Spatial Characterization of Western Interior Seaway Paleoceanography Using Foraminifera, Fuzzy Sets and Dempster-Shafer Theory

SPATIAL CHARACTERIZATION OF WESTERN INTERIOR SEAWAY PALEOCEANOGRAPHY USING FORAMINIFERA, FUZZY SETS AND DEMPSTER-SHAFER THEORY

Samuel N. Lockshin

A Thesis

Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

August 2016

Committee:

Margaret Yacobucci, Advisor

Peter Gorsevski

Sam Lockshin

Margaret Yacobucci, Advisor

The spatial paleoceanography of the entire Western Interior Seaway (WIS) during the

Cenomanian-Turonian Oceanic Anoxic Event has been reconstructed quantitatively for the first time using Geographic Information Systems. Models of foraminiferal occurrences—derived from Dempster-Shafer theory and driven by fuzzy sets of stratigraphic and spatial data—reflect water mass distributions during a brief period of rapid biotic turnover and oceanographic changes in a greenhouse world. Dempster-Shafer theory is a general framework for approximate reasoning based on combining information (evidence) to predict the probability (belief) that any phenomenon may occur. Because of the inherent imprecisions associated with paleontological data (e.g., preservational and sampling biases, missing time, reliance on expert knowledge), especially at fine-scale temporal resolutions, Dempster-Shafer theory is an appropriate technique because it factors uncertainty directly into its models. Locality data for four benthic and one planktic foraminiferal species and lithologic and geochemical data from sites distributed throughout the WIS were compiled from four ammonoid biozones of the Upper Cenomanian and

Early Turonian stages. Of the 14 environmental parameters included in the dataset, percent silt, percent total carbonate, and depositional environment (essentially water depth) were associated with foraminiferal occurrences. The inductive Dempster-Shafer belief models for foraminiferal occurrences reveal the positions of northern and southern water masses consistent with the oceanographic gyre circulation pattern that dominated in the seaway during the Cenomanian-

Turonian Boundary Event. The water-mixing interface in the southwestern part of the WIS was mostly restricted to the Four Corners region of the US, while the zone of overlap of northern and iv southern waters encompassed a much larger area along the eastern margin, where southern waters occasionally entered from the tropics. In addition to its paleospatial significance, this study introduces a rigorous, quantitative methodology with which to analyze paleontological occurrence data, assess the degree of uncertainty and prioritize regions for additional data collection. v

This work is dedicated to Occam for showing scientists how to properly use a razor. vi ACKNOWLEDGMENTS

I extend my sincerest thanks to Dr. Peg Yacobucci for her many hours of aid and guidance during the completion of this document. Her scientific knowledge, wisdom and good attitude have been imparted on this work and on the way by which I will conduct future research.

I thank Dr. Peter Gorsevski for introducing new software and the power of Bayesian statistics to me and for spending lots of time going over the modeling process to ensure a firm grasp on the methods. I also sincerely appreciate the many conversations I had with Dr. Andy Gregory that helped to formulate the idea and analysis methods for this work and for always asking great

(albeit hard to answer) questions. A special thanks goes to Dr. Cori Myers for her collaboration with the data collection process. To work with such bright people has been both an honor and humbling experience for which I am grateful. vii

TABLE OF CONTENTS

Page

INTRODUCTION………………………………………………………………………...... 1

CHAPTER I. BACKGROUND…………………………………….……………………….. 4

1.1 Tectonic overview………………………………………………………………. 4

1.2 Paleoceanography and stratigraphy during the Cenomanian-Turonian

Interval…………………...……………………………………………………… 5

1.3 Spatial modeling approach……………………………………………………... 11

1.3.1 Fuzzy set theory……………………………………………………...... 12

1.3.2 Dempster-Shafer theory……………………………………………...... 13

CHAPTER II. METHODS………………………………………………………………….. 19

2.1 Data collection and spatial analysis…...…………………………………………. 19

2.2 Spatial interpolation……………………………………………………………… 21

2.3 Choosing foraminifera to model….…...…………………………………………. 23

2.4 Implementing fuzzy..…...... …………………………………………. 25

2.5 Modeling species distributions with Dempster-Shafer theory...... 29

2.5.1.1 Depositional Environment....…………………………………...... 30

2.5.1.2 Carbonate content...….…….…………………………………...... 31

2.5.1.3 Silt content.….……….…….…………………………………...... 31

2.5.1.4 Latitudinal extent…….…….…………………………………...... 31

2.5.1.5 Longitudinal extent.….…….…………………………………...... 32

CHAPTER III. RESULTS…………………………………………………………………... 42

3.1 M. mosbyense (Late Cenomanian) results...…………………………………...…. 42 viii

3.2 S. gracile (Late Cenomanian) results.………………………………...…………. 43

3.3 N. juddii (Uppermost Cenomanian) results……….……………………………... 45

3.4 W. devonense (Earliest Turonian) results...……….……………………………... 47

CHAPTER IV. DISCUSSION………………………………...……………………………. 65

4.1 Interpretation of results……………………….……………………………...…. 42

4.2 Dempster-Shafer theory: A befitting model that addresses

potential uncertainties…………...……………………………………………….. 76

4.3 Fuzzy power………………………………………………………………………. 79

4.4 Future work…………………..……...…………………………………………… 80

CHAPTER V. CONCLUSIONS…………………………………………………………… 84

REFERENCES……………………………………………………………………………… 87

APPENDIX A. INTERPOLATION STATISTICS………………………………………… 99

APPENDIX B. ALL FUZZY CONTROL POINTS..……………………………………… 101

APPENDIX C. FORAMINIFERAL ABSENCE FIGURES….…………………………… 105

APPENDIX D. CODES……………………………………….…………………………… 112

APPENDIX E. DATA SOURCES…………………………….…………………………… 119

APPENDIX F. TIME-LAPSE VIDEO OF WATER MASS DISTRIBUTIONS...... ……. 120 ix

LIST OF FIGURES

Figure Page

1 Map of the Western Interior Seaway ...... 17

2 Stratigraphic column of the Rock Canyon, CO, section ...... 18

3 Map of the Western Interior Seaway with localities ...... 33

4 Semivariogram plot ...... 34

5 Common fuzzy functions ...... 34

6 Fuzzification process ...... 35

7 Fuzzy layers for Rotalipora greenhornensis presence ...... 36

8 Fuzzy layers for Rotalipora greenhornensis absence ...... 37

9 Input interpolated surfaces for M. mosbyense zone ...... 48

10 Input interpolated surfaces for S. gracile zone ...... 49

11 Input interpolated surfaces for N. juddii zone ...... 50

12 Input interpolated surfaces for W. devonense zone ...... 51

13 Latitude and longitude rasters ...... 52

14 Interpolated surfaces for Late Cenomanian time zones ...... 53

15 Interpolated surfaces for Latest Cenomanian/Early Turonian ...... 54

16 Benthic oxygenation trends over time ...... 55

17 Presence images for Rotalipora greenhornensis during M. mosbyense zone ...... 56

18 Presence images for Rotalipora greenhornensis during S. gracile zone ...... 57

19 Presence images for Valvulineria loetterlei during S. gracile zone ...... 58

20 Presence images for Ammobaculites spp. during S. gracile zone ...... 59

21 Belief images for Valvulineria loetterlei with varying levels of ignorance ...... 60 x

22 Interval images and histograms for Valvulineria loetterlei with varying levels of

ignorance…………………………………………………………….…………….. 61

23 Presence images for Neobulimina albertensis during N. juddii zone ...... 62

24 Presence images for Gavelinella dakotensis during N. juddii zone ...... 63

25 Presence images for Neobulimina albertensis during W. devonense zone ...... 64

26 Presumable water mixing extent during OAE2 ...... 82

27 Distribution of Heterohelix spp. across the CTB ...... 83 xi

LIST OF TABLES

Table Page

1 Coding scheme for environmental parameters ...... 38

2 Properties of modeled foraminifera ...... 40

3 Fuzzy control points ...... 41 1

INTRODUCTION

The paleoceanography of the Western Interior Seaway (WIS) of North America has been studied extensively to interpret the prevailing climatic and environmental conditions of this vast epicontinental seaway in the Late Cretaceous greenhouse world. Numerous works (e.g., Eicher and Worstell, 1970; Kauffman 1984; Elder, 1985; 1987; 1990; 1991; Leckie, 1985; Pratt, 1985;

Arthur et al., 1987; Kennedy and Cobban, 1991; Leckie et al., 1998; Schröder-Adams et al.,

2001; Caron et al., 2006; Corbett and Watkins, 2013; Lowery et al., 2014; Elderbak et al., 2014; and others) have focused on the Cenomanian-Turonian Boundary Event (CTB) and the coeval

Oceanic Anoxic Event 2 (OAE2), which is associated with rapidly changing oceanographic conditions and attendant complex chemical and biotic responses in the WIS, including maximum sea level rise and significant faunal turnovers ca. 94-93 million years ago (Ma) (e.g., Eicher and

Worstell; 1970; Kauffman, 1984, 1985; Elder, 1990, 1991; Leckie et al., 1998; Elderbak et al.,

2014; Lowery et al., 2014).

Rich and varied molluscan and foraminiferal faunas characterize the Late Cretaceous sequences deposited in the epeiric seaway, reflecting the meeting and mixing of two disparate oceanic regions (Cobban and Scott, 1972; Kauffman, 1977; McNeil and Caldwell, 1981; Leckie et al., 1998). Preliminary research (e.g., Cobban, 1971; Cobban and Scott, 1972) centered on the biostratigraphy and significance of molluscan assemblages, from which a high-resolution ammonoid zonation has been devised (Cobban et al., 2006). This detailed scheme allows for the stratigraphic comparison of worldwide Late Cretaceous strata to those in the WIS (e.g., Monnet,

2009). In addition to a highly refined biostratigraphy, bentonite beds derived from volcanic ash deposits constitute ideal isochrons thus providing a precise geochronologic framework with which to constrain major events in the WIS (Desmares et al., 2004, 2007; Caron et al., 2006). 2

More recent studies (e.g., Leckie, 1985; Eicher and Diner, 1985, 1989; Leckie et al., 1998;

Elderbak et al., 2014; Lowery et al., 2014) have paid much attention to foraminiferal occurrences to interpret paleoecological and paleoceanographic conditions in the seaway during peak transgression periods, including the CTB. These studies have relied on singular localities to assess regional biotic and oceanographic conditions. No study to date has integrated all available locality data to quantitatively summarize and interpret these conditions throughout the entire seaway during the important extinction event.

This research examines the spatial and temporal distribution (paleobiogeography) of planktic and benthic foraminifera to characterize water mass distributions and paleoenvironments in the Cretaceous WIS spanning the Cenomanian-Turonian (ca. 94-93 Ma) time interval. Specific questions include: What are the spatial distributions of foraminifera in the WIS during the CTB?

What environmental factors are associated with these species distributions? In what ways do foraminiferal distributions spatially constrain the dynamic position of the northern and southern water masses across the CTB, including their oceanic front? These questions will aid in reconstructing water mass characteristics and assessing biotic response to ocean anoxia during periods of climate warming. Moreover, no attempt has previously been made to model the dynamic position of the oceanic front, that is, the interface between the southern Tethyan and the northern Boreal waters, within in the Cretaceous WIS.

To directly deal with the inherent uncertainties (e.g., preservational biases, imprecise chronostratigraphy, incomplete sampling) associated with paleontological datasets, spatial analysis techniques that account for this uncertainty were employed using geographic information systems (GIS). Fuzzy sets (Zadeh, 1965) and Dempster-Shafer (DS) theory (Shafer,

1976 after Dempster, 1967) constitute two appropriate techniques. Both methods have been used 3 successfully in GIS analyses (Malczewski, 1999; Eastman, 2015). In addition to providing the first robust quantitative reconstruction of the paleoceanography of the entire seaway, integrating fuzzy and DS theory provides a powerful modeling approach because they take uncertainties and prior knowledge into consideration.

CHAPTER I. BACKGROUND

1.1. Tectonic overview

The WIS extended approximately 6000 km meridionally across the middle of North

America (present-day United States and Canada) for much of the Late Cretaceous (i.e., from the

Albian to Maastrichtian). It established a connection between climatically disparate warm and cold water masses originating in the tropics (Tethys Sea; hereafter “southern” waters) and Arctic region (Boreal realm; “northern” waters), respectively (Fig. 1; Hay et al., 1993; Fisher et al.,

1994; Caron et al., 2006). During the Late Jurassic and Cretaceous time, crustal loading produced by the tectonically active Sevier Orogenic Belt led to the development of the Western

Interior Basin (WIB). The WIB was an Andean-style foreland that existed eastward of the main accretionary and compressive forces of the tectonic regime (Jordan, 1981; Kauffman, 1985;

Sageman et al., 1997). Prior to the union of the two oceanic realms in earliest Middle

Cenomanian time, the WIB, composed predominantly of a complex network of alluvial plains draining into the Canadian Arctic, experienced several flooding episodes by Boreal waters at its northern terminus during the Aptian Stage (Kauffman, 1984; Hay et al., 1993; see Stanley,

2005).

Continued flexural deformation of the North American Cordillera contemporaneous with rising global sea level resulted in extensive flooding of the depressed tectonic block and subsequent infilling of the foreland basin by the epicontinental seaway ca. 100 Ma (Jordan, 1981;

Kauffman, 1985; Hay et al., 1993). Multiple third- and fourth-order transgressive episodes ensued during Aptian-Maastrichtian times (Kauffman, 1984). The WIS attained widths of up to

2000 km and depths exceeding 250 m along its central deepest axis during the peak transgression episode in Late Cenomanian-Early Turonian time (Fig. 1; Kauffman, 1984, 1985; Sageman and 5

Arthur, 1994). The Cretaceous WIS remains the last seaway to extend across the continent joining two distinct oceanic realms (Hay et al., 1993).

Bordered by the Sevier highlands to the west, the WIS extended eastward onto a flat, low-lying stable cratonic platform and may have reached as far as Eastern Iowa and the Hudson

Bay area during peak transgression phases (Hay et al., 1993). According to Schröder-Adams et al. (2001), a restricted basin may have existed further northeast in Manitoba if a topographic high occurred to the west in south-central Saskatchewan. Their interpretation is based on the presence of thinly-laminated black shales likely deposited in a stagnant, stratified water column that created a severely anoxic environment for benthic communities (Schröder-Adams et al., 2001).

Erosion of the Sevier highlands supplied the WIS with terrigenous sediment and freshwater input along the western margin of the seaway (Kauffman, 1984; Hay et al., 1993;

Leckie et al., 1998). In general, multiple cyclothems (transgressive-regressive sedimentary sequences) characterize the seaway, reflecting primarily global eustatic sea level variations but also secondary tectonic and sedimentological influence (Kauffman, 1984; Caldwell et al., 1993;

Sageman et al., 1997). Along the western flank of the seaway, thick siliciclastic sequences dominate where clastic influx is high, whereas fine-grained pelagic carbonates accumulated with less siliciclastic input in the central and eastern portions of the seaway (Kauffman, 1984;

Sageman et al., 1997). Recently, however, Elderbak et al. (2014) have demonstrated that fluvial and deltaic systems constituted a major source for terrigenous sediment input into the eastern portion of the seaway.

1.2. Paleoceanography and stratigraphy during the Cenomanian-Turonian Interval

OAE2, a global marine anoxic event marked by a ~2‰ heavy (positive) excursion of whole-rock ∂13C during the Cenomanian-Turonian interval (e.g., Pratt and Threlkeld, 1984; Pratt, 6

1985; Tsikos et al., 2004), has been attributed to increased marine productivity and subsequent burial of organic matter in response to an abrupt influx of micronutrients in the oceans. Increased productivity was likely the result of one or more of the following: seafloor spreading during crust production; Large Igneous Province (LIP) emplacement; increased nutrient supply from continental weathering associated with an intensified carbon cycle driven by increased volcanic

CO2 output (Leckie et al., 1998; Jenkyns, 2010; Lowery et al., 2014). OAE2 caused significant evolutionary turnovers for mollusks (e.g., Elder, 1991), calcareous nannofossils (e.g., Bralower,

1988) and foraminifera (e.g., Eicher and Worstell, 1970; Leckie, 1985; Leckie et al., 1998) in the

WIS.

