Distance to nearest intermittent stream	5	100	89.0	445.2
Distance to nearest lake inlet/outlet	6	100	93.0	557.8
Distance to nearest lake, wetland, organic soil, or stream	14	100	98.0	1371.9
Distance to nearest major ridge or divide	4	100	100.0	400.0
Distance to nearest minor ridge or divide	6	100	97.8	586.6
Distance to nearest permanent lake inlet/outlet	4	100	85.4	341.6
Distance to nearest permanent wetland inlet/outlet	4	100	91.0	363.8
Distance to oak woodland	6	100	93.3	559.8
Distance to paper birch	3	100	99.9	299.7
Distance to pine barrens or flats	3	100	93.2	279.7
Distance to prairie	9	100	89.7	807.3
Distance to river bottom forest	3	100	88.5	265.6
Distance to sugar maple	7	100	89.2	624.1
Distance to well-drained soils	3	100	100.0	300.0
Elevation	10	100	98.9	989.0
Height above surroundings	17	100	98.4	1673.6
On alluvium	3	100	74.7	224.1
On river terraces	4	100	93.9	375.6
Prevailing orientation	1	100	100.0	100.0
Relative elevation	2	100	88.0	176.0
Size of major watershed	6	100	86.7	520.1
Size of minor watershed	4	100	66.8	267.0
Size of nearest lake	5	100	90.9	454.6
Size of nearest permanent lake	2	100	99.1	198.2
Slope	6	100	92.4	554.2
Surface roughness	8	100	86.5	692.3
Vegetation diversity within 1 km	10	100	89.7	897.1
Vertical distance to permanent water	9	100	100.0	900.0
Vertical distance to water	4	100	97.4	389.7

8.6.3.2 Survey Probability Model

The survey probability models developed in Mn/Model Phase 3 have no precedent. Their development was prompted by the realization that past surveys in Minnesota have been strongly biased in favor of locations near water and that known sites may be absent from other locations simply because no surveys have been conducted there. The survey probability models were developed as a CRM tool to identify the kinds of landscapes that have not been adequately surveyed in the past. Survey potential (Figure 8.6) should be interpreted as the probability for each cell that its environment is similar to places where surveys have occurred. The gain statistic for these models can be seen as a measure of the degree of survey bias, with more biased survey patterns producing higher gain statistics.

The average survey probability model predicts 85 percent of surveyed places in 43 percent of the region's land area, producing a gain statistic of 0.562463 and a Kappa coefficient of stability of 0.56. This implies that, overall, the models perform significantly better than by chance, leading to the conclusion that surveys in the state exhibit a significant amount of locational bias. This bias is apparent in the composite map of the regional models (Figure 8.6).

Since the majority of past surveys have occurred near water, then the majority of the cells near water have been categorized as high survey potential (Figure 8.6). This is particularly apparent in the four regions with the greatest survey bias, as evidenced by strong to very strong gain statistics (0.7 or greater, Table 8.6.14). These models occur in:

Border Lakes
Laurentian Highland
Littlefork-Vermilion Uplands (combined with Agassiz Lowlands and Aspen Parklands)
St. Louis Moraines/Tamarack Lowlands

All of these, except the Laurentian Highlands, also have strong Kappa values (>0.5), another indicator of the strength of the survey bias. Bias is not a function of the number of places surveyed, though Littlefork-Vermilion Uplands has had the second lowest number of surveys recorded. Border Lakes has more than ten times as many sites as this region and also shows a very high degree of survey bias, probably because of the kinds of places that are accessible in that region. Whether these regions have lower or higher than average numbers of surveys, their surveys have been confined to a limited set of environmental situations, primarily near lakes and rivers. These regions will require additional surveys in the low survey potential zone to provide a more balanced picture of the distribution of their archaeological resources.

Table 8.6.14. Survey Probability Model Performance for All 20 Regions Modeled in Phase 3.

