The Role of Scale in Ecological Inference: Implications for Interpreting Hominin Paleoecology

by Andrew Du

B.S. in Evolutionary Anthropology, May 2009, Rutgers University M.Phil. in Hominid Paleobiology, June 2013, The George Washington University

A Dissertation submitted to

The Faculty of The Columbian College of Arts and Sciences of The George Washington University in partial fulfillment of the requirements for the degree of Doctor of Philosophy

January 31, 2017

Dissertation Directed By:

Anna K. Behrensmeyer Curator of Vertebrate Paleontology National Museum of Natural History, Smithsonian Institution

Bernard A. Wood University Professor of Human Origins

The Columbian College of Arts and Sciences of The George Washington University certifies that Andrew Du has passed the Final Examination for the degree of Doctor of

Philosophy as of November 11, 2016. This is the final and approved form of the dissertation.

The Role of Scale in Ecological Inference: Implications for Interpreting Hominin Paleoecology

Andrew Du

Dissertation Research Committee:

Anna K. Behrensmeyer, Curator of Vertebrate Paleontology, National Museum of Natural History, Smithsonian Institution, Dissertation Co-Director

Bernard A. Wood, University Professor of Human Origins, Dissertation Co-Director

S. Kate Lyons, Research Geologist for the Evolution of Terrestrial Ecosystems Program, Smithsonian National Museum of Natural History, Committee Member

René Bobe, Associate Research Professor of Anthropology, Committee Member

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© Copyright 2017 by Andrew Du All rights reserved

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Dedication

The author wishes to dedicate this work to his parents, Syung-Ching (James)

Du and Huihsin (Gloria) Du, for sacrificing so much during their lifetimes just so their son can pursue a very peculiar career.

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Acknowledgments

There is not enough space in an “Acknowledgments” section to reasonably thank all the people who have helped and influenced me since I first started studying anthropology ten years ago. I will do my best but will inevitably leave off some very important people and for that, I apologize in advance.

I should perhaps start off by thanking Harrison Ford, for it was his very excellent (and sometimes accurate) portrayal of an archaeologist that got me interested in archaeology at a very young age (Sam Neill did the same with paleontology). From there, I took an Intro to Archaeology course at Rutgers to fulfill some general curriculum requirement, and I should thank Chris Lepre for spending too much time on early hominins and getting me hooked on paleoanthropology. Rob

Blumenschine then took the baton with his Intro to Human Evolution course, and I knew this is what I wanted my college major to be. For being excellent teachers, research advisors, and just endless fountains of knowledge to sate my incessant question-asking, I thank (in no particular order) Craig Feibel, Rhonda Quinn, Rob

Blumenschine, Jack Harris, Rob Scott, Ryne Palombit, Carmel Schrire, and Gail

Ashley. I would also like to thank the graduate students during my time there for making me feel welcome and never looking down their noses at me (again in no particular order): Jay Reti, Mike Pante, Steve Merritt, Emmanuel Ndiema, Melanie

Crisfield, Pam Weis, Susan Coiner-Collier, Darcy Shapiro, and Sarah Hlubik. To wrap up the “Rutgers paragraph,” I would again especially like to thank Jack Harris for advising my honors thesis and giving me so many opportunities to do field work and research. I can now appreciate just how special it is for a professor to devote so

v much time and energy to an undergraduate. Lastly, I’d like to thank Rob

Blumenschine for instilling in me a love of bones and taphonomy, and perhaps more importantly, a love of theory, philosophy of science, and overall analytical rigor.

For introducing me to fieldwork, I must thank the National Museums of Kenya and the Koobi Fora Field School (class of 2007) and their directors and staff: Jack

Harris, Dave Braun, Purity Kiura, Emmanuel Ndiema, Brian Richmond, René Bobe,

Carolyn Dillian, Steve Merritt, Paul Watene, Ben Sila, and Tom Mukuyu. I would return time and time again (even way into grad school, which I did not expect!) to conduct research at this wonderful region and to teach young, eager students. I must also thank Rob Blumenschine and Jackson Njau for letting me visit and help out with fieldwork at Olduvai Gorge, a truly remarkable site. I also would like to thank Rick

Potts, Kay Behrensmeyer, Alison Brooks, John Yellen, and Briana Pobiner for putting up with me and letting me come to Olorgesailie. And finally, thanks to Kay

Behrensmeyer and Robin Whatley for allowing me to help out for one field season at

Petrified Forest National Park. All my field experience has made me a better paleontologist, taphonomist, and geologist both in and out of the field.