An important exception to the widespread anoxic conditions occurred in the WIS, where decreased burial of organic carbon and increased diversification of both planktic and benthic foraminifera suggests local oxygenated conditions prevailed in the epicontinental seaway (Eicher and Worstell, 1970; Leckie, 1985; Pratt, 1985; Leckie et al., 1998). A major incursion of well- oxygenated, warm water of normal salinity into the seaway from the tropics (Caldwell et al.,

1993) likely engendered the abrupt diversification “event” during Sciponoceras gracile time

(Leckie, 1985; Eicher and Diner, 1985), which was supplanted shortly thereafter by the northward advancement of poorly-oxygenated water masses from the Tethyan realm, concurrent with the positive excursion of ∂13C (Caldwell et al., 1993; Eicher and Diner, 1985; Leckie, 1985;

Leckie et al., 1998; Lowery et al., 2014).

The transition to a heavier carbon signature occurred simultaneously with the deposition of the Bridge Creek Limestone Member of the Greenhorn Formation in the central axis of the seaway (Elder and Kirkland, 1985; Caron et al., 2006). The "Pueblo" section at Rock Canyon, west of Pueblo, CO, has been intensely researched since the 1960s (e.g., Cobban and Scott, 7

1972; Elder and Kirkland, 1985; Caron et al., 2006; Desmares et al., 2007) thanks to its dense faunal record and lithologic completeness, reinforcing its status as the Global Boundary

Stratotype Section (GSSP) for the base of the Turonian Stage (Fig. 2; Kennedy et al., 2005).

Rhythmically alternating sequences of highly burrowed limestone and laminated marlstone beds characterize the offshore member (Caron et al., 2006). Additionally, cm-thick marls and calcareous shales intercalate the marl component, which are interrupted by bentonites and local discontinuities (Caron et al., 2006). The alternating sequence of light-colored limestone and dark calcareous shale or marlstone has been suggested to be in tune with the ~41 ka obliquity cycle

(Fischer et al., 1985; Eicher and Diner, 1989).

Leckie et al. (1998), following Eicher and Worstell (1970), identified the occurrence of three foraminiferal biofacies zones at Rock Canyon that reflect changes in oceanographic conditions caused by incursions of multiple southern water masses during the CTB: (1) a basal

“benthonic zone” representing the diversification of both benthic and planktic species caused by an influx of well-oxygenated bottom water from the south coeval with maximum transgression of the Greenhorn Sea (WIS); (2) a planktic zone characterized by reduced planktic diversity and depauperate benthics linked to (3) an increase of biserial forms at the base of the uppermost

Neocardioceras juddii ammonoid zone contemporaneous with a negative ∂18O signature. This negative shift is interpreted to result from the development and expansion of an oxygen minimum zone (OMZ) into the seaway, widely known as the “Heterohelix Shift” (Fig. 2; Leckie et al., 1985, 1998; Pratt, 1985). Such foraminiferal trends are also observed in the Big Bend region of Texas to the Black Hills of South Dakota (Leckie, 1985; Lowery et al., 2014). Thus, foraminiferal trends at Rock Canyon prove to be good indicators of water mass incursions during transgressional and high stand periods. 8

Paleoceanographic and paleoenvironmental conditions of the WIS in North America during the Cenomanian-Turonian interval have therefore largely been inferred from foraminiferal occurrences (e.g., Eicher and Worstell, 1970; Eicher and Diner, 1985; Leckie et al., 1998;

Elderbak et al., 2014; Lowery et al., 2014). Of these, one study (Eicher and Diner, 1985) has gleaned information on water mass characteristics of the entire WIS across the CTB using distribution and diversity trends of foraminiferal assemblages.

Eicher and Diner (1985) qualitatively reconstructed water mass distributions based on the distribution of three distinct benthic biofacies (agglutinated, mixed, calcareous) and planktic diversity patterns recorded in the Greenhorn Formation. They summarized water mass distribution trends during Cenomanian-Turonian time as follows. Late in Graneros time, agglutinated benthics with northern affinities occupied the entire seaway, likely reflecting hyposaline conditions that were inhospitable to planktics (Eicher and Diner, 1985). Early in

Greenhorn time, coeval with the deposition of the Hartland Shale Member, the lack of benthics in the central axis of the seaway is interpreted to result from an incursion of poorly-oxygenated waters from the south (Eicher and Diner, 1985). Agglutinated and mixed (agglutinated and calcareous) benthic species occupied the western and eastern margins of the WIS at this time, likely reflective of dominant circulation patterns of the seaway (Eicher and Diner, 1985).

During latest Cenomanian time, an abrupt increase in calcareous benthic foraminifera present (termed the “Benthonic Zone” by Eicher and Worstell, 1970) in the central portion of the seaway is attributed to the arrival of warm, well-oxygenated bottom waters from the Tethyan realm concurrent with the deposition of the Bridge Creek Limestone Member (Fig. 2; Eicher and

Diner, 1985). Benthic agglutinated faunas still occupied the western extremity of the WIS during this time, suggesting that cold, hyposaline northern waters inhospitable to calcareous 9 foraminifera migrated southward along this margin (Eicher and Diner, 1985). Alternatively, high freshwater input supplied by the Sevier highlands may have led to the development of hypoxic conditions along the western flank of the seaway (Kauffman, 1984).

Several studies (Jewell, 1993; Hay et al., 1993; Fisher et al., 1994; Slingerland et al.,

1996) have attempted to reconstruct the complex circulation patterns and water mass behavior in the Late Cretaceous WIS by employing one or more paleontological, sedimentological and numerical modeling techniques. Hay et al. (1993) proposed three scenarios describing the interaction between southern and northern water masses with variable salinities, densities and temperatures in the seaway. They favored a model depicting the production of a third intermediate water mass occurring along a front where the two masses met. The newly formed entity would have been more and less dense than its southern and northern parent masses, respectively. It would have therefore exited the seaway via a deep-water current to the south, injecting a poorly-oxygenated intermediate water mass into the Tethyan ocean (Hay et al., 1993).

Fisher et al. (1994) attributed an abrupt lateral facies change between calcareous shale and noncalcareous shale in southeastern Montana to represent the boundary, or oceanic front, between the Tethyan and Boreal water masses in the mid- to Late Cretaceous WIS. Changes in water mass boundaries were identified from foraminifera and calcareous nannofossil distributions and were temporally constrained to the Late Cenomanian Sciponoceras gracile zone by bentonite marker beds. In general, southern waters supported calcareous benthic and planktic foraminifera as well as agglutinated forms while northern waters only hosted agglutinated benthics (Fisher et al., 1994). The dynamic orientation of the oceanic front was therefore interpreted on the basis of foraminiferal distributions for time intervals constrained by bentonite beds (Fisher et al., 1994). The northern and southern water masses were of distinct 10 salinity, temperature and density. At times, however, the front was near vertical and the two water masses exhibited the same density but varying temperature and salinities (Fisher et al.,

1994). Furthermore, in accordance with the conclusions drawn by Eicher and Diner (1985), calcareous foraminifera in addition to calcareous nannoplankton that infiltrated the seaway during peak transgression periods are responsible for the calcareous facies within the WIS

(Fisher et al., 1994).

Slingerland et al. (1996) developed a circulation model for the Early Turonian WIS that considered the paleobathymetry, temperatures and salinities of the Boreal and Tethyan oceans and mean annual wind stresses. They concluded that a strong counterclockwise gyre prevailed along the entire extent of the seaway. Coastal jets delivered water into the northern and southern extremities derived from Eastern and Western coastal margins, respectively, and simultaneously drew in surface Tethyan and Boreal waters (Slingerland et al., 1996). The gyre model, although depicting the Early Turonian WIS, may have prevailed during Late Cenomanian time as well, as foraminiferal distributions accord with this scenario during peak transgression (Eicher and Diner,

1985).

Moreover, the interface joining the two distinct water masses may have provided ideal conditions for a high-fertility zone characterized by diverse nannofossil assemblages (Kauffman,

1984; Fisher and Hay, 1999). Specifically, the relative abundance of calcareous nannofossil taxa suggests highly productive surface waters existed along the oceanic boundary during the Late

Cenomanian, promoting assemblage diversity due to passive transport of coccolithophores and reduced nitrogen upwelling (Fisher and Hay, 1999). This high productivity may have supported a diverse endemic molluscan fauna (Kauffman, 1984). Despite being known to occur based on biotic evidence, the fundamental question of ‘where did this front exist in space?’ remains. 11

1.3. Spatial modeling approach

Although foraminiferal distribution patterns have been qualitatively assessed to infer oceanographic conditions of the Cretaceous WIS (e.g., Eicher and Diner, 1985), their use as proxies for reconstructing the spatial distribution of water masses and paleoenvironments for the entire WIS across the CTB has been largely underrepresented in the literature (Leckie et al.,

1998). For example, a transgressive pulse of warm, normal-marine southern waters is known to have infiltrated the southeastern portion of the seaway, but no quantitative constraints have been placed on the location of this water mass for each ammonoid zone (Fig. 2). Moreover, no study to date has incorporated the inherent uncertainties of paleontological analyses directly into the modeling process.

Bayes Theorem provides an ideal means of modeling spatial phenomena with uncertainties by integrating subjective (i.e., degree of belief) and conditional (e.g., the likelihood that an event will happen based on what has already happened) probabilities (Malczewski, 1999;

Gorsevski et al., 2003; 2005). Formally, Bayesian theorem requires a prior probability (or base rate) that the decision maker deems a particular hypothesis being true and a conditional probability that states the probability of the evidence being true given that the hypothesis is true

(this is sometimes termed likelihood in Bayesian statistics) (Malczewski, 1999). By combining the prior and conditional probabilities with our current evidence (the data), a posterior probability is obtained. The posterior probability represents the probability (or degree of confidence) that an event will occur by updating the prior probability with the conditional information (Malczewski, 1999). The posterior probability can then be updated as new information becomes available. 12

Bayesian methods therefore allow for the inclusion of a priori knowledge and do not rely on the assumption that one true parameter value exists (e.g., a fixed mean or that a foraminifer definitely existed at a location) for the population (Malczewski, 1999). Unlike frequentist statistics, then, there exists a distribution of values (the posterior probability distribution) that represents the population parameter (i.e., belief in foraminiferal occurrences in the WIS) of interest in Bayesian statistics (Malczewski, 1999).

Although analysis within a Bayesian framework is appropriate for data with known uncertainties, DS theory—an extension of Bayesian probability theory—is preferred because it does not require complete knowledge of prior and conditional probabilities due to its ability to factor ignorance directly into the model (Gorsevski et al., 2005). “Ignorance” includes any vagueness, including incomplete knowledge and imprecise information, about the data

(Gorsevski et al., 2005). For paleontological data, ignorance can include true species absences, preservational biases, imprecise geochronologies, missing time, incomplete data collection and/or documentation. In order to feed the DS theory model, the data first need to be converted to fuzzy sets.

1.3.1. Fuzzy set theory

Zadeh (1965) first formulated fuzzy sets. Fuzzy sets refer to mathematical sets that have a continuum of grades of membership on the unit interval [0, 1] (Zadeh, 1965). In other words, unlike crisp (also called sharp, hard or Boolean) sets, which can only designate full membership

(0 or 1) of objects to a particular class, fuzzy sets can take on any real value in the range [0, 1]. It is important to note that membership within a fuzzy set does not represent a probability; rather, fuzzy only gives the possibility (or grade) of membership. 13

As an example, consider what constitutes “shallow” in the WIS during peak transgression. Certainly, the basin center (> 150 meters) is not shallow, whereas < 5 m shoreward is (Thomson et al., 2011). What about 10, 7 or 5.001 m deep? Clearly the grade from shallow to deep is not sharp, and fuzzy can assign partial memberships to all depths between what we consider definitely shallow (5 m; designated as 0) and deep (150 m; 1 or full membership). In other words, any depths ≥ 150 m are quantified as 1 (deep) and those ≤ 5 m are

0 (shallow) and all depths in between fall somewhere on (0, 1). Depths of 10 m might have a membership of 0.08 on this range (depending on the fuzzy function applied to the original data), and are interpreted as very shallow, but not the shallowest.

Moreover, fuzzy methods are also useful for classes that are not clearly defined or for which membership is impossible to determine cleanly (Longley et al., 2010). This makes them particularly attractive for paleontological analyses such as this one because environments are averaged or “condensed” over entire ammonoid zones (or across entire stages in other studies) and therefore could include variability in their compositions. For example, fuzzy sets can account for the transition from a nearshore-offshore to completely offshore environment as sea level rises during the N. juddii zone. This soft classification scheme therefore deals directly with the uncertainty—including the nature and decision-making—about the data, but is itself not a direct measure of uncertainty (Eastman, 2015).

1.3.2. Dempster-Shafer theory

Dempster (1967) formalized belief functions—those that depict the concept of upper and lower probability—and Shafer further developed the theory in A Mathematical Theory of

Evidence (1976). Like fuzzy sets, the DS theory of evidence is attractive for this study because uncertainty (i.e., ignorance) about the data is allowed in the decision-making process during 14 modeling (Shafer, 1976; Gorsevski et al., 2005). DS theory directly represents this uncertainty via the imprecise inputs (i.e., the fuzzy set layers) that fuel the models. Another advantage is that this uncertainty can be quantitative or anecdotal.

DS theory aggregates many lines of evidence to support hypotheses (i.e., propositions) that predict the epistemic probability (i.e., degree of belief) that any phenomenon may occur

(Shafer, 1976; Eastman, 2015). Since ignorance is included in the knowledge base, the DS model is able to determine the degree to which an hypothesis is supported based on our current state of incomplete information (Eastman, 2015). This makes DS theory a particularly enticing modeling approach because if there is little evidence (and/or high uncertainty) to support a particular hypothesis (e.g., species presence), then the analyst can give the degree of belief low weight at the beginning of the analysis (Shafer, 1976). This simple judgment is how ignorance is incorporated directly into the model.

Belief, it follows, is defined as the degree to which evidence supports a given hypothesis; plausibility is the inability to refute that hypothesis; and the belief interval (the difference between plausibility and belief) indicates the level of uncertainty about the hypothesis (Shafer,

1976; Eastman, 2015). Thus, belief represents the lower bound for an unknown probability function, and plausibility constitutes its upper bound. A formal definition of DS theory (after

Dempster, 1967; Shafer, 1976 and Gorsevski et al., 2005), including its belief, plausibility and interval outputs, follows below.

Let Θ be the set of all possible hypotheses. This is called the frame discernment and is equivalent to state space in probability terms. The power set 2Θ includes all possible (mutually exclusive) combinations of hypotheses plus the empty set ϕ. For example, if the frame of discernment includes two hypotheses (i.e., Θ = {X, Y}), then the number of hypotheses = 22 = 4 15 and the possible combinations are [X], [Y], [X, Y] and ϕ. The empty set represents a hypothesis that is known to be false.

Hypotheses [X] and [Y] are called singleton hypotheses because each subset contains one basic element, whereas [X, Y] is a non-singleton hypothesis because each subset contains more than one element. Each subset is referred to as a focal element. An assignment on the interval [0,

1] is given to each focal element based on the available evidence. Thus, the value 0 represents no belief in a hypothesis whereas the value 1 signifies total belief. Values between 0 and 1 indicate partial beliefs. Uncertainty is the amount of evidence not assigned to any particular subset and is quantified by 1 minus the sum of all supporting evidence for a subset.

The theory of evidence then assigns an exact belief, or mass, m, to each focal element X in the power set Θ such that the sum of all masses equals to one at all times. This exact belief

(mass) is commonly referred to as the basic probability assignment (BPA) and must satisfy

∑ 푚(푋) = 1 and 푚(휙) = 0 푋⊂Θ

where m(X) is the BPA of set X in Θ, ϕ is the empty set and Θ is the universal set of all possible outcomes or frame of discernment.

Belief and plausibility functions are then derived from the BPA. Belief, defined above, is calculated from all subsets of the chosen hypothesis (i.e., for the belief in [X, Y], the beliefs in

[X], [Y] and [X, Y] will be summed) and is given by

퐵푒푙(푋) = ∑ 푚(푌) 푌⊂푋 16

Plausibility, as defined above, represents the maximum degree of belief and is obtained by subtracting the BPAs associated with all the subsets contributing to the hypothesis X from 1.

Plausibility is thus

푃푙푠(푋) = ∑ 푚(푌) 푌∩푋= 휙

where  is the intersection operator (elements that belong to both subsets X and Y).