Modeled Region	Survey Probability Models
Modeled Region	Surveyed Places	Survey Frequency	% area Hi/Med	% surveys predicted	Gain	Kappa
Agassiz Lowlands	195	0.01087	36.38	87.17	0.58265	0.63303
Anoka Sand Plain	1016	0.19894	54.04	84.95	0.36386	0.55217
Aspen Parklands	722	0.06863	57.68	93.07	0.38025	0.59768
Big Woods	1993	0.24824	53.32	84.7	0.37048	0.42355
Blufflands	1363	0.27889	38.65	85.03	0.54545	0.64309
Border Lakes	2230	0.23876	18.89	82.73	0.77167	0.72217
Chippewa Plains	1685	0.19973	40.19	84.28	0.52314	0.52964
Coteau Moraines /Inner Coteau	1002	0.09024	54.62	84.03	0.34994	0.58797
Glacial Lake Superior Plain/ North Shore Highlands/ Nashwauk Uplands	1100	0.10435	44	83.9	0.47557	0.63578
Hardwood Hills	1509	0.07685	57.66	86.42	0.33279	0.31642
Laurentian Highlands	746	0.3926	14.90	84.58	0.82384	0.40028
Littlefork-Vermilion Uplands	207	0.0365	20.63	88.88	0.76788	0.70685
Mille Lacs Uplands	1543	0.09835	33.53	84.58	0.60357	0.62430
Minnesota River Prairie	2667	0.08498	44.63	83.24	0.46384	0.65697
Oak Savanna	733	0.1067	39.93	87.45	0.5434	0.49516
Pine Moraines & Outwash Plains	1593	0.1096	43.21	83.99	0.48553	0.59663
Red River Prairie	1051	0.05716	44.94	84.87	0.47048	0.53891
Rochester Plateau	615	0.11574	72.77	84.72	0.14105	0.56311
St. Croix Moraines And Outwash Plains (Twin Cities Highlands)	641	0.26005	61.78	87.05	0.29029	0.44529
St. Louis Moraines/ Tamarack Lowlands	870	0.07718	24.37	82.18	0.70846	0.54660
AVERAGE BY REGION	1174.05	0.142718	42.81	85.39	0.562463	0.56078
STATEWIDE EVALUATION	23443	-	43.29	84.67	0.488721	-

¹Site frequency is the number of surveyed places per square kilometer within a region.

Eight regions represent the least biased surveys, evidenced by low gain statistics (<0.5) and higher Kappa coefficients (>0.5):

Agassiz Lowlands
Anoka Sand Plain
Aspen Parklands
Blufflands
Coteau Moraines/Inner Coteau
Minnesota River Prairi
Pine Moraines and Outwash Plains
Red River Prairie
Rochester Plateau

Even in these regions, however, the proclivity to survey environments near water are evident in the model (Figure 8.6).

Contributions of Individual Variables

All 44 Phase 3 variables contributed to the survey probability models (Table 8.6.15). Moreover, each variable contributed, on average, to eight survey probability models compared to an average of six site probability models per variable. Relative elevation, distance to bedrock used for tools, prevailing orientation, size of minor watershed, and vertical distance to water each contributed to fewer than four models. Distance to edge of nearest large lake, height above surroundings, and distance to nearest lake, wetland, organic soil, or stream each contributed to more than 12 models and had the highest cumulative probabilities.

The higher number of models per variable may be attributable to the larger numbers of variables in the survey probability models. Since the number of variables in an individual model seems to be a function of the number of data points, and there are far more surveyed places than known sites, this result should be expected.

Only two variables failed to achieve a maximum probability of 100 in any model. These were relative elevation and distance to bedrock used for tools. Their maximum probabilities were 76.8 and 88.6 respectively. The average cumulative probability for variables in the survey probability models is 74.7. This high value is also a function of having more variables in each model. The variables with higher than average cumulative probabilities include:

past and present surface hydrology (distance to nearest lake, wetland, organic soil, or stream; distance to edge of nearest large lake; direction to nearest water or wetland; distance to edge of nearest perennial river or stream; distance to nearest confluence between perennial or intermittent streams and large rivers; distance to nearest permanent lake inlet/outlet; size of nearest permanent lake; distance to edge of nearest area of organic soils; distance to glacial lake sediment)
vegetation (distance to river bottom forest; distance to hardwoods; distance to aspen-birch, distance to oak woodland; distance to pine barrens or flats; vegetation diversity within 1 km)
topography (height above surroundings; size of major watershed; distance to nearest major ridge or divide; elevation; distance to nearest minor ridge or divide)