For my time at George Washington University, I have to thank my fellow students and the faculty for making my time there enjoyable and for intellectually stimulating discussions. These are (again in no particular order) David Patterson,

Tyler Faith, Dave Green, Amanda Henry, Erin-Marie Williams, Cheryl Stimpson,

Karyne Rabey, Amy Bauernfeind, Habiba Chirchir, Kes Schroer, Kevin Hatala,

Andrew Zipkin, Jen Baker, Serena Bianchi, Liz Renner, Heather Dingwall, Laura

Reyes, Amelia Villaseñor, Chrisandra Kufeldt, Katie Ranhorn, Laurence Dumouchel,

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Kelly Ostrofsky, Jonathan Reeves, Sean Lee, Eve Boyle, Angie Peña, Alex Prucha,

Sergio Almécija, Dave Braun, Alison Brooks, Erin Vogel, Ashley Hammond,

Andrew Barr, Mark Grabowski, Neil Roach, Brian Villmoare, Chet Sherwood, René

Bobe, Bernard Wood, and Shannon McFarlin.

Being at GW, I was fortunate enough to also be a part of the community at the

Smithsonian National Museum of Natural History. There, I must thank Gene Hunt,

Pete Wagner, and Carl Simpson for patiently entertaining my questions. But perhaps my most fervent intellectual engagement with the Smithsonian was through our weekly journal club, the Ecology Reading Group, which was my trial by fire training in community ecology and macroecology. Every Friday, we would discuss the grander ideas and methods in an ecology paper, and some of my most enjoyable academic discussions took place there. Therefore, I must thank Kay Behrensmeyer,

Kate Lyons, David Patterson, Amelia Villaseñor, Nathan Jud, Anikó Tóth, Matt

Davis, Silvia Pineda-Munoz, Dani Fraser, Laura Soul, Advait Jukar, and Antoine

Bercovici.

I was fortunate (lucky?) enough to realize early on in my graduate career how important quantitative methods were, not only for analyzing data, but also for framing research questions, ensuring a logical progression of ideas, understanding data, etc. This was due to a simultaneous stumbling upon a book (Stratigraphic

Paleobiology by Mark Patzkowsky and Steve Holland, which was ironically purchased at an archaeology conference), which introduced me to quantitative paleobiology, and my joining the Evolution of Terrestrial Ecosystems working group

(thanks to Kay Behrensmeyer and Kate Lyons). Later on, Gene Hunt and Josh Miller

vii helped with my R training, and my participation in the Paleobiology Database

Workshop in Analytical Paleobiology (run primarily by John Alroy) and Brian

McGill’s Advanced Biometry course at University of Maine helped shore up my statistical and coding proficiency.

Lastly, I’d like to thank my dissertation committee one by one. I thank Kate

Lyons for her macroecological knowledge, always helpful advice, and for teaching me the difference between systematic bias and random noise; René Bobe for hands- on lessons in faunal IDs in the field and introducing me to paleoecology when I was a young undergraduate; Brian McGill for being a macroecological contrarian and publishing papers that have been most influential on my thinking. I also have to thank him for hosting me for a semester at the University of Maine, where he let me sit in on his Community Ecology and Advanced Biometry courses, as well as be a part of his lab; Bernard Wood for helping me out in a myriad of ways, both within and outside of academia. Without him, I likely would not have had the confidence and mental energy to finish my PhD; and last (but never least), I thank my advisor

Kay Behrensmeyer. I first met Kay in my final year at Rutgers when she came to give a talk. She was an idol to me back then but over the years, I’ve gotten to know the more human side of Kay. I have never met a more hyper-observant researcher with a purer love for fieldwork and for the science. But perhaps the most important lesson I have learned from Kay is her willingness to put her family (Bill, Kristina, and Sarah) above all else. Some things are just more important than science.

All of the aforementioned people have influenced me in countless ways and have made me the researcher that I am today. Ten years ago, I would have never

viii envisioned myself becoming so interdisciplinary (and moving away from

“traditional” paleoanthropology), drawing upon the strengths of each field I study.

Stephen Jay Gould definitely had it right when he emphasized the importance of contingency in the evolution of life.

These are my academic muses. For personal, existential ones that helped get me through graduate school, I thank Bruce Springsteen and David Foster Wallace.