To allow for the aggregation of two lines of evidence (i.e., masses), m1 and m2, to support a particular focal element in Θ, Dempster-Shafer theory employs Dempster’s rule of combination:

∑ 푚1(푋)푚2(푌) 푤ℎ푒푛 푋 ∩ 푌 = 푍 (푚1 ⊕ 푚2)(푍) = 1 − ∑ 푚1(푋) 푚2(푌) 푤ℎ푒푛 푋 ∩ 푌 = ∅

where (m1  m2)(Z) is the BPA for the new hypothesis [Z] and  is the logical operator exclusive or (elements belonging to X or Y but not to both). The combined set must satisfy Z ≠

ϕ, and the denominator functions as the normalizing factor by summing the products of sets X and Y where their intersection is null. If the denominator equals to zero, then the two pieces of evidence are not combinable. Dempster’s rule of combination is commutative and associative so multiple lines of evidence can be assembled in any order. This makes DS theory an appealing modeling technique because as new information is discovered, it can be added to the already established knowledge base.

Fig. 1. Map of the Western Interior Seaway. Paleogeographic reconstruction during peak transgression (Early Turonian) time. Yellow dot is the Rock Canyon section near Pueblo, Colorado. After Elderbak et al. (2014). 18

Fig. 2. Stratigraphic column of the Rock Canyon, CO, section. Major oceanographic and foraminiferal events in the WIS are summarized at right. Stages, ammonoid zones, foraminiferal zones and lithostratigraphy are shown at left. Capital letters represent major bentonite marker beds. H. Shale M. = Hartland Shale Member. Modified from Figure 4 in Elderbak et al. (2014). 19

CHAPTER II. METHODS

2.1. Data collection and spatial analysis

Foraminiferal occurrence and associated stratigraphic data for various Bridge Creek

Limestone and equivalent Canadian strata deposits were culled from numerous research articles,

Masters theses and PhD dissertations. These data were collected following the methods described in Myers et al. (2015) and served as inputs for spatial statistical (DS theory) models that model foraminiferal occurrences in order to delineate large-scale water mass distributions for the entire WIS across the CTB (Table 1). For an example on how to extract geological and environmental data from a stratigraphic section, see Figure 3 in Myers et al. (2015). Localities are represented as points in space. Stratigraphic (e.g., total siliciclastic sediment content) and geochemical/environmental (e.g., organic carbon) attribute data of the Bridge Creek Limestone

Member were time-averaged according to ammonoid zones established by Kennedy and Cobban

(1991), which bracket the CTB (ca. 94-93 Ma) in the WIS (Fig. 2).

Four ammonoid zones, Metoicoceras mosbyense (M. mosbyense), Sciponoceras gracile

(S. gracile), Neocardioceras juddii (N. juddii) and Watinoceras devonense (W. devonense), comprise this time interval (Fig. 2). Foraminiferal species data were collected as presence/absence (as opposed to abundance) within an ammonoid zone for each locality. The ammonoid zone M. mosbyense spans approximately 620,000 years; S. gracile zone ca. 240,000 years; N. juddii zone ca. 300,000 years and W. devonense zone ca. 170,000 years (Cobban et al.,

2006; Sageman et al., 2006). Thus, data binning occurs commensurate with ascending stratigraphic levels (delineated by bentonites) for each locality over a “brief” geological period of 1.3 million years (Fig. 2). 20

Foraminiferal occurrence data were collected for 31 unique sites and stratigraphic/environmental data were obtained for 43 well-distributed localities for a total of 198 unique records (Fig. 3). Of the possible 43 locations, 32 points were available for analyzing the foraminiferal and environmental parameters for M. mosbyense zone; 37 for S. gracile zone; 38 for N. juddii zone and 35 for W. devonense zone. Environmental data were also collected for

Pseudaspidoceras flexuosum and Vascoceras birchbyi zones but were not used for analysis here because oceanic conditions during these times were consistent with those dominant in W. devonense, and data accessibility was limited to 28 localities for each zone (Fig. 2). Locality data with coarser resolution than ammonoid zones were omitted from the analysis, so only ammonoid-zone level foraminiferal and stratigraphic data were recorded. Additionally, locality data availability was mainly limited by erosion/non-deposition of sediments and/or lack of collection for certain ammonoid zones.

Following collection, spatial data were imported into the GIS software ArcMap (version

10.3; ESRI, 2015) for display as point features with reference to their geographic coordinates

(Fig. 3). The data were projected into Albers Equal Area Conic in accordance with the USGS

Decision Support System (http://mcmcweb.er.usgs.gov/DSS/, USGS, 2014) that specifies how to transform continental-scale data. Shorelines were created as polyline shapefiles for M. mosbyense and S. gracile (after Fisher et al., 1994), N. juddii (Slingerland et al., 1996) and Early

Turonian (W. devonense – V. birch; Elderbak et al., 2014) time zones. Polygon masks were then generated using the open-source GIS software QGIS (version 2.10; QGIS Development Team,

2015) from these shoreline files to define the extent within which to constrain the spatial analysis. 21

Exploratory data analysis (EDA) was carried out in RStudio, GeoDa (Anselin et al.,

2006) and ArcGIS Geostatistical Analyst to complement traditional visual data inspection in

ArcGIS and QGIS. Histograms, kernel density functions, trend analysis, and scatter, box and normal QQ plots revealed which of the variables are closely associated with either foraminiferal presence or absence (Table 1). To effectively characterize the paleoceanography for the entire seaway, and to supply inputs for fuzzy sets and the DS belief model, continuous raster grid surfaces that represent attribute information were constructed from the discrete location (point) data—a process known as spatial interpolation.

2.2. Spatial interpolation

Kriging is a widely used probabilistic interpolation method that considers the statistical nature of the data (Chang, 2010). It differs from deterministic interpolation techniques (e.g., inverse distance weighting and spline) by providing information on the prediction uncertainty of the interpolated surface (Chang, 2010). Kriging assumes that spatial correlation, or spatial dependence, exists in the dataset; that is, points that are closer together are expected to have more similar values than those further apart (Tobler, 1970). Kriging computes the semivariance to quantify this relationship. Semivariance is given by

1 2 훾(ℎ) = [푧(푥 ) − 푧(푥 )] 2 푖 푗

where 훾(ℎ) is the semivariance between known points, 푥푖 and 푥푗, separated by distance ℎ; and 푧 is the variable value (Chang, 2010). 22

Kriging then uses a semivariogram—a function that quantifies the spatial correlation among all sample locations—to determine the contribution of measured points to predict the values at unsampled locations by fitting a model through a plot of semivariance (y-axis) versus ℎ

(analogous to fitting a regression line through ostensibly linear data) (Fig. 4; Krivoruchko, 2012).

For an in depth discussion on classical kriging (and spatial interpolation methods in general), see

Chang (2010).

Classical kriging techniques that rely on a single semivariogram are held to several strong assumptions, namely stationarity. Stationarity means the data mean and the semivariogram values are identical at each location (Krivoruchko, 2012). Additional important assumptions are that the data follow a Gaussian (normal) distribution and the estimated semivariogram is the true semivariogram of the data. All of the assumptions discussed above are rarely satisfied in reality

(Krivoruchko, 2012). Empirical Bayesian kriging (EBK) is a type of kriging that deals directly with these uncertainties.

The value of EBK is its ability to account for uncertainty in the interpolation estimation by generating a distribution of semivariograms, as opposed to a single semivariogram, characteristic of classical kriging methods (Krivoruchko, 2012). By producing many semivariograms of local data subsets (that can be transformed if non-Gaussian and/or detrended),

EBK provides better estimation at unsampled locations for small datasets. This is especially beneficial for this study, where data availability is limited by a precise chronostratigraphy, the availability of already-sampled locations, preservational biases and potential inconsistencies during field collection. Therefore, each attribute was analyzed during EDA to produce the best- fit interpolation model using EBK by taking statistical descriptors (root mean square and mean), trends and (non-) normality into account (Table 1). Best-fit surfaces (models) have a mean and 23 root mean square equal to 0 and a root mean square standardization of 1. These models had a cell size of 7000 m because this size provided optimal processing time without reducing any spatial detail of the attributes on the resultant interpolated surfaces. (For a complete list of the unique

EBK parameters for each attribute per time zone, see Appendix A.)

2.3. Choosing foraminifera to model

The paleobiogeography of foraminifera constitutes a well-suited proxy for water mass distributions in the WIS (Eicher and Diner, 1985; Leckie et al., 1998). The foraminifera that were modeled were chosen to reflect the significant biotic/paleoceanographic events of the seaway from the Late Cenomanian to Early Turonian (Table 2). Rotalipora greenhornensis was modeled for M. mosbyense and S. gracile zones because it was probably the most stenotopic planktic species in the WIS during CTB time, reflective of warm, deep, normal-marine, stratified waters (Leckie et al., 1998). Benthic conditions during the M. mosbyense zone were inhospitable to nearly all benthic calcareous species (e.g., Leckie et al., 1998; Elderbak et al., 2014). Coupled with limited documentation of agglutinated (northern) species, the attribute oxygen was modeled to characterize the benthic oxygenation conditions for Late Cenomanian time (Table 1).

Benthic conditions improved during the S. gracile zone (concurrent with the “Benthonic

Zone” of Eicher and Worstell, 1970), and foraminiferal documentation for this time is robust for the entire seaway. Valvulineria loetterlei, a calcareous benthic species, was used to define the extent of the southern water mass entering from the Tethyan Sea. Ammobaculites spp., a northern agglutinated genus, is a proxy for the location of the northern water mass. Rotalipora greenhornensis was modeled to reconstruct the surface water conditions for the S. gracile zone.

Across the CTB, as sea level rose and neared its maximum depth, hypoxic to dysoxic benthic conditions prevailed in the epicontinental sea (e.g., Leckie et al., 1998). During this time, 24

Neobulimina albertensis—a low oxygen tolerant, supposed infaunal benthic calcareous species with Tethyan affinities—was nearly ubiquitous in the southern and eastern portions of the seaway (e.g., Leckie et al., 1998; Elderbak et al., 2014). This species is representative of the dominant benthic conditions for the N. juddii and W. devonense zones. Coeval with dysoxic benthos at the stage boundary were poor surface water conditions, reflected by the dominance of

Heterohelix spp. throughout the entire seaway (i.e., the “Heterohelix Shift” coined by Leckie et al., 1998). Therefore, Neobulimina albertensis was modeled to reveal benthic conditions during the N. juddii and W. devonense zones. Maps depicting the range of Heterohelix spp. portray the dominant surface water conditions during these times.

Another low oxygen-tolerant benthic calcareous species, Gavelinella dakotensis, was modeled to depict general areas of low oxygen content and regions affected by local high nutrient influx. Its brief dominance over Neobulimina albertensis in the western margin of the sea adjacent to the Sevier highlands at the base of the N. juddii zone is attributed to increased delivery of organic matter to the WIS by terrestrial or marine systems—as evidenced by a negative ∂18O excursion and coeval kaolinite/illite influx to the region—coincident with peak abundance of Gavelinella dakotensis (Leckie et al., 1998). Though specific to the western seaway, its dominance reached as far eastward as northeastern Arizona and southwestern

Colorado (Fig. 1; Leckie et al., 1998).

Along the eastern corridor in the US, its short-lived prevalence is interpreted to reflect reduced dissolved oxygen content levels as opposed to increased detritus input like that occurring contemporaneously along the western margin (Fig. 1; Elderbak et al., 2014). Later, during W. devonense time, the shift back to Neobulimina dominance is attributed to subtle changes in the balance between organic matter influx and benthic oxygen content (Leckie et al., 25

1998). Leckie et al. (1998) interpret its dominance to mainly reflect dissolved oxygen levels at the sediment-water interface given that more normal marine conditions existed (as indicated by a widespread positive ∂18O signature and no significant detrital clay spikes) during this time.

For each foraminifer, the original data were parsed by species presence, absence or no data per locality per time zone. At localities where no foraminifera had been looked for/sampled/documented, if they are present at nearby locations with similar attribute data, then they are inferred to be present at those locations based on spatial autocorrelation (i.e., proximity) and homogenous geologic conditions. For instance, Valvulineria loetterlei is known to occur at

Rock Canyon and Deora, CO—deep water areas with high (low) carbonate (silt) content. It is presumed, then, to have occurred at Graneros and Las Animas, CO, nearby places also with high

(low) carbonate (silt) content but no biotic documentation. Caution was exercised during this procedure, as most sites with no foraminiferal data remained flagged as no data, especially in northern areas where occurrence data are sparse.

2.4. Implementing fuzzy

Following interpolation of environmental parameters and selection of which foraminifera to model, the interpolated environmental surfaces needed to be “fuzzified” to serve as inputs for the DS belief module. To derive the fuzzy layers, control points need to be assigned to the original interpolated layer to transform the data onto a [0, 1] set using one of several fuzzy functions (Fig. 5). Figure 5 displays only common increasing and decreasing fuzzy functions, but symmetrical functions (e.g., trapezoidal and triangular) may be more appropriate for other situations where data take on a middle value and decrease membership as the values increase or decrease. For instance, the fuzzification of the latitudinal extent of a tropical taxon could best be 26 represented by a trapezoidal function whose membership decreases as latitude values increase toward each pole (see Figure 1 in Gorsevski et al., 2006 for symmetrical function examples).

The derivation of fuzzy layers can be done based on the statistical nature of the data and/or expert knowledge (Gorsevski et al., 2003; Robinson, 2003). Here, I take a combined approach. The fuzzification process was based on the statistical relationship between the environmental variables and foraminiferal occurrences, while the level of ignorance was driven by expert paleontological knowledge (Fig. 6 and Table 3; see fuzzification example below). The variables that co-vary significantly (i.e., no random association) with species presence and/or absence are depositional environment, latitudinal and longitudinal extent, and total carbonate and silt content (Table 1).

The interpolated rasters were imported into the integrated GIS and remote sensing software TerrSet (formerly IDRISI) (Clark Labs, 2015). TerrSet has advanced spatial analytic tools such as fuzzy methods, DS belief and Bayesian models (among many more), most of which are primarily oriented toward raster analyses. Custom Python and ArcPy scripts converted the

ArcGIS GRID/ASCII rasters to the TerrSet raster (.rst) file type to speed up data processing during the file import stage. Points of known species occurrences and absences as well as those with no foraminiferal data were overlain onto the interpolated surfaces. Histograms and their statistical descriptors (e.g., mean) were generated for the interpolated surfaces with the species layers as masks to identify the attribute values at each specific species location. This procedure was carried out separately for three layers—species presence, species absence and no data—for each attribute per the M. mosbyense through W. devonense ammonoid zones. Example custom

Python scripts that control the above procedures (as well as the fuzzification process described below) are available in Appendix D. 27

The derivation and justification of fuzzy control points is itself a fuzzy process (e.g.,

Gorsevski et al., 2003; 2005; Eastman, 2015). To arrive at appropriate control points, I present an example using the calcareous benthic species Valvulineria loetterlei. V. loetterlei is a southern water tropical taxon and therefore exists where carbonate is the dominant sediment type (Leckie et al., 1998). Draping species presence and absence locations on the total carbonate raster for S. gracile, we see that, indeed, its presence is associated with high (mean = 48%) carbonate values, while its absence corresponds to low (mean = 7%) carbonate values (Fig. 6). This is promising

(and expected), but at what carbonate value will presence be totally supported (i.e., = 1) or no longer supported (i.e., completely absent)?

The carbonate layer was fuzzified using monotonically increasing and decreasing sigmoidal functions (Figs. 5 and 6). The monotonically increasing function was applied to the presence data because presence is associated with high carbonate values. Control point a, which defines the value at which presence begins to be supported, was chosen to be 10% carbonate to account for a few occurrences of V. loetterlei at locations with low carbonate content. This is the value where its support is zero but begins to rise as the carbonate values increase. Its upper bound, specified by control point b, is where presence is absolutely supported. Since most presences occur at ≥ 50% carbonate, and its absence is doubted at these high values, b is designated as 50%. Any occurrence associated with above 50% carbonate is assigned a full membership value of 1.

However, this membership assignment does not make room for ignorance, so the entire surface was multiplied by a scalar value (0.8) to lower the certainty of the association between presence and total carbonate. This scalar was chosen based on expert knowledge: sections with less carbonate rocks where the species occurred could exist but just have not yet been sampled 28

(so the value reflects a limited number of samples); poor preservation potential upon death and/or post-depositional dissolution in northern waters could have prevented the organism from being preserved; total carbonate percentage is merely associated with (and is not a cause of) presence, that is, high carbonate content does not necessitate foraminifer presence. Nevertheless, the association between carbonate content and species presence is pronounced, so the belief (0.8) in the certainty of this association remains fairly high.

Low carbonate values correspond to absence of V. loetterlei, so a monotonically decreasing sigmoidal curve is appropriate (Figs. 5 and 6). Control point c indicates the value at which full membership begins to decline, while control point d signifies no membership at all.