These variables are more heavily weighted towards water features than are those for the site probability models. Presumably, these variables represent Minnesota archaeologists' mental models of where sites are likely to be found. These models appear to emphasize:

proximity to water, particularly large lakes (distance to nearest lake, wetland, organic soil, or stream; distance to edge of nearest large lake; distance to edge of nearest perennial river or stream; size of nearest permanent lake).
topographic position (height above surroundings; size of major watershed; distance to nearest major ridge or divide; elevation; distance to nearest minor ridge or divide). Field archaeologists tend to focus surveys on higher places in the local landscape (small rises on floodplains, tops of bluffs, positions with a wide viewshed). The role of watershed size is not clear, though it may be a function of the large numbers of surveys conducted along major rivers within the state.
proximity to sources of shelter and firewood (distance to river bottom forest; distance to hardwoods; distance to aspen-birch, distance to oak woodland; distance to pine barrens or flats). It is difficult to say whether these features were directly selected by archaeologists, by reference to Marschner (1974), for locating surveys or whether they were selected by the modeling process because of their relationships with other variables. For example, the deliberate decision to survey valley bottoms and bluff tops could indirectly result in distance to river bottom forest becoming a significant variable. Interviews with archaeologists about their mental models may clarify the role of these variables.
protection from fire (direction to nearest water or wetland). Although archaeologists are aware that sites tend to be found on the protected northern and eastern sides of lakes, their mental models apparently do not consider the effectiveness of rolling or steep terrain to slow or stop the spread of fire.
proximity to features providing evidence of former water bodies (distance to edge of nearest area of organic soils; distance to glacial lake sediment). Glacial lake sediment and organic soils are both evidence of the location and extent of water bodies before the present. Although these features appear to be important to archaeologists, they do not appear as prominently in the site probability models. This is probably explained by the proclivity of archaeologists to look for older, more significant sites. Since these sites are rare, however, they make up only a very small portion of the archaeological database. Consequently, any environmental factors associated with their presence have little significance in the site probability models.
an emphasis on looking for sites near stream confluences and locations where streams enter lakes or wetlands (distance to nearest confluence between perennial or intermittent streams and large rivers; distance to nearest permanent lake inlet/outlet). These features may be interpreted as nodes on transportation networks. Lake and wetland inlets and outlets may also be locations of wild rice beds, an important seasonal food source.
proximity to a wide range of ecological resources (vegetation diversity within 1 km). Like the other vegetation variables, it is unclear whether this variable has been used deliberately to locate surveys or whether it is simply correlated with other variables, such as terrain or proximity to water, that are more explicit components of the archaeologists' mental models.

Table 8.6.15. Performance of all Phase 3 Variables in the Best Survey Probability Models.

Number of models where each variable had probability greater than zero, the maximum probability recorded, mean probability, and cumulative probability.

Variable	# of Models	Max Prob	Mean Prob	Cumulative Prob
Direction to nearest water or wetland	11	100	99.9	1098.6
Distance to aspen-birch	10	100	100.0	1000.0
Distance to bedrock used for tools	2	88.6	84.8	169.6
Distance to Big Woods	6	100	97.0	581.8
Distance to brushlands	4	100	88.1	352.4
Distance to conifers	7	100	82.1	574.5
Distance to edge of nearest large wetland	8	100	90.7	725.8
Distance to edge of nearest area of organic soils	11	100	98.4	1082.9
Distance to edge of nearest large lake	14	100	97.5	1365.6
Distance to edge of nearest perennial river or stream	12	100	86.7	1039.8
Distance to edge of nearest swamp	6	100	100.0	600.0
Distance to glacial lake sediment	11	100	99.9	1098.4
Distance to hardwoods	12	100	94.2	1130.3
Distance to mixed hardwoods and pine	6	100	98.8	592.7
Distance to nearest confluence between perennial or intermittent streams and large rivers	10	100	99.6	995.8
Distance to nearest intermittent stream	9	100	78.3	704.7
Distance to nearest lake inlet/outlet	10	100	99.5	994.6
Distance to nearest lake, wetland, organic soil, or stream	17	100	95.7	1626.2
Distance to nearest major ridge or divide	10	100	98.5	985.2
Distance to nearest minor ridge or divide	10	100	80.1	800.7
Distance to nearest permanent lake inlet/outlet	7	100	99.8	698.5
Distance to nearest permanent wetland inlet/outlet	10	100	98.2	982.4
Distance to oak woodland	9	100	100.0	900.0
Distance to paper birch	4	100	94.9	379.5
Distance to pine barrens or flats	8	100	94.2	753.5
Distance to prairie	6	100	93.6	561.8
Distance to river bottom forest	12	100	98.2	1178.2
Distance to sugar maple	5	100	98.2	491.0
Distance to well-drained soils	5	100	90.3	451.7
Elevation	9	100	97.6	878.3
Height above surroundings	14	100	98.2	1375.0
On alluvium	4	100	89.1	356.5
On river terraces	8	100	89.7	717.7
Prevailing orientation	3	100	89.6	268.9
Relative elevation	2	76.8	71.2	142.4
Size of major watershed	12	100	99.3	1191.8
Size of minor watershed	3	100	99.6	298.9
Size of nearest lake	5	100	75.2	375.8
Size of nearest permanent lake	8	100	95.3	762.7
Slope	4	100	98.7	394.8
Surface roughness	4	100	100.0	400.0
Vegetation diversity within 1 km	9	100	92.1	829.2
Vertical distance to permanent water	7	100	99.9	699.5
Vertical distance to water	3	100	80.8	242.4