The Turkana Basin Institute Database was kindly provided by Mikael Fortelius and Meave Leakey. For data collected at Amboseli National Park, Kay

Behrensmeyer would like to thank David Western, Josh Miller, Fred Lala, Erustus

Kanga, Mwebi Ogeto, and many others who helped over the years of bone surveying. Institutional support was provided by Kenya Wildlife Service, National

Museums of Kenya, and the Smithsonian Institution. Funding for my dissertation research was primarily through National Science Foundation IGERT DGE-080163 and two small grants from the Explorer’s Club.

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Abstract of Dissertation

The Role of Scale in Ecological Inference: Implications for Interpreting Hominin Paleoecology

Modern and fossil ecological data exist at very different taxonomic, spatial, and temporal scales. For modern ecology, data are typically collected at the species-level, cover square meter quadrats to the entire globe, and span days to decades at most. For fossil assemblages, spatial scale might be comparable to that studied by modern ecologists, but fossil data are taxonomically and temporally much coarser (respectively, order-, family-, genus-level at best, and 104-108 years). Recent research has shown that ecological patterns and the processes affecting them change across scale. Therefore, using modern ecological theory and methods to study fossil data is an incommensurate exercise and potentially produces spurious results. Moreover, scale varies by orders of magnitude even among fossil assemblages, so comparing fossil sites without an appreciation of scale may also lead to ambiguous conclusions.

I argue that a disregard of scale within paleoanthropology has contributed to its inability to synthesize seemingly disparate paleoecological results into a coherent, unified framework. As a result, paleoanthropology has remained relatively stagnant regarding its understanding of how paleoecological processes drove hominin evolution. With this in mind, I adopt scale as a central theme in my dissertation and attempt to understand how ecological pattern and process change across modern and fossil scales in East African large mammal communities, and if these scale differences can be analytically reconciled.

The results from my three research chapters show ecological patterns (and the relevant processes driving them) fundamentally change across modern and fossil scales.

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Thus, modern and paleoecological theory and data are each incomplete: modern ecologists need to analyze fossil data if they want to study ecology at large time scales, and paleoecologists need to examine modern data and theory in order to understand smaller-scale processes; simple extrapolation and interpolation will not do. For paleoanthropologists, that means it is less than straightforward to infer smaller-scale ecological processes (e.g., paleoenvironmental reconstruction, interspecific interactions) from fossil assemblages, and caution should be exercised when attempting to do so. I by no means offer a panacea for this scale issue, but hopefully my research will make paleoanthropologists more cognizant of scale and encourage future research on this topic.

Only then can we finally begin to understand what exactly were the important ecological drivers affecting hominin behavior and evolution.

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Table of Contents

Dedication ...... iv

Acknowledgments ...... v

Abstract of Dissertation ...... x

List of Figures ...... xiii

List of Tables ...... xvi

Chapter 1: Introduction ...... 1

Chapter 2: Applying the core-transient paradigm to large mammal paleo-communities in the Omo-Turkana Basin ...... 9

Chapter 3: Spatial, temporal, and taxonomic scaling of richness in the skeletal assemblage of a modern East African large mammal community ...... 87

Chapter 4: Extrapolating richness in a modern large mammal community to predict fossil community richness: how ecologically different is the modern from the past? ...... 143

Chapter 5: Conclusions ...... 184

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List of Figures

Chapter 2: Applying the core-transient paradigm to large mammal paleo-communities in the Omo-Turkana Basin

1. Map of Omo-Turkana Basin and chronostratigraphic framework showing the study’s location and time period ...... 54

2. Body size distributions for the Koobi Fora, Nachukui, and Shungura Formations ...... 55

3. Relationship between number of occupied members and mean relative abundance for the Koobi Fora, Nachukui, and Shungura Formations ...... 56

4. Species frequency distribution of number of occupied members for the Koobi Fora,

Nachukui, and Shungura Formations ...... 57

5. Per-member sampling probability for each species for the Koobi Fora, Nachukui, and Shungura Formations ...... 58

6. Observed species ranges and member occupancies for the Koobi Fora Formation ...... 59

7. Observed species ranges and member occupancies for the Nachukui Formation ...... 60

8. Observed species ranges and member occupancies for the Shungura Formation ...... 61

9. Comparison of observed number of core species with expected from the binomial null model ...... 62

10. Observed vs. expected number of core species within each taxonomic family using the hypergeometric null model for the Koobi Fora Formation ...... 63