The absence data are a little more straightforward than for presence: no absences occur at > 16% carbonate (Fig. 6). Complete absence is defined as 0 – 10% carbonate, after which the belief in absence begins to decline (c = 10). Although no absences are associated with values above 16%, disbelief in absence is extended a bit to account for possible missing points so as to relax the overall membership possibility. Therefore, complete disbelief in absence is set slightly higher (d

= 20). Like the fuzzy presence support layer, its absence support counterpart was multiplied by a scalar factor (0.7) to account for the imprecision of expert knowledge fueling the model. Notice that the scalar value here is less than that used for presence support because paleontologists are always less certain that a species definitely did not exist at a locality due to potential preservational and collection biases. Expert knowledge about paleontology thus directly factors into the modeling process.

2.5. Modeling species distributions with Dempster-Shafer theory

Dempster-Shafer Weight-of-Evidence modeling was carried out to evaluate the probability (belief in DS terms) that a foraminiferal species will occur in any pixel location

(paleobiogeography) on a surface representing the entire WIS. The analysis was performed for the four ammonoid zones spanning the CTB (M. mosbyense, S. gracile, N. juddii and W. devonense) using the geospatial modeling software TerrSet (Eastman, 2015). The large-scale spatial distribution of the water masses (spatial paleoceanography) such as their locations and interactions was visualized, summarized and interpreted from the belief maps for a given time period. The physical characteristics of these masses like salinity, temperature and water column stratification were therefore interpreted from the species’ modeled occurrences as well.

Indirect lines of evidence (i.e., the fuzzified variable surfaces derived from environmental parameter data) that are associated with existing foraminiferal occurrences were aggregated to support the following hypotheses in the frame of discernment: [presence], [absence] or

[presence, absence]. No direct evidence (such as distance to known species presences) fueled the models. Distance to known sites is not an input in order to not overweigh known locations during modeling. I am interested in areas that do not have known foraminifera, for which the known sites do not provide direct information. Therefore, the evidence from the environmental variables is largely indirect. I know the relationship between carbonate content and foraminiferal presence, so I use that relationship to fuzzify or transform the interpolated environmental spatial models into an image of membership possibility (designated as a value on the interval [0, 1]) for all pixels (Fig. 6). Furthermore, because the objective is to portray the water mass locations in the seaway, high belief in presence along potential water-mixing interfaces will unrealistically make it seem the water mass abruptly ends where belief plummets (i.e., where the other water 30 component dominates). For these reasons, the known points tend to not be visible on the resulting belief models. Thus, the belief surfaces look continuous or “smooth” (see Results section).

Each piece of evidence was derived independently of the others to avoid erroneous results stemming from fusing cumulative beliefs (Jøsang and Pope, 2012). Ignorance is accounted for in the model because each line of evidence is related to the hypothesis only indirectly, and evidence that is not known to undoubtedly support either presence or absence can support both (i.e., [presence, absence]). Ignorance is represented numerically as 1 minus the highest value of the fuzzy layer (e.g., a layer with maximum support of 0.8 will have 0.2 ignorance).

I am most interested in the evidence supporting the element [presence], though all lines of evidence will affect the total belief in this hypothesis. For this reason the relationship between the variables and species presence/absence must be explicit. A detailed example of arriving at how each variable relates to the occurrence of the calcareous planktic species Rotalipora greenhornensis is discussed below. The following fuzzy layers appear in Figs. 7 and 8. Table 3 provides a complete list of fuzzy control points for modeling Rotalipora greenhornensis during the S. gracile zone. (All fuzzy control points for all species are reported in Appendix B.)

2.5.1.1. Depositional environment. Deep-dwelling planktic species tend to be absent in shallow neritic oceanic environments along dominantly siliciclastic margins (Fig. 3 in Leckie et al., 1998). Therefore, if in a shallow environment, there is reason to believe that they are not there (just as we can rule out human settlements on very steep slopes). Presence is supported in deeper environments where high populations of planktic species flourish (Leckie et al., 1998).

However, offshore environments do not require planktic species to exist there (as gently sloping 31 areas do not necessitate settlements). Thus, the variable depositional environment supports species absence only (Fig. 8).

2.5.1.2. Carbonate content. Rotalipora greenhornensis is a calcareous species associated with warm, deep, subtropical waters (Leckie et al., 1998). Its occurrence corresponds to the southern Tethyan waters in which carbonate-rich sediments were deposited. High carbonate values therefore support species presence, whereas low values support its absence (the disbelief in presence).

2.5.1.3. Silt content. High silt content occurs along the western margin where siliciclastic input from the Sevier highlands entered the seaway (Elder, 1991). Furthermore, northern water agglutinated species dominate these regions over calcareous species (Leckie et al., 1998). The species resides in clear, warm waters where turbidity (likely brought on by terrigenous input) is low (Leckie et al., 1998). Therefore, high silt content (where carbonate content tends to be low) supports Rotalipora greenhornensis absence and low silt content is linked to its presence. Note that silt and carbonate content are not inversely proportionate to each other; carbonate content includes all carbonate fractions (i.e., limestones and chalk), whereas silt content is total siliciclastics minus clay (which is generally ubiquitous in the seaway) and sand. Total carbonate and total siliciclastic fields are inverse to each other (Table 1). In addition, the boundaries between high and low values of the silt and carbonate rasters for each time zone are not identical, making them suitable individual inputs (see Results section).

2.5.1.4. Latitudinal extent. This foraminifer is associated with warm waters that came into the WIS from low latitudes, so low latitudes support its presence, while high latitudes support absence. 32

2.5.1.5. Longitudinal extent. Eastern longitudes favor species presence because the southern tropical waters in which the foraminifer dwelled flowed along the seaway’s eastern margin (Slingerland et al., 1996). Western longitudes—where the warm Tethyan waters did not flow—therefore promote species absence.

Belief, plausibility and belief interval images were extracted from the knowledge base for the [presence], [absence] and [presence, absence] hypotheses following belief modeling. For each presence and absence hypothesis, the plausibility maps inherently have higher values than belief because belief represents the minimum probability for the distribution of the species while plausibility represents the maximum probability for the distribution of the species. For this study, the belief interval (the difference between probability and belief) maps reveal where the species is most likely to occur if more data are gathered there. Note that belief ≤ 0.99 (even though the scale on the belief maps goes from 0 to 1 for aesthetic purposes), since some degree of ignorance is included in each model. Plausibility, on the other hand, can equal to 1.

Fig. 3. Map of the Western Interior Seaway with localities. Seaway mask is for S. gracile zone. 1 = sill. 2 = Four Corners region. 3 = Rock Canyon/ Central axis of seaway. 4 = Black Hills. 5 = Manitoba Escarpment. 6 = Bainbridge River; Saskatchewan-Manitoba frontier. 7 = Alberta sections. 8 = NW Territories. Other figures that have numbered localities refer to the number scheme introduced in this figure. 34

Fig. 4. Semivariogram plot. Points that exist closer to each other in space have lower semivariance. Blue line indicates estimated equation (model) that produces interpolated surface.

Fig. 5. Common fuzzy functions. Top row: sigmoidal. Middle: J-shaped. Bottom: Linear. Left column shows monotonically increasing curves. Right shows monotonically decreasing curves. 35

Fig. 6. Fuzzification process. Example shows how to fuzzify the attribute total carbonate using a sigmoidal curve (dashed blue line) for Valvulineria loetterlei presence (left) and absence (right). See section 2.4 Implementing Fuzzy for details. Values a, b, c and d are control points (see Fig. 5). Control points have the same units as the attribute total carbonate.

Fig. 7. Fuzzy layers for Rotalipora greenhornensis presence. Seaway mask shown is for S. gracile zone. From left to right: total carbonate, silt content, latitude and longitude. Values do not reach 1.0 to account for ignorance in the modeling process.

Fig. 8. Fuzzy layers for Rotalipora greenhornensis absence. Seaway mask shown is for S. gracile zone. From left to right: depositional environment, total carbonate, silt content, latitude and longitude. Values do not reach 1.0 to account for ignorance in the modeling process.

Table 1. Coding scheme for environmental parameters. Modified from Table 1 in Myers et al. (2015).

Environmental Description Parameter (attribute) Approximate fraction of each grain size within a marine Percent clay, silt, sand sedimentary package per ammonoid zone. Approximate fraction of siliciclastic and carbonate (mainly Percent siliciclastics, limestone) sediments within a marine sedimentary package per carbonates ammonoid zone. Approximate fraction of chalk within a marine sedimentary Percent chalk package per ammonoid zone. Approximate degree of burrowing and other within-sediment trace maker activity within a sedimentary package per ammonoid zone. Degree of Bioturbation Decimals delineate relative abundance of trace maker activity within a sedimentary package. 1. Minimal Less than 25% sediments show bioturbation 2. Moderate 25-50% sediments show bioturbation 3. Moderate-High 50-75% of sediments show bioturbation 4. High 75-100% of sediments show bioturbation Approximate thickness of sedimentary beds. Decimals delineate Bedding Style relative abundance of bedding thickness within a marine sedimentary package per ammonoid zone. 1. laminated < 1 cm-scale bedding 2. thin cm-scale bedding 3. moderate dm-scale bedding 4. thick m-scale bedding Relative water depth with respect to storm and fair-weather wave Inferred Water Depth bases. Decimals delineate relative placement within an energy zone. 0. Subaerial Above mean tide line; including delta plain and marsh settings. Between mean low tide and mean high tide; including delta plain 1. Upper Intertidal and marsh settings.

Between mean low tide and fair weather wave base; including 2. Lower Intertidal upper and middle shoreface settings, delta plain and marsh settings. Between fair weather and storm wave base; including delta front 3. Shallow Subtidal and prodelta slope settings and lower shoreface settings. Below storm wave base; including delta front and prodelta slope 4. Offshore/Basin settings. Inferred sedimentary environment of deposition. Decimals Depositional Environment delineate relative placement within depositional environments. Peritidal; beach and channel deposits, high sediment deltaic 1. Estuarine/Delta Plain environments, shallow estuarine. 2. Lagoonal/Delta Front Near-shore, protected subtidal including shelf lagoons, delta 39

platform, and delta front; frequently heterolithic fine-grained lithofacies with storm deposits; wave-agitated environments including bars, oolite shoals, biohermic areas; above wave base, may or may not be steep. Dominated by sand and silt deposits; shallow open shelf and 3. Inner Shelf/Prodelta prodelta environments, below fair-weather wave base, but evidence of storm deposits. Dominated by dark clay-muds; deeper open shelf and fore-delta 4. Midshelf environments; fine-grained sediments; low frequency of storm re- working. Dominated by impure clayey carbonate muds; below storm wave 5. Outer Shelf base. Dominated by carbonate muds; deep water; black shales; lower 6. Basin oxygen concentration. Inferred O2 content of the water column at the water-sediment Oxygenation interface. Decimals delineate relative placement within oxygenation zones. 1. Subaerial 2. Normal Marine / Diverse shelly taxa including epifauna and infauna; bioturbated. Aerobic Shell epifauna and burrowers dominant; laminated to burrowed 3. Dysoxic sediments. No macrofauna; anaerobic S-bacteria; laminated sediments; iron 4. Anoxic speciation geochemistry. Average δ13C, δ18O, and total organic carbon per marine sediment δ13C, δ18O, TOC package per ammonoid zone.

Table 2. Properties of modeled foraminifera. Calc. - calcareous, Aggl. - agglutinated

Time Zone Taxon Test Type Living Mode Water Water Mass Indicator Temperature

M. mosbyense/ Rotalipora greenhornensis Calc. Planktic Warm Southern waters; Normal surface O2 S. gracile S. gracile Valvulineria loetterlei Calc. Benthic Warm Location of southern water mass; well- oxygenated bottom waters

S. gracile Ammobaculites spp. Aggl. Benthic Cold Location of northern water mass; well- oxygenated bottom waters

N. juddii/ Neobulimina albertensis Calc. Benthic Warm Tethyan intermediate waters; depleted bottom-water O2 W. devonense N. juddii Gavelinella dakotensis Calc. Benthic Warm Tethyan intermediate waters; depleted bottom-water O2; local nutrient influx

Table 3. Fuzzy control points. The example given is for Rotalipora greenhornensis during the S. gracile zone.* Interpolated attribute layers were converted to fuzzy membership sets to be rendered as recognizable inputs for the Dempster-Shafer models. Control point units are the same as the attribute units (e.g., latitude control points are in decimal degrees, silt in percent, etc.).

Hypothesis Input Layer Fuzzy Function a b c d Degree of Confidence (1 – Ignorance) Presence Total Carbonate Sigmoidal-M. Increasing** 10 50 50 50 0.8 Presence Silt Sigmoidal- M. Decreasing 15 15 15 46 0.7 Presence Latitude Sigmoidal- M. Decreasing 42 42 42 47 0.8 Presence Longitude Sigmoidal- M. Increasing -110 -99.5 -99.5 -99.5 0.75

Absence Dep. Env. User-Defined*** 1 - 0.5 2 - 0.5 3 - 0.15 4, 5, 6 - 0 0.5 Absence Total Carbonate Sigmoidal- M. Decreasing 15 15 15 47 0.7 Absence Silt Sigmoidal- M. Increasing 15 42 42 42 0.6 Absence Latitude Sigmoidal- M. Increasing 35 50 50 50 0.7 Absence Longitude Sigmoidal- M. Decreasing -111 -111 -111 -100 0.65

*For the complete list of fuzzy control points, see Appendix B. **"M" = Monotonically. ***User-Defined functions require both the attribute value (first number) and the control point value.

CHAPTER III. RESULTS

Figures 9 – 12 display the interpolated surfaces used in the DS models for four ammonoid zones. In general, high (low) carbonate (silt) occurs in the eastern and southeastern sectors of the seaway, while high (low) silt (carbonate) characterize its northern, western and southwestern sections (Figs. 9 – 12). Depositional environment rasters include the sill (described in Lowery et al., 2014) and the restricted basin put forward by Schröder-Adams et al. (2001) located in the southern and northeastern seaway, respectively (Figs. 9 – 12). Latitude and longitude rasters constitute additional evidence (Fig. 13). The remaining layers (water depth, clay and benthic oxygen) summarize the geological and physical oceanographic conditions of the seaway for each time zone (Figs. 14 – 16). Water depth and clay content increase towards the basin center, as expected (Figs. 14 and 15). Clay content tends to be high along the western limb as well, reflecting terrigenous input into the subsiding basin (Figs. 14 and 15).

The following subsections go over the results in terms of the hypothesis [presence].

Where presence values are low, absence values are high because absence is the disbelief in presence. Hence, absence is discussed in terms of low belief in presence. Appendix C contains all the layers supporting the hypothesis [absence]. The spatial extents of belief values generally inversely resemble those on the presence maps; however, belief in absence is always less than belief in presence because more ignorance was assigned to the fuzzy layers supporting foraminiferal absences (Table 3).

3.1. M. mosbyense (Late Cenomanian) results

The presence belief map of Rotalipora greenhornensis defines the extent of the calcareous planktic species during Late Cenomanian (M. mosbyense) time (Fig. 17). High presence belief values (≥ 0.80) occur in the southeastern portion of the seaway, whereas low 43 values (≤ 0.15) comprise the southwestern, western and northern sections (Fig. 17). Belief values progressively wane northward along the northeastern margin of the WIS (Fig. 17). The belief map shows that this species is most likely missing from the northern and western regions (belief

≤ 0.001) (Fig. 17).

The boundary between predominantly species presence and absence begins along the southwestern margin of the WIS near Carthage and El Vado, New Mexico, travels to Lower

Piedra and Mesa Verde, Colorado, extends northeastward near Hot Springs, South Dakota, and abruptly cuts through the Black Hills before terminating in the Manitoba Escarpment (Figs. 3 and 17). For each presence and absence hypothesis, the plausibility maps have higher values than belief and thus constitute the upper bound on probability (Fig. 17).

Dysoxic to anoxic benthic oxygen conditions persisted throughout this time slice, with a few hypoxic pockets occurring along the seaway’s western margin (Table 1 for coding; Fig. 16).

In general, bottom-water oxygenation was higher in regions occupied by the northern waters

(i.e., the western and northern portions) of the WIS (Fig. 16).