8.6.3.3 Survey Implementation Model

The survey implementation model is an overlay and reclassification of the site probability and survey probability models (Section 7.5.1.3 and Table 7.9). Its primary feature is that it shows areas that have both a low site potential and a low survey potential as being unknown. In this zone, it is likely that site potential is low primarily because these environmental settings have not been adequately surveyed. This zone occupies 49.54 percent of the state's land area and contains five percent of modeled sites and 13 percent of single artifacts (Figure 8.7 and Table 8.6.16). The deficiency of surveys in this region is further highlighted by the low proportions of negative survey points (13 percent) found here. Nearly fifteen percent of test sites were found in the unknown zone, compared to eight percent in the low and possibly low probability zones. This may indicate a somewhat greater emphasis for surveying the unknown areas, as suggested by the Mn/Model implementation plan (Chapter 11).

In regions where the survey probability models are unstable (Table 8.6.14), the unknown area may not be well-identified and may in reality include portions of areas classified as low and possibly low potential. Likewise, unstable site probability models (Table 8.6.11) may have similar effects. Consequently, Kappa coefficients for the site and survey probability models for each region should be considered when using the implementation models to guide future surveys.

The low site potential areas that coincide with medium and high survey potential are assigned site potential values possibly low and low respectively. These are depicted on the map in two shades of yellow. These zones occupy 24 percent of the state's area and contain seven percent of the modeled sites and 15 percent of the single artifacts. However, 34.5 percent of negative survey points are in these zones.

The patterns for the medium and high site potential zones follow those on the site probability models, with the only difference being that these zones are weighted by survey potential. Sites in the medium probability zones are more likely to be found in areas that have higher survey potential (10 percent of modeled sites in 6.5 percent of the state's land area) ) than in areas with lower potential for surveys (2 percent of modeled sites in 2.5 percent of the state's land area). For comparative purposes, this can be reduced to 1.54 vs. 0.8 percent of sites per each one percent of land area. In the high site potential zones, this discrepancy is even greater. By far the largest group of modeled sites (65 percent) is found in the high site potential zone that also has high survey potential (eight percent of the state's area). Only 7.5 percent of sites in the high site potential zone are found in low and medium survey potential locations, which together occupy 2.25 percent of the state's area. For comparison, consider this to be 8.13 vs. 3.33 percent of sites per each one percent of land area. It is apparent that the models are rather conservative about extending the high probability zone much beyond the well-surveyed parts of the landscape.

The majority of sites (77.34 percent) are found in areas where survey potential was rated as high. These are the low, medium, and high site potential classes in the survey implementation model. Another 10.75 percent of sites occur where survey potential is medium (possibly low, medium, and high site potential classes) and 4.92 percent occur where survey potential is low, but where site potential is medium or high (suspected medium and high site potential classes).

Table 8.6.16. Evaluation of Survey Implementation Model for All 20 Regions Modeled in Phase 3.