11. Observed vs. expected number of core species within each taxonomic family using the hypergeometric null model for the Nachukui Formation ...... 64

12. Observed vs. expected number of core species within each taxonomic family

xiii using the hypergeometric null model for the Shungura Formation...... 65

13. Multiple logistic regression coefficient estimates of ecological traits for the

Koobi Fora, Nachukui, and Shungura Formations ...... 66

14. Relationship between abundance and evenness for the Koobi Fora, Nachukui, and

Shungura Formations ...... 67

15. Comparison between observed and predicted live relative abundance from the

Koobi Fora Formation ...... 68

Chapter 3: Spatial, temporal, and taxonomic scaling of richness in the skeletal assemblage of a modern East African large mammal community

16. Map of Amboseli National Park ...... 116

17. Number of sampled transects for each time window length ...... 117

18. Scatterplot matrix of analyzed variables ...... 118

19. Model fits for the four species-time-area models ...... 119

20. Observed species richness as a function of time and area ...... 120

21. Rates of species accumulation as a function of time and area ...... 121

22. Interaction species-time-area model coefficients as a function of taxonomic scale ..... 122

23. Contour plots of predicted species-time-area model richness at different taxonomic scales ...... 123

24. Conceptual figures showing how sampling processes result in the coefficients estimated from the interaction species-time-area model ...... 124

Chapter 4: Extrapolating richness in a modern large mammal community to predict

xiv fossil community richness: how ecologically different is the modern from the past?

25. Plot showing the location of each Amboseli transect across space and through time ...... 165

26. Diagram showing the spatiotemporal scales at which the Amboseli and

Koobi Fora data were collected ...... 166

27. Model fits for species- and family-level species-time-area models ...... 167

28. Comparing predicted and observed squares family-level model coefficients ...... 168

29. Comparing predicted and observed Ileret species richness estimates ...... 169

30. Empirical species-time relationship combining Amboseli and Ileret data ...... 170

31. Conceptual figure illustrating the effect of the species pool on species accumulation with increasing spatiotemporal scale ...... 171

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List of Tables

Chapter 2: Applying the core-transient paradigm to large mammal paleo-communities in the Omo-Turkana Basin

1. Number of individuals and species (core and transient) for the Koobi Fora,

Nachukui, and Shungura Formations ...... 69

2. List of core species for the Koobi Fora, Nachukui, and Shungura Formations ...... 70

3. Multiple logistic regression coefficients of ecological traits for the Koobi Fora,

Nachukui, and Shungura Formations ...... 71

4. Body mass logistic regression coefficients within body mass classes for the

Koobi Fora, Nachukui, and Shungura Formations ...... 72

Chapter 3: Spatial, temporal, and taxonomic scaling of richness in the skeletal assemblage of a modern East African large mammal community

5. Summary of Amboseli transects ...... 126

6. Species-time-area model selection results ...... 127

7. Interaction species-time-area model coefficients at different taxonomic scales ...... 128

Chapter 4: Extrapolating richness in a modern large mammal community to predict fossil community richness: how ecologically different is the modern from the past?

8. Summary of Koobi Fora squares data ...... 172

9. Summary of Koobi Fora Ileret data ...... 173

10. Species-time-area model coefficients, good-of-fit, and prediction accuracy statistics at the species- and family-level ...... 174

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Chapter 1: Introduction

Paleoecology has been an important and consistent part of paleoanthropological research since the latter’s inception. Paleoecology’s role has mainly been to reconstruct the paleoenvironments of our hominin ancestors (Kappelman et al., 1997; Reed, 1997;

Bobe and Behrensmeyer, 2004; Cerling et al., 2011) or to elucidate interspecific interactions between hominin species and others (Winterhalder, 1980; Blumenschine,

1995; Brantingham, 1998; Werdelin and Lewis, 2013). Paleoenvironmental reconstruction is done using all sorts of proxies (e.g., faunal lists, stable isotope analyses, dental wear studies, etc.), and the most robust, general consensus thus far is that hominins were occupying mosaic habitats superimposed on a much larger-scale trend towards grassier environments (Reed, 1997; Bobe and Behrensmeyer, 2004; Bobe, 2006;

Kingston, 2007; Cerling et al., 2011, 2015; deMenocal, 2011; Levin et al., 2011;

Reynolds et al., 2015). The study of hominin interactions with other species has mostly been in the purview of zooarchaeologists, and the gamut runs from the passive scavenging of carcasses (Blumenschine, 1995) to hunting (Domı́nguez-Rodrigo, 1997)

(depending also on the time period of interest), with some speculative support that hominins were outcompeting other carnivorans and driving them to extinction (Werdelin and Lewis, 2013; Fortelius et al., 2016).