3.2. S. gracile (Late Cenomanian) results

The presence hypothesis map for Rotalipora greenhornensis shows high belief (≥ 0.9) in the southeastern WIS and low belief (≤ 0.1) in its northern sector (Fig. 18). Presence support dwindles along its northeastern margin, as in the M. mosbyense zone (Fig. 18). Unlike in the previous time zone, however, belief values remain relatively high (0.6 – 0.8) well into Manitoba

(Fig. 18). Just due northward near Bainbridge River, Saskatchewan, belief values drop considerably (≤ 0.05) (Figs. 3 and 18). Furthermore, presence is supported more than in M. mosbyense along the southwestern limb, albeit belief values (0.13 – 0.25) are fairly low nonetheless (Fig. 18). 44

The high-low belief boundary begins in southwest New Mexico (near the Carthage section), heads north into Colorado (close to Lower Piedra) and wraps northeastward into the

Black Hills before reaching into northeastern Canada in Saskatchewan (Fig. 18). Although known to be present at Hot Springs, SD, belief values based on the evidence are typically low around here (~0.3 – 0.4).

Figure 19 displays the belief in presence for the calcareous benthic species Valvulineria loetterlei during the S. gracile zone. Presence is highly supported in the southern and southeastern portion of the seaway, and also along its central axis (≥ 0.95 belief) (Fig. 19). High belief (≥ 0.8) extends into northeastern Canada but begins to decrease gradually past the Duck

Mountain, Manitoba section (Fig. 19). Low belief in presence (high in absence) occurs in the southwestern protrusion (0.14 ≤ belief ≤ 0.18), although it does not drop to very low (≤ 0.05) until northward of the Black Hills and into Canada (Fig. 19).

The presence-absence interface is sharp in the central and northeastern parts of the seaway, where it trends northeast from the Black Hills into Saskatchewan (Fig. 19). It is blurred, however, due southwest of the Black Hills, exhibiting a smooth gradient from high to low presence values at the Four Corners (i.e., where Utah, Arizona, New Mexico and Colorado meet) and in southwestern New Mexico (Fig. 19).

During the S. gracile zone, the agglutinated benthic genus Ammobaculites spp. exhibits high presence belief (≥ 0.85) in all regions of the WIS except the southeast and in a pocket in the northeast (Fig. 20). Belief values in this confined area in Canada range from 0.35 – 0.6 (Fig. 20).

Belief values along the eastern margin surrounding this isolated area are also relatively lower

(0.65 ≤ belief ≤ 0.85) than in the western sea, but remain fairly high nonetheless (Fig. 20). 45

The presence-absence line is located well south of the Black Hills, occurring north of the central and southeastern localities in Colorado and Nebraska known to host predominantly calcareous taxa (≤ 0.05 belief) (Fig. 20). The boundary commences in the middle of New Mexico due east of Carthage, separates the northern-central New Mexico (e.g., El Vado) and central

Colorado sections (e.g., Rock Canyon) and trends slightly northeastward before shifting due east into south central Nebraska (Fig. 20).

The belief and belief interval maps exhibiting varying belief levels in Valvulineria loetterlei presence are presented in Figures 21 and 22, respectively. Even with low belief support

(i.e., high ignorance), maximum belief in presence for Valvulineria loetterlei does not drop below 0.9 (Fig. 21). The interval map for the highest belief support reveals the areas with the largest uncertainties are in the Four Corners region in the southwest and near the Canadian-US boundary (i.e., North Dakota and Saskatchewan) in the northeastern WIS (Fig. 22). As belief support is reduced, these areas spatially expand (Fig. 22). However, the spatial extent does not significantly change going from medium to low belief support (Fig. 22; see Discussion).

Near-normal marine benthic oxygen conditions existed in the central and southwestern portions of the seaway during S. gracile time (x ≤ 2.15) (Fig. 16). Only in the north-central seaway did hypoxia/dysoxia continue (Fig. 16). Relative to M. mosbyense, though, this segment also saw some improvement (x ≅ 3). (Note the different scale ranges on the oxygenation maps in

Figure 16 when comparing among time zones.)

3.3. N. juddii (Uppermost Cenomanian) results

Presence belief for the calcareous benthic species Neobulimina albertensis is high (≥ 0.9) for a large extent of the southeastern, central and northeastern parts of the epicontinental sea

(Fig. 23). Belief in presence tapers along a northeastward-trending transect beginning in central 46

Arizona, splicing Wyoming and Montana before ending in Saskatchewan due north of

Bainbridge River (Fig. 23). Presence support does not fall below 0.14 in the southwestern margin and generally ranges from 0.2 to 0.5 (i.e., 0.8 to 0.45 for absence) (Fig. 23).

Presence support for the calcareous benthic foraminifer Gavelinella dakotensis exhibits similar spatial extents as that for Neobulimina albertensis (Fig. 24). High belief (≥ 0.9) in presence occurs in the southern, eastern and northeastern segments in the seaway (Fig. 24). The southwestern protrusion is the only region in the southern WIS that has relatively low belief values (0.23 – 0.53 for presence; 0.74 – 0.33 for absence) albeit they are higher than those for

Neobulimina albertensis (Figs. 23 and 24).

The presence-absence boundaries for both N. albertensis and G. dakotensis generally bisect the northwestern and southeastern portions of the seaway through Montana and into

Saskatchewan, though they are less pronounced due southwest through southern Montana, western Wyoming and central Utah (Figs. 23 and 24). In the southwest, the interfaces are less apparent, but occur near the Four Corners, separating the Lohali Point, AZ, and Red Wash, NM, sections (Figs. 23 and 24). Generally, belief values decline steadily across this frontier (Figs. 23 and 24).

Hypoxic to dysoxic benthic oxygenation returned to the seaway during this time (2.5 ≤ x

≤ 3.75) (Fig. 16). Values greater than 3.00 signify slightly worse conditions in the eastern and northern seaway segments (Fig. 16). Moreover, bottom-waters were more deprived of oxygen in a large region in the southwest as well (Fig. 16). Hypoxia characterizes the central and southwestern-most parts of the seaway, though, relatively, these are the most well-oxygenated areas during N. juddii (x ≅ 2.65) (Fig. 16).

3.4. W. devonense (Earliest Turonian) results

Figure 25 contains the presence belief map for Neobulimina albertensis during Early

Turonian time, displaying high support (≥ 0.87) for an extensive area of the seaway. The only areas not belonging to high presence support are the northern limb (belief ≤ 0.1) and the southwestern protrusion (0.16 ≤ belief ≤ 0.5 for presence; 0.45 ≤ belief ≤ 0.83 for absence) (Fig.

25). The presence-absence interface sections off the southwestern hook along the Arizona-New

Mexico boundary and mostly disappears along the western-central margin (Fig. 25). It then picks back up through central Montana and into Saskatchewan, near the Alberta-Saskatchewan boundary (Fig. 25). In all areas, the gradient is fairly gentle (Fig. 25).

Benthic oxygen conditions remained hypoxic to dysoxic during this time, although they improved somewhat in the central, southwestern and northeastern portions of the WIS (x ≤ 3.00)

(Fig. 16). Dysoxic conditions (x ≥ 3.25) persisted along the easternmost margin throughout the entire seaway and in its southwestern corner (Fig. 16).

5 5 5

4 4 4

3 3 3 2 2 2

Fig. 9. Input interpolated surfaces for M. mosbyense zone. From left to right: depositional environment, total carbonate (percent) and silt content (percent). Numbers represent localities introduced in Fig. 3.

5 5 5

4 4 4

3 3 3 2 2 2

Fig. 10. Input interpolated surfaces for S. gracile zone. From left to right: depositional environment, total carbonate (percent) and silt content (percent).

5 5 5

4 4 4

3 3 3 2 2 2

Fig. 11. Input interpolated surfaces for N. juddii zone. From left to right: depositional environment, total carbonate (percent) and silt content (percent).

5 5 5

4 4 4

3 3 3

2 2 2

Fig. 12. Input interpolated surfaces for W. devonense zone. From left to right: depositional environment, total carbonate (percent) and silt content (percent). 52

Fig. 13. Latitude and longitude rasters. Both layers were fuzzified for each time zone to serve as inputs for the Dempster-Shafer models. Seaway mask shown is for the S. gracile zone. Units in decimal degrees.

5 5 5 5

4 4 4 4

3 3 3 3 2 2 2 2

Fig. 14. Interpolated surfaces for Late Cenomanian time zones. Clay content (percent) and water depth for M. mosbyense zone (left) and S. gracile zone (right). Note varying scale bars between time zones. Localities (represented by numbers) have been assigned different colors for visibility purposes.

5 5 5 5

4 4 4 4

3 3 3 3 2 2 2 2

Fig. 15. Interpolated surfaces for Latest Cenomanian/Early Turonian. Clay content (percent) and water depth for N. juddii zone (left) and W. devonense zone (right). Note varying scale bars between time zones.

5 5

4 4

3 3

2 2

5 5

4 4

3 3 2 2

Fig. 16. Benthic oxygenation trends over time. Bottom left: M. mosbyense zone. Bottom right: S. gracile zone. Upper left: N. juddii zone. Upper right: W. devonense zone. Higher values indicate more anoxia; lower indicate normal marine conditions (Table 1). Note varying scale bars for each time zone. 56

5 5 5

4 4 4

3 3 3

2 2 2

Fig. 17. Presence images for Rotalipora greenhornensis during M. mosbyense zone. From left to right: belief, plausibility and belief interval.

5 5 5

4 4 4

3 3 3

2 2 2

Fig. 18. Presence images for Rotalipora greenhornensis during S. gracile zone. From left to right: belief, plausibility and belief interval.

5 5 5

4 4 4

3 3 3

2 2 2

Fig. 19. Presence images for Valvulineria loetterlei during S. gracile zone. From left to right: belief, plausibility and belief interval.

5 5 5

4 4 4

3 3 3 2 2 2

Fig. 20. Presence images for Ammobaculites spp. during S. gracile zone. From left to right: belief, plausibility and belief interval.

5 5 5

4 4 4

3 3 3

2 2 2

Fig. 21. Belief images for Valvulineria loetterlei with varying levels of ignorance. From left to right: low, medium and high ignorance.

5 5 5 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1

4 4 4

3 3 3

2 2 2

Fig. 22. Interval images and histograms for Valvulineria loetterlei with varying levels of ignorance. The histograms represent the relative uncertainty of values among the three interval images. The horizontal axis of the histograms goes from 0 to 1 in increments of 0.2. See subsection 4.2 in the Discussion section for more details. From left to right: low, medium and high ignorance.

5 5 5

4 4 4

3 3 3

2 2 2

Fig. 23. Presence images for Neobulimina albertensis during N. juddii zone. From left to right: belief, plausibility and belief interval.

5 5 5

4 4 4

3 3 3

2 2 2

Fig. 24. Presence images for Gavelinella dakotensis during N. juddii zone. From left to right: belief, plausibility and belief interval.

5 5 5

4 4 4

3 3 3

2 2 2

Fig. 25. Presence images for Neobulimina albertensis during W. devonense zone. From left to right: belief, plausibility and belief interval. 65

CHAPTER IV. DISCUSSION

4.1. Interpretation of results

Maps depicting the distribution of foraminiferal species visually summarize water mass distributions, including their surface and bottom conditions, and “fill in” where data did not previously exist. The geographic range of Rotalipora greenhornensis reveals the extent of southern, warm, normal-marine stratified waters, as this species is considered the most stenotopic genus in the Greenhorn Sea (Leckie et al., 1998, after Eicher, 1969). The belief map for Rotalipora greenhornensis reflects the location of well-oxygenated surface waters that persisted during Late Cenomanian (M. mosbyense) time right before OAE2 (Fig. 17). Moreover, very low (approximately ≤ 0.05) belief values (i.e., where belief in absence is high) indicate the locations where northern waters dominate. This is a general rule for all southern water taxa and also holds true for the contrary: where belief in northern water foraminiferal presence is low, southern waters likely persisted. Thus, where belief in Rotalipora presence begins to dwindle

(e.g., where yellow grades to red to purple in Figure 17), mixing between the northern and southern water masses most likely occurred.

The stenotopic Rotalipora greenhornensis reveals the southern water mass was restricted to the central southeastern section of the seaway, including Rock Canyon and all Kansas sections

(Fig. 17). The water mass terminated south of Manitoba, perhaps as far south as northeastern

Nebraska/northwest Iowa because the species was not found at the Ponca State Park, NE, or

Sioux City, IA, sections (Diner, 1992; Elderbak et al., 2014). Moreover, belief values (0.3 – 0.4) are fairly low in this region (Fig. 17).

According to the presence belief map (x ≤ 0.25), the Tethyan waters probably did not extend too far into the Four Corners sector of the seaway (Fig. 17). Rotalipora greenhornensis is 66 very rare (represented by 2 specimens) and absent at Mesa Verde, CO, and Red Wash, NM, respectively, for the duration of the CTB (Leckie et al., 1998). Leckie et al. (1998) interpreted mixing between the northern and southern water masses along a topographic high (“forebulge”) region near Mesa Verde. Although the southern waters entered this area, northern waters dominated due to the governing estuarine circulation (Slingerland et al., 1996) and as evidenced by the lack of calcareous foraminifera (Leckie et al., 1998). The presence map documents this water-mixing interface in the southwest-central WIS as belief values quickly change from high to low (Fig. 17). This interpretation also agrees with that of Eicher and Diner (1985), who concluded mixed to agglutinated assemblages persisted in this region during the deposition of the

Bridge Creek Limestone member.

Generally speaking, the bottom-water landscape of the entire WIS lacked oxygen and ventilation during the early Late Cenomanian, as hypoxic to anoxic conditions prevailed during this time (Fig. 16). Nevertheless, a large-scale trend of better-oxygenated northern/western waters and poorly-oxygenated southern/eastern waters is evident (Fig. 16). This trend is reflective of the physical chemistry of the water masses: northern, hyposaline, colder waters can hold more dissolved oxygen than their southern, warmer, stratified counterparts (Hay et al.,

1993). The map produced here spatially and numerically constrains this continental-wide trend for the first time (Fig. 16).

During the time of S. gracile, the physical oceanographic and biotic conditions of the

WIS changed drastically. A southern transgressive pulse, coeval with OAE2 and the “Benthonic

Zone” of Eicher and Worstell (1970), brought much improved benthic oxygen conditions to the seaway (Figs. 2 and 16). This amelioration is represented by highly diverse ammonoid and bivalve (Elder, 1991), foraminifera (Leckie et al., 1998; Elderbak et al., 2014) and microfossil 67

(e.g., Corbett and Watkins, 2013) assemblages in the United States WIS and by similar foraminiferal diversifications in the Canadian sections (Prokoph et al., 2013).

The belief map for Rotalipora greenhornensis shows that the stratified southern water mass mostly dominated the southeastern and central WIS again (Fig. 18). During S. gracile, however, Tethyan waters advanced northward along the seaway’s eastern margin (e.g., Elderbak et al., 2014), which is represented by the higher (≥ 0.5) belief values for Rotalipora presence along this border (Fig. 18). As in M. mosbyense time, the northern and southern waters probably met along a front in the southwestern seaway and at the Black Hills (Fig. 18; Fisher et al., 1994;

Leckie et al., 1998). The boundary spans west-central New Mexico and into the Four Corners region (Figs. 3 and 18). The location of the interface may also be influenced by the paucity of microfossil data in this region, because no foraminiferal data exists for the Carthage, El Vado and Lower Piedra sections, all of which occur along or near this boundary.

Moreover, the species is not known to have occurred at Sioux City, IA (Elderbak et al.,

2014), or northward at the Manitoba sections (Diner, 1992; Schröder-Adams et al., 2001), where belief values are still relatively high (0.59 and 0.87, respectively) (Figs. 3 and 18). This disagreement is probably due to the combination of the local geologic conditions and the nature of the dataset used in this study. Rotalipora greenhornensis is common in deeper, “blue water” settings, so its occurrence is mostly limited to distal sites (Leckie et al., 1998). High sedimentation along the eastern margin of the seaway as evidenced by the deposition of a thick sandstone sequence with high-energy structures at Sioux City, IA, may have also interrupted water stratification in Iowa and nearby sections, which could explain the lack of planktics there

(Elderbak et al., 2014). 68

Furthermore, no data points were available for North Dakota, so the indirect evidence with which to constrain the model was indecisive and hence the model shows both high and low belief in these regions (Fig. 18). Note also the complex spatial pattern of belief values in this region (Fig. 18). This example highlights the complexity of extrapolating local conditions to explain large-scale spatial variations, especially with small datasets. Nevertheless, the belief map shows comparatively low belief along the eastern edge of the US seaway (i.e., the eastern

Dakotas and Minnesota), and high belief offshore through the central Dakotas and in the Black

Hills (Fisher et al., 1994), thus successfully documenting the location of the deeper portions of the Tethyan sea contemporaneous with the beginning of OAE2 (Fig. 18).