Site Potential	Region (30 meter cells)		Random Points		Negative Survey Points		Single Artifacts		Modeled Sites
	#	%	#	%	#	%	#	%	#	%

Unknown	120,328,861	49.54	23,020	49.20	2335	14.67	92	12.76	370	5.43
Possibly Low	31,063,043	12.79	6037	12.90	1771	11.13	36	4.99	217	3.19
Low	27,046,150	11.14	5164	11.04	3567	22.41	75	10.40	247	3.63

Suspected Medium	6,206,642	2.56	1230	2.63	142	0.89	23	3.19	155	2.28
Possibly Medium	7,935,094	3.27	1484	3.17	385	2.42	23	3.19	177	2.60
Medium	15,917,082	6.55	2909	6.22	2280	14.33	74	10.26	604	8.87

Suspected High	2,208,561	0.91	478	1.02	71	0.45	16	2.22	180	2.64
Possibly High	3,326,216	1.34	6037	12.90	204	1.28	32	4.44	338	4.96
High	19,917,051	8.20	3859	8.25	5057	31.78	348	48.27	4414	64.84

Water	7,722,839	3.18	1647	3.52	39	0.25	0	0.00	61	0.90
Steep Slopes	850,789	0.35	195	0.42	49	0.31	2	0.28	44	0.65
Mines	425,116	0.18	98	0.21	14	0.09	0	0.00	1	0.01

Total	242,887,444	100	46,792	100	15,914	100	721	100	6808	100

By excluding the unknown zone from consideration, it is possible to evaluate the performance of the site probability model within the kinds of ecological settings that are most likely to have been adequately surveyed. Table 8.6.17 provides recalculations of the percentages of each category of sample points within these site potential classes. Of the 6441 modeled sites found within this area statewide, 91.15 percent are within the six medium and high site potential classes, which constitute 45.28 percent of the adequately surveyed area. This produces a respectable gain statistic of 0.50324, indicating that the model performs significantly better than by chance alone. However, its poor performance compared to the site probability model (Section 8.6.3.1) may be attributable to survey bias, which results in a low level of distinction between places where sites are found and places where surveys have occurred. When future surveys extend the area that can be modeled as adequately surveyed, presumably a stronger model can be produced.

Table 8.6.17. Evaluation of Site Potential for Survey Implementation Model Outside the Unknown Zone.

Site Potential	Region (30 meter cells)		Random Points		Negative Survey Points		Single Artifacts		Modeled Sites
	#	%	#	%	#	%	#	%	#	%

Possibly Low	31,063,043	25.33	6037	20.72	1771	13.04	36	5.72	217	3.37
Low	27,046,150	22.06	5164	17.72	3567	26.27	75	11.92	247	3.83

Suspected Medium	6,206,642	5.06	1230	4.22	142	1.05	23	3.66	155	2.41
Possibly Medium	7,935,094	6.47	1484	5.09	385	2.84	23	3.66	177	2.75
Medium	15,917,082	12.98	2909	9.98	2280	16.79	74	11.76	604	9.38

Suspected High	2,208,561	1.80	478	1.64	71	0.52	16	2.54	180	2.80
Possibly High	3,326,216	2.71	6037	20.72	204	1.50	32	50.9	338	5.25
High	19,917,051	16.24	3859	13.24	5057	37.24	348	55.33	4414	68.56

Water	7,722,839	6.30	1647	5.65	39	0.29	0	0.00	61	0.94
Steep Slopes	850,789	0.69	195	0.67	49	0.36	2	0.32	44	0.68
Mines	425,116	0.35	98	0.34	14	0.10	0	0.00	1	0.02

Total	122,618,583	100	29,138	100	13,579	100	629	100	6438	100

8.6.3.4 Site Probability Model Developed from Statewide Database

Because of difficulties encountered when trying to produce comparable raw model scores for the 20 regional models, a single site probability model was developed from the entire statewide database (Section 7.7). To develop this model, a number of the Phase 3 variables had to be excluded because they were not present statewide. These included distance to paper birch, distance to Big Woods, distance to oak woodland, distance to mixed hardwoods and pine, distance to pine barrens or flats, distance to aspen-birch, distance to bedrock used for tools, distance to conifers, distance to nearest permanent wetland inlet/outlet, and distance to prairie. This left a total of 34 variables for modeling, of which 27 contributed to the model (Table 8.6.18). The only variables with less than 100 percent probability were size of nearest lake and size of nearest permanent lake. The large number of model variables is undoubtedly a function of the very large number of sites in the database.