In my opinion, paleoecologists have collected lots of interesting data, but the interpretive framework unifying all these disparate sources is lacking (or weak at best).

What does it mean when one site has 40% alcelaphins and another site has 30%? What does it mean when one site has δ13C pedogenic carbonate values that range from -13 to -3 while another site ranges from -4 to 3? This interpretive ambiguity is probably the main

1 reason the miscellaneous category, “mosaic,” exists and also why we focus on long-term averages and trends.

I argue here that our interpretive framework is incomplete, and it is this incompleteness that is preventing us from efficiently and effectively interpreting paleoecological data. This missing piece is an appreciation and an explicit focus on spatial, temporal, and taxonomic scale. Neo- and paleoecologists outside of paleoanthropology already appreciate the power of scale in their theory and analyses.

Specifically, they recognize that ecological pattern and process change as one’s scale of analyses changes and that seemingly disparate results can easily be explained away and unified by the concept of scale (Wiens, 1989; Levin, 1992; McGill, 2010; McGill et al.,

2015). A more difficult issue has been to try to bridge the “scale gap” that exists between modern and fossil data. This is important because modern ecologists need the long time depth of the fossil record to study large-scale processes (e.g., species extinction, speciation, climate and species response, etc.). Likewise, paleoecologists rely heavily on modern ecological theory and method in order to infer dynamics from static fossil patterns. However, a fruitful exchange between the two fields can only be achieved after one understands this scale gap and how ecological patterns change across scale.

Why would this be of importance to paleoanthropologists? The questions that paleoanthropologists are interested in exist at different scales. These include (going from the smallest scale to the largest) foraging for food (Sept, 1994), competition for resources with other species (Blumenschine et al., 1987), habitat filtering (Wood and Strait, 2004), and climate change driving evolutionary responses (Potts, 1998). Because ecological patterns and processes change across scale, the scale of one’s data needs to be

2 commensurate with the scale of the research question. And because the fossil record exists on large scales (e.g., large amounts of time-averaging, fossils only identifiable to genus or family), the natural question is can we even ask small-scale questions? The simultaneous study of scale in modern and fossil communities allows us to address this question.

To this end, I draw upon the modern large mammal dataset from Amboseli

National Park, Kenya and the fossil large mammal dataset from the Omo-Turkana Basin,

Ethiopia and Kenya for my dissertation research. I approach my main research goal using two complementary inferential frameworks: 1) In Chapter 2, I take a recently developed modern ecological theory (the core-transient theory [Magurran and Henderson, 2003;

Supp et al., 2015]) and apply it as is (without any scaling corrections) to the fossil record.

Core-transient theory classifies species into one of two categories (core or transient), and each category is associated with a number of ecological correlates which can be tested using the fossil record. 2) The second approach starts from the opposite inferential direction and attempts to extrapolate and scale up empirical modern ecological dynamics to the scales seen in the fossil record in an attempt to predict fossil patterns. Chapter 3 builds the extrapolation model by studying how richness scales with area, time, and taxonomic scale in the modern Amboseli community. Chapter 4 then takes this model to its logical conclusion by extrapolating temporal and taxonomic scale to generate predictions for richness patterns in the fossil record, specifically the Koobi Fora

Formation on the east side of the Omo-Turkana Basin. These predictions are then compared to empirical fossil patterns to see if large-scale ecosystems are indeed fundamentally different from smaller-scale ones, or if the observed differences are simply

3 due to scale disparities.

The ultimate aim of this dissertation is to understand how scale differences can be reconciled, which will enable the ecological research community to successfully integrate modern and fossil ecological data in order to study ecology across the full spectrum of scales available to us (i.e., from local habitats to continents, and from years to millions of years). For paleoanthropology, an appreciation of scale serves as an interpretive

“corrective lens,” which will allow us to understand which processes are important at which scales, whether certain processes simply cannot be inferred given the scale of one’s fossil dataset, and if any scale differences among datasets can be analytically resolved. This will ideally lead to the integration of seemingly distinct and messy paleoecological results into a unified theoretical framework. Or at the very least, a large portion of unexplained variation among our paleoecological datasets can be accounted for by scale differences. We can then finally begin to understand what exactly were the important ecological drivers affecting hominin behavior and evolution.