The geographic distributions of Valvulineria loetterlei and Ammobaculites spp. also act as indicators of the extent of the northern and southern water masses during S. gracile time and depict a clearer picture than those of Rotalipora greenhornensis (Figs. 19 and 20). The presence belief map of Valvulineria loetterlei indicates the general dimensions of the warm, well- oxygenated southern waters that dominated the southeastern and central WIS (Fig. 19). Tethyan waters reached into Canada along the eastern corridor and likely terminated due south of the

Saskatchewan sections (e.g., Bainbridge River; Schröder-Adams et al., 2001), because belief values drop (≤ 0.2) here after being high (~0.85) in the nearby Manitoba sections (Figs. 3 and

19). Correspondingly, the species is known to have occurred at Riding Mountain, Manitoba but not at the Bainbridge River, Saskatchewan section (Diner, 1992; Schröder-Adams et al., 2001).

Heading due southwest, southern waters extend through the central part of the seaway, terminating just due northwest of the Black Hills (Fig. 19). Although not found at the Four

Corners sections of Mesa Verde and Lohali Point, belief values remain greater than zero (~0.3) according to the indirect evidence of the environmental parameters. This region is probably an 69 area where water mixing between the northern and southern components occurred and is depicted by the fuzzy boundary from high to low belief (Fig. 19). This interpretation is supported by the presence of a rich biota of stenotopic infaunal and epifaunal bivalves, gastropods and echinoderms specific to this area and time zone (Elder, 1991). Perhaps the mixing of the two water masses provided optimal conditions for these animals to flourish, where well-oxygenated, normal salinity southern waters intermingled with colder, hyposaline, northern waters. The available sedimentological and environmental evidence used in this study suggest water mixing did occur in this region (visible where yellow grades to purple in Fig. 19). The belief map of

Valvulineria loetterlei thus effectively portrays the spatial layout of this southwestern oceanic front (Fig. 19).

The presence belief map depicting the geographic range of Ammobaculites spp. during S. gracile time constrains the whereabouts of the northern waters in the seaway (Fig. 20). Apart from dominating the northern portion of the WIS, the Boreal waters flowed along the western edge of the seaway and also prevailed in the Four Corners region (Fig. 20). In fact, the sharp gradient from high to low belief occurs in west-central Colorado and continues due south through New Mexico, suggesting southern Tethyan waters reigned here (Fig. 20).

According to the presence belief map, the northern water mass also extended to northeastern Nebraska and southwestern Iowa (Figs. 3 and 20). Although not reported from

Ponca State Park, NE, other benthic agglutinated species with northern affinities occurred here

(e.g., Reophex recta and Trochammina rainweteri) (Diner, 1992). Moreover, high silt content coupled with low carbonate values supports presence in this region (Fig. 10). Sedimentological data similarly most likely influenced the relatively low belief (~0.35) in the Manitoba sections

(e.g., Duck and Riding Mountain), where Ammobaculites spp. was known to have occurred 70

(Diner, 1992). Comparatively high carbonate values likely caused the belief to decrease because the sedimentological and biotic evidence suggest this region was a restricted lagoonal basin

(Schröder-Adams et al., 2001). Thus local depositional settings influence the overall picture of foraminiferal and hence water mass distribution interpretations in eastern Canada. Furthermore, analogous to the Rotalipora greenhornensis presence model in the area, more data from the

Dakota sections (especially North Dakota) would help further constrain the distribution of the species.

It is evident from the presence belief maps for Valvulineria loetterlei and Ammobaculites spp. that some overlap occurs in the extents of these taxa during S. gracile time (Figs. 19 and

20). This is the only ammonoid zone for which there is substantial documentation of northern agglutinated taxa, which is reflective of the dominant oceanic conditions of the seaway later across the CTB. During N. juddii and W. devonense times, low-oxygenated waters from the

Tethyan realm made their way into the northern and western parts of the seaway (Figs. 23-25;

Eicher and Diner, 1985; Leckie et al., 1998). Most previous works identified the dominance of

Neobulimina albertensis and Gavelinella dakotensis (modeled here) to the near exclusion of all other benthic foraminiferal species throughout the seaway during this time, except for in the northernmost portion (e.g., Thomson et al., 2011).

Thus, S. gracile is the only zone for which I modeled northern and southern water overlap; during the later time zones, the northern waters were probably displaced to areas with low belief in calcareous species’ presence (Figs. 23-25). It follows then that the fuzzy high-to- low belief boundary on the belief maps that depict the presence of southern water taxa for N. juddii and W. devonense zones indicates the main region of water mixing. Again, the main 71 restriction to precisely defining the northern water mass is data availability for the northern WIS, whether due to preservational issues, lack of sampling, or missing time.

Raster addition (a map overlay operation) of the belief maps of Valvulineria loetterlei and Ammobaculites spp. was carried out to further constrain the position of the oceanic front during S. gracile time (Fig. 26). Yellow and red colors represent regions where water mixing most likely and likely took place, which occurs in the southwestern portion and extends through the central (Black Hills) and northeastern sections of the seaway (Fig. 26).

According to this map, the Dakotas and eastern Canadian sections constitute a large area for water mixing (Fig. 26). My interpretation for this occurrence is twofold: in addition to the transgressive pulse of warm, normal-marine southern waters that entered this region via access along the eastern margin, the lack and paucity of data for North Dakota and the southern

Canadian sections resulted in somewhat lax constraints on the belief in species presence during modeling.

This region of mixing appears to go beyond the “endemic center”—the zone in which northern and southern macrofaunal biotas overlap—conceived by Kauffman (1984). In general, the two zones accord for the central portion of the seaway (i.e., the Dakotas and parts of

Manitoba and Saskatchewan), but are in disagreement for the northwestern and southwestern sections (see Fig. 7 in Kauffman, 1984). In the northwestern seaway (i.e., Montana, southern

Alberta and western Saskatchewan), it is possible that increased nutrient supply from terrigenous sources to the west enhanced macrofauna productivity, like that occurring contemporaneously in the southwestern seaway (Elder, 1991). Because no calcareous foraminifera have been found beyond the Black Hills in the central seaway (though they occurred to the east in Manitoba), no region of overlap exists here. Perhaps, then, the endemic center in the northwest is specific to 72 macrofauna (e.g., ammonite and bivalve) assemblages because the conditions were not hospitable to southern foraminifera. The occurrence of the water-mixing interface in the southwestern seaway does agree with the presence of an endemic molluscan fauna (Elder, 1991).

The water-mixing interface extends beyond the endemic center in the northeastern seaway, where the Dakotas and Manitoba meet (Fig. 26). This could be due to a lack of data for this region, but as aforementioned, mixed agglutinated and calcareous taxa did occur as far south as northeastern Nebraska (Eicher and Diner, 1985; Diner, 1992), so water mixing presumably did take place here. Complicating this interpretation, however, is the fact that southern waters near the Black Hills are known to support southern (calcareous) as well as northern (agglutinated) benthic foraminiferal types (Fisher et al., 1994). That the overlap shown in Fig. 26 represents southern waters that supported northern taxa (and not northern water extent) is rejected because no Ammobaculites spp. and very few agglutinates occurred in the central portion of the seaway during S. gracile (e.g., Rock Canyon, CO, and Kansas sections), which would have probably thrived in these well-oxygenated bottom waters (Leckie et al., 1998). This study therefore delivers approximate spatial constraints on the area of mixing between the two water masses

(Fig. 26).

As sea level continued to rise and OAE2 took hold in the seaway, waters that once supported diverse benthic and planktic faunas gave way to mostly inhospitable environments nearly ubiquitous throughout the seaway (e.g., Elder, 1991; Fisher et al., 1994; West et al., 1998;

Schröder-Adams et al., 2012; Prokoph et al., 2013; Lowery et al., 2014). Surface waters—once supporting diverse deep-water planktic foraminiferal assemblages—became dominated by

Heterohelix spp. during the N. juddii zone (“Heterohelix Shift”) (Fig. 2). Figure 27 displays the localities at which Heterohelix spp. specimens have been found, highlighting not only their 73 widespread reign but also the presumable expansion of the poorly-oxygenated Tethyan water mass (which this genus could tolerate), which persists until later across the CTB (Leckie et al.,

1998).

These dysoxic Tethyan intermediate waters breached further into the northern WIS

(displacing the Boreal waters northward) than their well-oxygenated counterparts did in S. gracile, as evidenced by the presence belief map for Neobulimina albertensis (Fig. 23). It follows that the northern and southern waters probably met along the NE-SW trending front in the seaway where belief values begin to drop off (Fig. 23). These waters did not penetrate far into the southwestern section of the seaway, as belief values are low (~0.2) and northern waters are known to have dominated here as well (Leckie et al., 1998; Elderbak et al., 2014). It is possible, however, that some water mixing did occur in the Four Corners region based on the belief gradient (Fig. 23).

Per the indirect evidence fueling the model, the low-oxygen tolerant epifaunal

Gavelinella dakotensis shows a similar distribution as Neobulimina albertensis, providing further spatial constraints on the extent of the Tethyan intermediate waters, OMZ and oceanic fronts

(Fig. 24). Higher presence belief values (~0.65) compared to those of the infaunal species (0.25) in the Four Corners southwestern region reflect the fact that increased nutrient supply associated with water-mass mixing (and possibly terrestrial erosion from the Sevier region) established local ideal conditions on which benthic foraminifera and mollusks could flourish in an otherwise low-oxygenated, mostly inhospitable sea (Figs. 23 and 24; Elder, 1991; Leckie et al., 1998).

Along the eastern margin, high belief in presence mainly reflects low levels of dissolved oxygen in the intruding Tethyan intermediate waters from the south (Fig. 24). Furthermore, the spike in Gavelinella abundance is not as prominent as that in the southwestern seaway during the 74 same time, so oxygen content rather than increased nutrient influx is deemed responsible for its brief dominance (Elderbak et al., 2014). Scarce foraminiferal data northward along the western margin limits interpretation of high belief in its presence (Fig. 24). The stratigraphic data predicts its occurrence northward along the western margin before terminating in Canada. Perhaps increased nutrient supply from the Sevier highlands is also responsible for its presence here (Fig.

24). Fortunately, where high values occur on the interval map in the western margin indicate where more field data will be useful in resolving this matter (Fig. 24).

In the eastern side of the WIS, both calcareous benthic species were found at Riding

Mountain (Diner, 1992), but not at the nearby Vermillion and Bainbridge River sections on the

Manitoba Escarpment (Fig. 3; Schröder-Adams et al., 2001; Prokoph et al., 2013). That the water masses met in this region constitutes a possible explanation; however, the boundary occurs slightly more due northwest on the belief maps (Figs. 23 and 24). Inhospitable benthic conditions

(i.e., anoxia) in a local restricted basin environment may be responsible for the abrupt termination of calcareous benthics (Schröder-Adams et al., 2001; Prokoph et al., 2013).

Curiously, though, diverse agglutinated benthics did thrive during the latest Cenomanian at Vermillion River to the nearly complete exclusion of calcareous forms, suggesting the northern waters dominated here and therefore the water mass boundary is sharp in Manitoba

(Fig. 3; Prokoph et al., 2013). More foraminiferal (especially for planktic and benthic agglutinates) and stratigraphic data would be beneficial to better identify the location of the water masses (and hence potential zones of mixing), similar to how the combination of

Valvulineria loetterlei and Ammobaculites spp. maps helped to constrain the regions of overlap during S. gracile time. 75

Also interesting is that, contra its infaunal analogue N. albertensis, Gavelinella dakotensis extends slightly further into the northern WIS (Fig. 24). Minor details aside, both maps reveal the full extent of the southern water mass for the first time and are in agreement that these waters reached—to some distance—into Canada. They also depict the homogeneity of low oxygen benthic conditions during OAE2.

During the earliest Turonian, right up to before the WIS reached its maximum extent and depth (in the Mammites nodosoides zone), the Tethyan intermediate waters and OMZ continued to expand northward along the eastern margin of the seaway (Elderbak et al., 2014). Benthic oxygen conditions improved a little compared to those in N. juddii, but dysoxia still reigned throughout (Fig. 16). Foraminiferal data from Elderbak et al. (2014) suggest slight improvements in surface water conditions and enhanced salinity stratification in the eastern WIS, although

Heterohelix spp. continues to dominate the planktic assemblages for the majority of the WIS until a return to normal-marine surface conditions during Mammites nodosoides (Figs. 2 and 27;

Leckie et al., 1998; Schröder-Adams et al., 2012; Prokoph et al., 2013; Elderbak et al., 2014).

Neobulimina albertensis encompasses a larger area in W. devonense time than during the

N. juddii zone, reflecting the expansion of the intermediate waters, but the general trend of dominance in the eastern and central portions of the seaway continues (Fig. 25). Only a minor northern agglutinated component persisted in the southwestern sea, so the poorly-oxygenated

Tethyan intermediate waters and OMZ likely dominated this region (Fig. 25; Leckie et al., 1998).

This is evidenced by the relatively high beliefs (0.5 – 0.75) in this region (Fig. 25). Water mixing still probably occurred here, but the northern waters’ influence is overshadowed by that of the

Tethyan realm because moderate to high belief values (≥ 0.5), indicating southern water presence, occur here and further east in central New Mexico/southern Colorado (Fig. 25). 76

In the northeastern WIS, high belief continues well into Manitoba and Saskatchewan, suggesting Tethyan waters entered then mixed with northern waters in this part of Canada (Figs.

3 and 25). This is consistent with Neobulimina albertensis occurrences at Riding Mountain

(Diner, 1992). A complete lack of benthics at the neighboring Bainbridge River and Vermillion

River sections is attributed to anoxia (Schröder-Adams et al., 2001; Prokoph et al., 2013).

Neobulimina albertensis was recovered at other localities along the Manitoba Escarpment, so it is possible dissolution or environments with poor preservation potential wiped out the remains of the species at the Bainbridge and Vermillion River sections (McNeil and Caldwell, 1981). More biotic and stratigraphic data collection in this region (as aforementioned) can resolve any inconsistencies.

4.2. Dempster-Shafer theory: A befitting model that addresses potential uncertainties

The Weight-of-Evidence belief model is decidedly suitable for this analysis because it incorporates expert paleontological knowledge to develop the evidence supporting the hypothesis that a foraminifer will exist at any location. It also explicitly takes into account ignorance due to incomplete information about the data, such as a lack of sites in space or whether or not a species did actually exist at a site where previous microfossil documentation is nonexistent (e.g., a failure to collect vs. a true absence). This ignorance can then be acknowledged in the final model, adding flexibility to the analysis because the relative uncertainty from the total available information can be addressed during data interpretation by considering the differences between the belief (minimum) and plausibility (maximum) probabilities of species occurrences (Eastman,

2015).

The sampling intervals with which the paleontologists/sedimentologists gathered rock data through sections in the field can greatly affect the numerical values of the environmental 77 codes. To address this and other potential data gathering uncertainties and create confidence constraints on species presence support, three DS models were run for Valvulineria loetterlei

(calcareous species representative of S. gracile benthic conditions), each with different levels of ignorance (high, medium and low) (Fig. 21; Appendix B). High ignorance is defined by input layer certainties between 0.2 and 0.5 (i.e., between 20 and 50% certainty in the data); medium ignorance is between 0.3 and 0.6 and low ignorance is the initial belief map (certainties between

0.6 and 0.85) (Figs. 19 and 21; Appendix B). Some overlap between high and medium ignorance schemes occurs because the relative certainty per layer is considered (e.g., 0.5 for total carbonate and 0.4 for silt for the medium scheme; see Appendix B).

The three belief interval maps were linearly stretched to be normalized to a scale of 0–1 for comparison. Histograms show the frequency of cell counts of each level of uncertainty where

0.8–1 is the highest possible uncertainty and 0–0.2 is the lowest to compare the relative uncertainty levels among the three maps (Fig. 22). The interval maps and histograms constitute only relative controls on uncertainty because the overall numeric value of the uncertainty is not being assessed, rather, just that data in these areas may be more ambiguous or complex than at other places.