The resulting model emphasizes the gross patterns in known site distribution (Figure 8.8) and does not articulate the local patterns within the landscape as finely as does the statewide model derived using regionalization (Figure 8.4). Consequently, sites that cannot be explained by large-scale environmental patterns or that depend on local variables are not as well predicted as in the regionalized model. However, this model does provide a more accurate representation of relative probabilities statewide (Figure 8.8). The consequence is that some regions (for instance the Twin Cities metro area and the Arrowhead Region) show very high concentrations of high site potential, while others (like the northern tier of counties west of the Arrowhead) show only limited occurrences of high site potential. Whether these results are interpreted as indicators of ecological settings preferred by hunter-gatherers or as artifacts of past survey efforts, this model is a useful point of comparison with the regionalized site probability model.

Table 8.6.18. Site Probability Model from Statewide Database.

Variable	S-Plus Regression Coefficient	Probability
Direction to nearest water or wetland (sine)	-0.2325406	100.0
Distance to edge of nearest large wetland	0.006508734	100.0
Distance to edge of nearest area of organic soils	0.004957566	100.0
Distance to edge of nearest large lake	-0.01192841	100.0
Distance to edge of nearest perennial river or stream	-0.01827615	100.0
Distance to edge of nearest swamp	0.01325694	100.0
Distance to hardwoods	-0.004220171	100.0
Distance to nearest confluence between perennial or intermittent streams and large rivers	-0.003289315	100.0
Distance to nearest intermittent stream	0.006548222	100.0
Distance to nearest lake inlet/outlet	-0.01227073	100.0
Distance to nearest lake, wetland, organic soil, or stream	-0.04851173	100.0
Distance to nearest permanent lake inlet/outlet	0.005728610	100.0
Distance to river bottom forest	0.002051763	100.0
Distance to sugar maple	0.003129357	100.0
Distance to well-drained soils	-0.005608923	100.0
Elevation	0.8425730	100.0
Height above surroundings	0.02045504	100.0
On river terraces	0.7578046	100.0
Prevailing orientation	-0.001215266	100.0
Relative elevation	0.02036699	100.0
Size of major watershed	-0.00001451567	100.0
Size of minor watershed	0.00004488181	100.0
Size of nearest lake	-0.00005703235	48.5
Size of nearest permanent lake	0.00006991912	69.9
Surface roughness	-0.01668705	100.0
Vegetation diversity within 1 km	0.3938607	100.0
Vertical distance to permanent water	-0.006548323	100.0

This model predicts 84.87 percent of all modeled sites within the high and medium probability zones, which constitute 33.65 percent of the state's area (Table 8.6.19). This produces a good gain statistic (0.60351), indicating that the model performs well and comes very close to meeting project goals. The site probability model developed as a composite of the regional models (Section 8.6.3.1) performs somewhat better because regionalization makes it possible to discern patterns within individual regions, not just statewide. Consequently, regionalization gives more weight to sites in regions with low site numbers.

This model tested well, predicting 82.81 percent of new sites. The gain statistic for the test population is 0.59365.

Because of time constraints, no preliminary models were run, so no Kappa coefficients could be calculated. Performing this analysis would be very useful, especially as a comparison to the stability patterns within the regional models. Also because of time constraints, no survey probability model was developed statewide. The development of survey probability and survey implementation models from the statewide database would also provide useful information for comparison with the regional models.

Table 8.6.19. Evaluation of Site Probability Model from Statewide Database.

		Low	Medium	High	Water	Steep slopes	Mines	Total
Region (30 meter cells)	#	152,146,814	23,271,112	58,469,737	7721980	850883	425122	242,885,648
	%	62.64	9.58	24.07	3.18	0.35	0.18	100.0

All random points	#	28804	4555	11501	1641	191	98	46790
	%	61.56	9.73	24.58	3.51	0.41	0.21	100.0

All negative survey points	#	6356	1698	7758	40	46	14	15912
	%	39.94	10.67	48.76	0.25	0.29	0.09	100.0

All modeled sites	#	926	500	5283	61	43	1	6814
	%	13.59	7.34	77.53	0.9	0.63	0.01	100.0

All test sites	#	155	63	746	10	3	0	977
		15.86	6.45	76.36	1.02	0.31	0	100.0

8.6.4 Phase 3 Results – Regional Models

The following sections report on the regionalized models. Reports are presented for 17 individual ECS subsections and for three sets of combined subsections (Figure 8.1). For six of the individual subsections reported, models are taken from modeling combinations of adjacent subsections, as described in Section 7.5.1.3. Only when two or more subsections share the same best site probability and survey probability models are they reported on in combination.

The regional model reports contain descriptions of the environmental context of the region, descriptions and evaluations of the site probability, survey probability, and survey implementation models for that region, and interpretations of the site probability and survey probability models. The order in which the models are presented is as follows:

8.7 Agassiz Lowlands

8.8 Anoka Sand Plain

8.9 Aspen Parklands

8.10 Big Woods
8.11 Blufflands

8.12 Border Lakes

8.13 Chippewa Plains

8.14 Coteau Moraines / Inner Coteau

8.15 Glacial Lake Superior Plain/Northshore Highlands/ Nashwauk Uplands

8.16 Hardwood Hills

8.17 Laurentian Highlands

8.18 Littlefork-Vermilion Uplands

8.19 Mille Lacs Uplands

8.20 Minnesota River Prairie

8.21 Oak Savanna

8.22 Pine Moraines & Outwash Plains

8.23 Red River Prairie

8.24 Rochester Plateau

8.25 St. Croix Moraines and Outwash Plains (Twin Cities Highlands)

8.26 St. Louis Moraines/ Tamarack Lowlands

8.27 Conclusion

Site probability models developed in Phase 3 of this project performed very well and met or exceeded project goals. However, several factors limit their overall quality. First and foremost, there are simply too few known sites in some parts of the state to impart a high level of confidence to the models for those areas. In some cases (for example, Laurentian Highlands, St. Louis Moraines and Tamarack Lowlands), the site probability models performed deceptively well. This can be explained by the very limited range of variation in the known sites' environments. This limited range of variation, in turn, results from survey bias, low survey numbers, and low site numbers. In such cases, model stability may be rather high. Again, this is deceptive, as the range of variability in the site environment data is too narrow to introduce sufficient uncertainty into the model. Thus, interpretation of all model results presented here should be tempered by the number of sites available for analysis within each subsection.

Similarly, when a large number of sites are taken from biased surveys, as in the Border Lakes subsection, the environmental variability of the site locations may still be low. The survey probability and survey implementation models were developed to address this kind of bias. However, survey bias may have been overestimated in this phase of the project, as surveys are not yet adequately mapped. A more complete mapping of surveys should reduce the amount of land classified as "unknown" in the survey implementation models.

These models may also include errors or inaccuracies attributable to site mapping problems. As only site centroids were mapped for this project, a more limited range of environments may have been analyzed than would have been included in the database if sites were mapped as polygons. Moreover, inaccurate or imprecise centroid locations may have resulted in the inclusion of atypical environments in the analysis. Improved site mapping will be an important component of future models.

Although the edge effect that was so conspicuous in the Phase 2 models (Figure 8.4b) is not as apparent, it can still be detected in the Phase 3 models (Figure 8.5), particularly along the margins of the Aspen Parklands, Oak Savanna, Rochester Plateau, Red River Prairie, and Nashwauk Uplands. These subsections all have low site numbers and low site frequencies. However, this is almost certainly not the entire explanation for the phenomenon. To some extent it may be an artifact of how the raw model values are classified into probability classes, which permits adjacent regions to have larger or smaller proportions of their areas classified as high and medium site probability. Other, sometimes more conspicuous, edge effects are apparent where elevation data of different qualities adjoin.

These models best predict more recent archaeological sites (i.e., those formed within the last 3500 years), as these make up a majority of the available data and will be the most closely associated with modern environmental variables. Combined with the landscape sediment assemblage interpretations (Chapter 12) and hydrologic modeling to identify locations of drained lakes, the site/environment relationships identified by these models may help develop models for earlier archaeological sites via reconstructions of pre-Woodland suitable habitats.

All of these limitations can be addressed in the next full modeling phase, which is scheduled to take place in about 2006-2007. Plans for those future enhancements are discussed in Chapter 10.

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The Mn/Model Final Report (Phases 1-3) is available on CD-ROM. Copies may be requested by visiting the contact page.

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Acknowledgements

MnModel was financed with Transportation Enhancement and State Planning and Research funds from the Federal Highway Administration and a Minnesota Department of Transportation match.

Copyright Notice

The MnModel process and the predictive models it produced are copyrighted by the Minnesota Department of Transportation (MnDOT), 2000. They may not be used without MnDOT's consent.