The stretched Valvulineria loetterlei belief interval maps and their accompanying histograms are displayed in Figure 22. Clearly, the areas with the highest uncertainty are where the water masses met and/or where data clusters are scant. The Four Corners, Manitoba

Escarpment and—to a lesser extent—the Black Hills and its surroundings constitute such regions

(Fig. 22). The areas with the highest uncertainties do not shift to other localities as ignorance increases; rather, the general regions remain fixed but their breadths expand (Fig. 22). 78

Interestingly, the cold-water indicator Ammobaculites spp. belief interval map shows the supposed front is located further south in the eastern seaway than depicted in the southern water taxa belief maps because the northern water mass extended further south along this margin, overlapping the southern waters in Nebraska and South Dakota (Fig. 20). As described above, this may reflect the extent of the northern waters into the eastern seaway but could also indicate that the southern waters supported the northern-affiliated taxon (Fisher et al., 1994). Because the taxon is absent from the Rock Canyon section and nearby localities in Colorado and Kansas in the central seaway axis where southern waters dominated during S. gracile, I conclude that the northern water mass is responsible for its presence in the eastern seaway (i.e., in Nebraska and the Dakotas). This interpretation is represented in both the Ammobaculites spp. belief map and the water-mixing map (Figs. 20 and 26).

Moreover, the histograms for Valvulineria loetterlei demonstrate that the uncertainty from medium to high ignorance schemes does not increase the amount of highly (≥ 0.8) potentially variable cells (Fig. 22). The moderately uncertain (0.4 – 0.6) cells become more abundant as ignorance increases among the three schemes (Fig. 22). Expectedly, cross-validation of the three surfaces indicates the one with the least ignorance is the best-fit model (Figs. 21 and

22). This is because it agrees with the presence data the most. As a final remark, these surfaces depicting the uncertainty (i.e., belief intervals) of species occurrences are important because they tell us what we do and do not know about the spatial oceanography of the WIS given our available foraminiferal knowledge base. High values on the belief interval maps suggest that further valuable information exists at these localities (see Future Works subsection below).

4.3. Fuzzy power

The power of fuzzy sets is that the control points can always be relaxed (i.e., separated further apart) if the analyst(s) cannot determine/agree on definite empty (0) or full (1) membership values. I used sigmoidal (or S-shaped or cosine) curves, but for some cases, linear,

J-shaped or trapezoidal may work better (Fig. 5; Eastman, 2015). For instance, linear transformations are usually more suitable for engineering analyses because some electronic devices output essentially linear data (Eastman, 2015). The type of fuzzy transformation curve therefore should reflect the nature of the data, if applicable.

Here, since the water masses comprising the WIS are non-stationary (and neither is their conjoining front), fuzzy was able to create smooth, transitional boundaries that reflect these dynamic positions by designating partial membership to the cells, thereby establishing a

“confidence” level to the degree to which these cells represent the true front. The fuzzy boundaries are also important because they express the expert knowledge, or belief, of where certainty in oceanographic conditions begin to drop off, thus offering another means by which to show researchers areas where more data would add to our current knowledge about the seaway.

Percent silt, percent carbonate, depositional environment, latitude and longitude parameters were used to model the distributions of foraminiferal presences for each time zone.

Although several of these variables—silt and carbonate content, for instance—appear to reveal the same information about the seaway (e.g., high (low) carbonate (silt) values are indicative of southern tropical waters), they are non-unique in that that they can be derived from multiple environments. For example, the presence of silt can be attributed to the proximity to a terrigenous source of sediment or be reflective of a medium-low energy environment.

Furthermore, the degree of association between these parameters and species occurrences varies 80 among variables both numerically and anecdotally. For example, Rotalipora greenhornensis presence is more strongly associated with carbonate values (this study) and southern tropical waters (Leckie et al., 1998), than silt values (i.e., distance to the Sevier Highlands). Hence the confidence levels assigned during the “fuzzification” of the layers (e.g., carbonate = 0.85 and silt

= 0.65) were scaled accordingly (see Appendix B for all ignorance levels).

4.4. Future work

Fisher et al. (1994) revealed the occurrence of an oceanic front in the Black Hills by using sedimentology and foraminifera as proxies. Using their data (among many other works), this contribution suggests the possible locations throughout the rest of the seaway where the front presumably occurred, therefore revealing the promising locations where further stratigraphic and paleontological research could be carried out to glean precise information about water mass distributions and their effects on biota in the WIS.

Regions of interest include (1) in the southwestern sea adjacent to the Sevier highlands where northern and southern waters met (due southeast of the Four Corners region; localities include Lower Piedra, CO; El Vado, NM; Carthage, NM); (2) at the Manitoba Escarpment where southern waters probably reach their most northern extent (Riding and Duck Mountains,

Manitoba; Vermillion River; Bainbridge River, Saskatchewan); and (3) at locations surrounding the “classic” front in the Black Hills (Bull Creek, WY; Stoneville Flats, MT; Torgerson Draw,

MT). Elder (1991) described the stratigraphy for region (1); McNeil and Caldwell (1981), Diner

(1992), Schröder-Adams et al. (2001) and Prokoph et al. (2013) for region (2) and Fisher et al.

(1994) for (3) (Fig. 3). All of these regions have high values on the belief interval maps, signifying a high degree of uncertainty; hence, further investigation will lead to more valuable information extraction for these sites (Eastman, 2015). Of course, it will also be beneficial to 81 look for foraminifera at unsampled locations, especially in the northern and central-southwestern

WIS where records of agglutinated foraminifera (both planktic and benthic) are sparse.

Fig. 26. Presumable water mixing extent during OAE2. Yellow and red colors indicate oceanic front location during S. gracile zone. Dark purple represents the unaltered northern and southern waters. Numbered locations are the same as in Fig. 3. 83

Fig. 27. Distribution of Heterohelix spp. across the CTB. Note ubiquitous range, barring the NW Territories. 84

CHAPTER V. CONCLUSIONS

The belief maps produced in this study define the spatial distributions of five foraminiferal taxa during four ammonoid zones across the Cenomanian-Turonian Boundary

Event. Percent silt, percent total carbonate and depositional environment are the environmental parameters that are associated with foraminiferal occurrences. The degree of overlap of the benthic taxa Valvulineria loetterlei and Ammobaculites spp. represents the areas of water mixing during S. gracile time, coeval with the onset of Oceanic Anoxic Event 2. The areas of diminishment in presence belief for the southern-water taxa indicate the potential water-mixing interfaces during M. mosbyense, N. juddii and W. devonense zones.

Much information regarding the paleoceanography and species distributions of the

Western Interior Seaway was gleaned visually and quantitatively from the maps produced in this study. In addition to its rigorous methodological innovations, this study provides the first quantitative spatial constraints on the paleoceanography of the entire Western Interior Seaway during an important extinction event using numerical foraminiferal and sedimentological data as proxies. It adds the first geospatial component to our understanding of WIS oceanography using modern GIS technology, though future works may be more interested in the novel methodology, species distributions or interpolated environmental surfaces—all of which are introduced here as well.

This work reveals the areas of northern and southern water mixing, based on foraminiferal distributions, which may be more extensive than previously thought. Apart from its dynamic nature, the oceanic front typically trends NE-SW across the seaway based on the sedimentological, biotic, environmental and spatial data used to fuel the Dempster-Shafer model.

These indirect pieces of evidence integrate the oceanographic gyre circulation models postulated 85 by Slingerland et al. (1996) and Leckie et al. (1998). The fuzzy boundaries and interval maps give confidence levels to where certainty of oceanographic conditions (in addition to the front location) begins to diminish and also keys researchers on where to gather useful data for future studies.

This innovative work demonstrates that coarse-grained water mass distributions can be quantitatively modeled for the entire WIS at the very fine temporal scale of ammonoid biozones, averaging less than 350 kyr in duration. The novel application of fuzzy sets and Dempster-Shafer theory to assess and interpret the significance of foraminiferal distributions for paleoceanographic reconstruction constitutes a new methodology to be added to the nascent field of modeling ancient species distributions (e.g., Malizia and Stigall, 2011; Myers et al., 2015).

This study effectively:

 added a geospatial component to existing foraminiferal datasets for the WIS;

 put paleontological and stratigraphic data into a more rigorous quantitative context, with

which computational models were able to reconstruct the oceanography of the WIS

during a key extinction event;

 used inductive reasoning to support previous interpretations of oceanographic conditions

in the seaway;

 delivered spatial constraints on the non-stationary oceanic front(s), with uncertainty built-

in thanks to fuzzy and Dempster-Shafer theory;

 demonstrated the value of Dempster-Shafer theory and fuzzy sets to paleontological

analyses by incorporating ignorance and uncertainties into the models;

 “filled in” (interpolated) geological, stratigraphic and biotic conditions in places where

data were not available/did not exist previously; 86

 generated spatial models of these conditions that will be useful in future studies and can

be improved on with more data;

 and clued researchers in on the best localities for meaningful data collection for WIS

investigations in the future to help understand environments that existed during this

greenhouse period in Earth history and biotic responses to environmental change.

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9958(65)90241-X

APPENDIX A. INTERPOLATION STATISTICS

All layers were created using the Empirical Bayesian Kriging (EBK) technique.

Root Mean RMS Attribute Time Zone Mean Settings Square (RMS) Standardized Depositional Env. M. mosbyense 0.16 0.71 1.01 Transformation: Log empirical Depositional Env. S. gracile 0.15 0.73 0.95 Transformation: Empirical Depositional Transformation: Empirical. Semivariogram: Whittle Env. N. juddii 0.10 0.81 1.00 Detrended. 4 sectors Depositional Transformation: Empirical. Semivariogram: Whittle Env. W. devonense 0.05 0.70 1.00 Detrended. 4 sectors

Total Carbonate M. mosbyense 0.32 17.52 0.95 4 sectors with 45˚ offset Total Carbonate S. gracile 1.00 14.69 0.92 4 sectors Total Carbonate N. juddii 0.41 21.44 1.04 Transformation: Empirical. 4 sectors Total Carbonate W. devonense 0.99 26.61 0.91 Transformation: Empirical. 4 sectors

Silt M. mosbyense 0.55 19.83 0.99 4 sectors with 45˚ offset Silt S. gracile 0.33 15.62 0.97 4 sectors with 45˚ offset Silt N. juddii 0.66 16.11 0.98 4 sectors Silt W. devonense 0.04 17.53 0.98 4 sectors with 45˚ offset

Clay M. mosbyense - 12.48 0.95 Semivariogram: Power; 4 sectors with 45˚ offset Transformation: Log empirical. 4 sectors with 45˚ Clay S. gracile 0.25 12.94 0.98 offset Clay N. juddii 0.03 12.02 0.98 Transformation: Log empirical. 4 sectors 100

RMS Attribute Time Zone Mean RMS Standardized Settings

Clay W. devonense 0.07 13.57 0.99 Transformation: Empirical. 4 sectors with 45˚ offset

Transformation: Log empirical; Semivariogram: K- Water Depth M. mosbyense - 0.28 1.02 Bessel detrended; 4 sectors with 45˚ offset Transformation: Log empirical; 4 sectors with 45˚ Water Depth S. gracile 0.06 0.34 0.93 offset Transformation: Log empirical; 4 sectors with 45˚ Water Depth N. juddii 0.05 0.45 1.03 offset Water Depth W. devonense 0.02 0.31 0.98 Transformation: Empirical; 4 sectors with 45˚ offset

Oxygenation M. mosbyense 0.01 0.33 1.01 Transformation: Log empirical. 4 sectors Oxygenation S. gracile 0.01 0.49 1.03 Transformation: Log empirical. 4 sectors Transformation: Empirical. Semivariogram: Whittle Oxygenation N. juddii 0.01 0.33 1.01 detrended Transformation: Empirical. Semivariogram: Whittle

Oxygenation W. devonense 0.02 0.46 1.01 detrended

101

APPENDIX B. ALL FUZZY CONTROL POINTS

Key: R. green. = Rotalipora greenhornensis; V. loet. = Valvulineria loetterlei; Ammob. sp. = Ammobaculites spp.; Neo. alber. = Neobulimina albertensis; Gave. dak. = Gavelinella dakotensis. Sig. M. = Sigmoidal Monotonically.

Time Zone Taxon Input Layer Fuzzy Function a b c d Degree of Confidence (1 - Ignorance)

M. mosbyense R. green. Total Carbonate Sig. M. Increasing 16 35 35 35 0.8 M. mosbyense R. green. Silt Sig. M. Decreasing 13 13 13 41 0.7 M. mosbyense R. green. Latitude Sig. M. Decreasing 41 41 41 46 0.8 M. mosbyense R. green. Longitude Sig. M. Increasing -110 -99.5 -99.5 -99.5 0.75 S. gracile R. green. Total Carbonate Sig. M. Increasing 10 50 50 50 0.8 S. gracile R. green. Silt Sig. M. Decreasing 15 15 15 46 0.7 S. gracile R. green. Latitude Sig. M. Decreasing 42 42 42 47 0.8 S. gracile R. green. Longitude Sig. M. Increasing -110 -99.5 -99.5 -99.5 0.75 S. gracile V. loet. Total Carbonate Sig. M. Increasing 10 50 50 50 0.8; 0.5; 0.4* S. gracile V. loet. Silt Sig. M. Decreasing 20 20 20 48 0.7; 0.4; 0.3 S. gracile V. loet. Latitude Sig. M. Decreasing 44 44 44 50 0.85; 0.6; 0.5 S. gracile V. loet. Longitude Sig. M. Increasing -107 -103.5 -103.5 -103.5 0.85; 0.6; 0.5 S. gracile Ammob. sp. Total Carbonate Sig. M. Decreasing 10 10 10 47 0.8 S. gracile Ammob. sp. Silt Sig. M. Increasing 11 50 50 50 0.7 S. gracile Ammob. sp. Latitude Sig. M. Increasing 35 46 46 46 0.85 S. gracile Ammob. sp. Longitude Sig. M. Decreasing -109 -109 -109 -99.5 0.85 102

Time Zone Taxon Input Layer Fuzzy Function a b c d Degree of Confidence (1 - Ignorance)

N. juddii Neo. alber. Total Carbonate Sig. M. Increasing 5 40 40 40 0.75 N. juddii Neo. alber. Silt Sig. M. Decreasing 25 25 25 55 0.65 N. juddii Neo. alber. Latitude Sig. M. Decreasing 44 44 44 51 0.9 N. juddii Neo. alber. Longitude Sig. M. Increasing -111 -104 -104 -104 0.9 N. juddii Gave. dak. Total Carbonate Sig. M. Increasing 5 45 45 45 0.75 N. juddii Gave. dak. Silt Sig. M. Decreasing 30 30 30 55 0.8 N. juddii Gave. dak. Latitude Sig. M. Decreasing 44 44 44 51 0.9 N. juddii Gave. dak. Longitude Sig. M. Increasing -113 -104 -104 -104 0.9 W. devonense Neo. alber. Total Carbonate Sig. M. Increasing 10 45 45 45 0.8 W. devonense Neo. alber. Silt Sig. M. Decreasing 25 25 25 40 0.75 W. devonense Neo. alber. Latitude Sig. M. Decreasing 43 43 43 51 0.9 W. devonense Neo. alber. Longitude Sig. M. Increasing -111 -104 -104 -104 0.9

Absence Layers

Time Zone Taxon Input Layer Fuzzy Function a b c d Degree of Confidence (1 - Ignorance) M. mosbyense R. green. Dep. Environment User-Defined 1 - 0.5 2 - 0.5 3 - 0.15 4, 5, 6 - 0 0.5 M. mosbyense R. green. Total Carbonate Sig. M. Decreasing 12 12 12 33 0.7 M. mosbyense R. green. Silt Sig. M. Increasing 17 42 42 42 0.6 103

Time Zone Taxon Input Layer Fuzzy Function a b c d Degree of Confidence (1 - Ignorance)

M. mosbyense R. green. Latitude Sig. M. Increasing 35 49 49 49 0.7 M. mosbyense R. green. Longitude Sig. M. Decreasing -111 -111 -111 -98 0.65 S. gracile R. green. Dep. Environment User-Defined 1 - 0.5 2 - 0.5 3 - 0.15 4, 5, 6 - 0 0.5 S. gracile R. green. Total Carbonate Sig. M. Decreasing 15 15 15 47 0.7 S. gracile R. green. Silt Sig. M. Increasing 15 42 42 42 0.6 S. gracile R. green. Latitude Sig. M. Increasing 35 50 50 50 0.7 S. gracile R. green. Longitude Sig. M. Decreasing -111 -111 -111 -100 0.65 S. gracile V. loet. Total Carbonate Sig. M. Decreasing 10 10 10 20 0.7; 0.4; 0.3* S. gracile V. loet. Silt Sig. M. Increasing 16 40 40 40 0.6; 0.3; 0.2 S. gracile V. loet. Latitude Sig. M. Increasing 36 48 48 48 0.75; 0.5; 0.4 S. gracile V. loet. Longitude Sig. M. Decreasing -108.5 -108.5 -108.5 -103.5 0.75; 0.5; 0.4 S. gracile Ammob. sp. Total Carbonate Sig. M. Increasing 15 50 50 50 0.7 S. gracile Ammob. sp. Silt Sig. M. Decreasing 10 10 10 40 0.6 S. gracile Ammob. sp. Latitude Sig. M. Decreasing 35 35 35 46 0.75 S. gracile Ammob. sp. Longitude Sig. M. Increasing -107 -99.5 -99.5 -99.5 0.75 N. juddii Neo. alber. Total Carbonate Sig. M. Decreasing 5 5 5 40 0.75 N. juddii Neo. alber. Silt Sig. M. Increasing 15 55 55 55 0.65 N. juddii Neo. alber. Latitude Sig. M. Increasing 44 52 52 52 0.8 N. juddii Neo. alber. Longitude Sig. M. Decreasing -112 -112 -112 -102 0.8 104

Time Zone Taxon Input Layer Fuzzy Function a b c d Degree of Confidence (1 - Ignorance)

N. juddii Gave. dak. Total Carbonate Sig. M. Decreasing 0 0 0 40 0.75 N. juddii Gave. dak. Silt Sig. M. Increasing 30 55 55 55 0.7 N. juddii Gave. dak. Latitude Sig. M. Increasing 44 52 52 52 0.8 N. juddii Gave. dak. Longitude Sig. M. Decreasing -113 -113 -113 -101 0.8 W. devonense Neo. alber. Total Carbonate Sig. M. Decreasing 10 10 10 40 0.7 W. devonense Neo. alber. Silt Sig. M. Increasing 20 40 40 40 0.65 W. devonense Neo. alber. Latitude Sig. M. Increasing 44 52 52 52 0.8 W. devonense Neo. alber. Longitude Sig. M. Decreasing -112 -112 -112 -102 0.8

*High, medium, low ignorance

105

APPENDIX C. FORAMINIFERAL ABSENCE FIGURES

Absence images for Rotalipora greenhornensis during M. mosbyense zone. From left to right: belief, plausibility and belief interval. 106

Absence images for Rotalipora greenhornensis during S. gracile zone. From left to right: belief, plausibility and belief interval.

107

Absence images for Valvulineria loetterlei during S. gracile zone. From left to right: belief, plausibility and belief interval.

108

Absence images for Ammobaculites spp. during S. gracile zone. From left to right: belief, plausibility and belief interval.

109

Absence images for Neobulimina albertensis during N. juddii zone. From left to right: belief, plausibility and belief interval.

110

Absence images for Gavelinella dakotensis during N. juddii zone. From left to right: belief, plausibility and belief interval.

111

Absence images for Neobulimina albertensis during W. devonense zone. From left to right: belief, plausibility and belief interval.

112

APPENDIX D. CODES

1. Code for converting ArcMap rasters to ASCII format:

# Imports arcpy site package and sets environment. import arcpy from arcpy import env arcpy.env.overwriteOutput = True env.workspace = "E:/GISPaleoThesis/GISLayers"

# Creates a list that grabs all files beginning with “sg_”. rlist = arcpy.ListRasters("sg_*") for r in rlist: print r

# The try/except statement will print an error if the code does not run properly. try: # Converts raster to ascii, specifying the folder destination. for raster in rlist: outASCII = "E:/GISPaleoThesis/GISLayers/" + raster + ".asc" arcpy.RasterToASCII_conversion(raster, outASCII) except: arcpy.AddError("Raster to ASCII tool could not execute") print ("Raster to ASCII tool could not execute") print arcpy.GetMessages() 113

2. Code that imports ASCII files from ArcGIS into TerrSet:

# Imports the TerrSet COM extension (like "import arcpy") and operating system. import win32com.client import os import glob # glob will help create a list with a specific pattern (e.g., *.txt)

# Sets the directory for os operations. os.chdir("E:/GISPaleoThesis/GISLayers")

# Launches the TerrSet application and renders it an object on which to perform functions. terrset = win32com.client.Dispatch("IDRISI32.IdrisiAPIServer")

# Sets current working directory. terrset.SetWorkingDir("E:/GISPaleoThesis/GISLayers")

# Defines a list that will call the ASCII files to be imported. rlist = glob.glob("*.asc") ##print rlist

# For loop will convert ASCII files to .rst format. for raster in rlist: terrset.RunModule('ARCRASTER', '4*' + raster + '*' + raster.replace('.asc', '') + '_ts.rst' + '*1*ALBERSUS*Meters*1', 1, '', '', '', '', 1) terrset.DisplayFile(raster.replace('.asc', '') + '_ts.rst', 'quant') print "Done!" 114

3. Code that displays histogram overlain by taxa masks:

# Imports the TerrSet COM extension (like "import arcpy") and operating system. import win32com.client import os

# Sets the directory for os operations. os.chdir("E:/Fall2015/GISF15/Project/DataPlay")

# Launches the TerrSet application and renders it an object on which to perform functions. (Like arcpy.*) terrset = win32com.client.Dispatch("IDRISI32.IdrisiAPIServer")

# Sets current working directory. terrset.SetWorkingDir("E:/Fall2015/GISF15/Project/DataPlay")

# Creates a list of input images. inputImages = ["mm_dep_bsian_ts.rst", "mm_tc_bsian2_ts.rst", "mm_silt_use1_ts.rst", "mm_lat_ts.rst", "mm_lon_ts.rst"] mask = ["mm_RGREEN_PR.rst", "mm_RGREEN_ABR.rst", "mm_RGREEN_NOR.rst"]

# For loop runs the Histogram Display module for all images in above list. for image in inputImages: terrset.RunModule('HISTO', '1*' + image + '*' + mask[0] + '*1*1*1*#*#*1', 1, '', '', '', '', 1)

115

4. Code that fuzzifies interpolated environmental surfaces:

# Imports the TerrSet COM extension (like "import arcpy") and operating system. import win32com.client import os

# Sets the directory for os operations. os.chdir("E:/Fall2015/GISF15/Project/DataPlay")

# Launches the TerrSet application and renders it an object on which to perform functions. (Like arcpy.*) terrset = win32com.client.Dispatch("IDRISI32.IdrisiAPIServer")

# Sets current working directory. terrset.SetWorkingDir("E:/Fall2015/GISF15/Project/DataPlay")

# Creates several objects to pass the FUZZY and SCALAR parameters into. inputImages = ["mm_dep_bsian_ts.rst", "mm_tc_bsian2_ts.rst", "mm_silt_use1_ts.rst", "mm_lat_ts.rst", "mm_lon_ts.rst"]

# These text files hold the parameters (control points and scalar) to pass into the macro. The with statements “read” over each line in the file. with open('cp_project.txt') as f: line = f.readlines() f.close() with open('scalarvalues.txt') as text: scalar = text.readlines() text.close()

# Creates the fuzzy layers from the list of rasters above, then rescales them for uncertainty. terrset.RunModule('FUZZY', '1*' + inputImages[1] + '*1*mm_tc_tmpp_py.rst' + line[0], 1, '', '', '', '', 1) terrset.RunModule('SCALAR', 'mm_tc_tmpp_py.rst*mm_tc_fzp_py.rst*3*' + scalar[0], 1, '', '', '', '', 1)

# Run the same set of modules several times, each with different inputs and parameters. terrset.RunModule('FUZZY', '1*' + inputImages[1] + '*1*mm_tc_tmpa_py.rst' + line[1], 1, '', '', '', '', 1) terrset.RunModule('SCALAR', 'mm_tc_tmpa_py.rst*mm_tc_fza_py.rst*3*' + scalar[0], 1, '', '', '', '', 1) terrset.RunModule('FUZZY', '1*' + inputImages[2] + '*1*mm_silt_tmpp_py.rst' + line[2], 1, '', '', '', '', 1) 116 terrset.RunModule('SCALAR', 'mm_silt_tmpp_py.rst*mm_silt_fzp_py.rst*3*' + scalar[1], 1, '', '', '', '', 1) terrset.RunModule('FUZZY', '1*' + inputImages[2] + '*1*mm_silt_tmpa_py.rst' + line[3], 1, '', '', '', '', 1) terrset.RunModule('SCALAR', 'mm_silt_tmpa_py.rst*mm_silt_fza_py.rst*3*' + scalar[1], 1, '', '', '', '', 1) terrset.RunModule('FUZZY', '3*' + inputImages[3] + '*1*mm_lat_tmpp_py.rst' + line[4], 1, '', '', '', '', 1) terrset.RunModule('SCALAR', 'mm_lat_tmpp_py.rst*mm_lat_fzp_py.rst*3*' + scalar[0], 1, '', '', '', '', 1) terrset.RunModule('FUZZY', '3*' + inputImages[3] + '*1*mm_lat_tmpa_py.rst' + line[5], 1, '', '', '', '', 1) terrset.RunModule('SCALAR', 'mm_lat_tmpa_py.rst*mm_lat_fza_py.rst*3*' +scalar[0], 1, '', '', '', '', 1) terrset.RunModule('FUZZY', '3*' + inputImages[4] + '*1*mm_lon_tmpp_py.rst' + line[6], 1, '', '', '', '', 1) terrset.RunModule('SCALAR', 'mm_lon_tmpp_py.rst*mm_lon_fzp_py.rst*3*' + scalar[2], 1, '', '', '', '', 1) terrset.RunModule('FUZZY', '3*' + inputImages[4] + '*1*mm_lon_tmpa_py.rst' + line[7], 1, '', '', '', '', 1) terrset.RunModule('SCALAR', 'mm_lon_tmpa_py.rst*mm_lon_fza_py.rst*3*' +scalar[2], 1, '', '', '', '', 1) terrset.RunModule('FUZZY', '4*' + inputImages[0] + '*1*mm_dep_fza_py.rst*2*depencp.txt', 1, '', '', '', '', 1)

# Displays the rescaled fuzzy files in TerrSet. fuzzy_list = ['mm_tc_fzp_py.rst', 'mm_dep_fza_py.rst', 'mm_lon_fza_py.rst', 'mm_lon_fzp_py.rst', 'mm_lat_fza_py.rst', 'mm_lat_fzp_py.rst', 'mm_silt_fza_py.rst', 'mm_silt_fzp_py.rst', 'mm_tc_fza_py.rst']

# Finally, this for loop lets us know it is done! for x in fuzzy_list: terrset.DisplayFile(x, 'quant') print "Done!"

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5. Sample macro for modeling foraminiferal distributions with Dempster-Shafer Theory:

OVERLAY 2*E:\GISPaleoThesis\IDRISI_test\ones.rst*E:\GISPaleoThesis\IDRISI_test\site.rst*E:\GISPaleoThesis\IDRISI_test\TMPIG0.rst

OVERLAY 2*E:\GISPaleoThesis\IDRISI_test\ones.rst*E:\GISPaleoThesis\IDRISI_test\nonsite.rst*E:\GISPaleoThesis\IDRISI_test\TMPIG1.rst

DEMPSTER E:\GISPaleoThesis\IDRISI_test\~IKB$.ikb*E:\GISPaleoThesis\IDRISI_test\~DS$.iml*N

OVERLAY 3*E:\GISPaleoThesis\IDRISI_test\site.rst*E:\GISPaleoThesis\IDRISI_test\nonsite.rst*E:\GISPaleoThesis\IDRISI_test\1-1-1.rst

OVERLAY 3*E:\GISPaleoThesis\IDRISI_test\TMPIG0.rst*E:\GISPaleoThesis\IDRISI_test\nonsite.rst*E:\GISPaleoThesis\IDRISI_test\1-2-1.rst

OVERLAY 3*E:\GISPaleoThesis\IDRISI_test\site.rst*E:\GISPaleoThesis\IDRISI_test\TMPIG1.rst*E:\GISPaleoThesis\IDRISI_test\1-1-2.rst

OVERLAY 3*E:\GISPaleoThesis\IDRISI_test\TMPIG0.rst*E:\GISPaleoThesis\IDRISI_test\TMPIG1.rst*E:\GISPaleoThesis\IDRISI_test\1-2-2.rst

INITIAL E:\GISPaleoThesis\IDRISI_test\ones.rst*1*1*1*1*E:\GISPaleoThesis\IDRISI_test\1-1-1.rst

OVERLAY 2*E:\GISPaleoThesis\IDRISI_test\ones.rst*E:\GISPaleoThesis\IDRISI_test\1-1-1.rst*E:\GISPaleoThesis\IDRISI_test\stdtmp.rst

OVERLAY 42*E:\GISPaleoThesis\IDRISI_test\1-2-1.rst*E:\GISPaleoThesis\IDRISI_test\stdtmp.rst*E:\GISPaleoThesis\IDRISI_test\std_m1.rst

OVERLAY 42*E:\GISPaleoThesis\IDRISI_test\1-1-2.rst*E:\GISPaleoThesis\IDRISI_test\stdtmp.rst*E:\GISPaleoThesis\IDRISI_test\std_m2.rst

OVERLAY 42*E:\GISPaleoThesis\IDRISI_test\1-2-2.rst*E:\GISPaleoThesis\IDRISI_test\stdtmp.rst*E:\GISPaleoThesis\IDRISI_test\std_m3.rst

OVERLAY 1*E:\GISPaleoThesis\IDRISI_test\std_m1.rst*E:\GISPaleoThesis\IDRISI_test\std_m2.rst*E:\GISPaleoThesis\IDRISI_test\b3-1.rst

OVERLAY 1*E:\GISPaleoThesis\IDRISI_test\b3-1.rst*E:\GISPaleoThesis\IDRISI_test\std_m3.rst*E:\GISPaleoThesis\IDRISI_test\b3-2.rst

OVERLAY 1*E:\GISPaleoThesis\IDRISI_test\std_m1.rst*E:\GISPaleoThesis\IDRISI_test\std_m3.rst*E:\GISPaleoThesis\IDRISI_test\p1-1.rst

OVERLAY 1*E:\GISPaleoThesis\IDRISI_test\std_m2.rst*E:\GISPaleoThesis\IDRISI_test\std_m3.rst*E:\GISPaleoThesis\IDRISI_test\p2-1.rst

OVERLAY 1*E:\GISPaleoThesis\IDRISI_test\std_m1.rst*E:\GISPaleoThesis\IDRISI_test\std_m2.rst*E:\GISPaleoThesis\IDRISI_test\p3-1.rst

OVERLAY 1*E:\GISPaleoThesis\IDRISI_test\p3-1.rst*E:\GISPaleoThesis\IDRISI_test\std_m3.rst*E:\GISPaleoThesis\IDRISI_test\p3-2.rst 118

OVERLAY 2*E:\GISPaleoThesis\IDRISI_test\~p1.rst*E:\GISPaleoThesis\IDRISI_test\~B1.rst*E:\GISPaleoThesis\IDRISI_test\~I1.rst

OVERLAY 2*E:\GISPaleoThesis\IDRISI_test\~p2.rst*E:\GISPaleoThesis\IDRISI_test\~B2.rst*E:\GISPaleoThesis\IDRISI_test\~I2.rst

OVERLAY 2*E:\GISPaleoThesis\IDRISI_test\~p3.rst*E:\GISPaleoThesis\IDRISI_test\~B3.rst*E:\GISPaleoThesis\IDRISI_test\~I3.rst

119

APPENDIX E. DATA SOURCES

List of foraminiferal and stratigraphic data sources. The format is ‘author(s) (year)’.

Batt (1993) Fisher et al. (2003) Bowman and Bralower (2005) Hattin (1975) Brenner et al. (1981) Leckie (1985) Caron et al. (2006) Leckie et al. (1997) Corbett and Watkins (2013) Leckie et al. (1998) Desmares et al. (2007) Lowery et al. (2014) Diner (1992) Merewether (1996) Eicher and Worstell (1970) Prokoph et al. (2013) Elder (1987) Sageman et al. (2006) Elder (1991) Schröder-Adams et al. (2001) Elder and Kirkland (1985) Schröder-Adams et al. (2012) Elderbak et al. (2014) Setterholm (1994) Fisher et al. (1994) Thomson et al. (2011)

120

APPENDIX F. TIME-LAPSE VIDEO OF WATER MASS DISTRIBUTIONS

A time-lapse video summarizing Western Interior Seaway water mass distributions during the

Cenomanian-Turonian Boundary Event is available as a supplemental material to this document in the OhioLINK Electronic Theses and Dissertations Center. The file name is suppl_timelapse_watermasses_Lockshin.mp4.