4

References

Blumenschine, R.J., 1995. Percussion marks, tooth marks, and experimental

determinations of the timing of hominid and carnivore access to long bones at

FLK Zinjanthropus, Olduvai Gorge, Tanzania. Journal of Human Evolution. 29,

21–51.

Blumenschine, R.J., Bunn, H.T., Geist, V., Ikawa-Smith, F., Marean, C.W., Payne, A.G.,

Tooby, J., Merwe, N.J. van der, 1987. Characteristics of an Early Hominid

Scavenging Niche [and Comments and Reply]. Current Anthropology. 28, 383–

407.

Bobe, R., 2006. The evolution of arid ecosystems in eastern Africa. Journal of Arid

Environments. 66, 564–584.

Bobe, R., Behrensmeyer, A.K., 2004. The expansion of grassland ecosystems in Africa in

relation to mammalian evolution and the origin of the genus Homo.

Palaeogeography, Palaeoclimatology, Palaeoecology. 207, 399–420.

Brantingham, P.J., 1998. Hominid–Carnivore Coevolution and Invasion of the Predatory

Guild. Journal of Anthropological Archaeology. 17, 327–353.

Cerling, T.E., Andanje, S.A., Blumenthal, S.A., Brown, F.H., Chritz, K.L., Harris, J.M.,

Hart, J.A., Kirera, F.M., Kaleme, P., Leakey, L.N., Leakey, M.G., Levin, N.E.,

Manthi, F.K., Passey, B.H., Uno, K.T., 2015. Dietary changes of large herbivores

in the Turkana Basin, Kenya from 4 to 1 Ma. Proceedings of the National

Academy of Sciences. 112, 11467–11472.

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Cerling, T.E., Wynn, J.G., Andanje, S.A., Bird, M.I., Korir, D.K., Levin, N.E., Mace, W.,

Macharia, A.N., Quade, J., Remien, C.H., 2011. Woody cover and hominin

environments in the past 6 million years. Nature. 476, 51–56. deMenocal, P.B., 2011. Climate and Human Evolution. Science. 331, 540–542.

Domı́nguez-Rodrigo, M., 1997. Meat-eating by early hominids at the FLK 22

Zinjanthropus site, Olduvai Gorge (Tanzania): an experimental approach using

cut-mark data. Journal of Human Evolution. 33, 669–690.

Fortelius, M., Žliobaitė, I., Kaya, F., Bibi, F., Bobe, R., Leakey, L., Leakey, M.,

Patterson, D., Rannikko, J., Werdelin, L., 2016. An ecometric analysis of the

fossil mammal record of the Turkana Basin. Philosophical Transactions of the

Royal Society B: Biological Sciences. 371, 20150232.

Kappelman, J., Plummer, T., Bishop, L., Duncan, A., Appleton, S., 1997. Bovids as

indicators of Plio-Pleistocene paleoenvironments in East Africa. Journal of

Human Evolution. 32, 229–256.

Kingston, J.D., 2007. Shifting adaptive landscapes: Progress and challenges in

reconstructing early hominid environments. American Journal of Physical

Anthropology. 134, 20–58.

Levin, N.E., Brown, F.H., Behrensmeyer, A.K., Bobe, R., Cerling, T.E., 2011. Paleosol

carbonates from the Omo Group: Isotopic records of local and regional

environmental change in East Africa. Palaeogeography, Palaeoclimatology,

Palaeoecology. 307, 75–89.

Levin, S.A., 1992. The Problem of Pattern and Scale in Ecology: The Robert H.

MacArthur Award Lecture. Ecology. 73, 1943–1967.

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Magurran, A.E., Henderson, P.A., 2003. Explaining the excess of rare species in natural

species abundance distributions. Nature. 422, 714–716.

McGill, B.J., 2010. Matters of Scale. Science. 328, 575–576.

McGill, B.J., Dornelas, M., Gotelli, N.J., Magurran, A.E., 2015. Fifteen forms of

biodiversity trend in the Anthropocene. Trends in Ecology & Evolution. 30, 104–

113.

Potts, R., 1998. Environmental hypotheses of hominin evolution. American journal of

physical anthropology. 107, 93–136.

Reed, K.E., 1997. Early hominid evolution and ecological change through the African

Plio-Pleistocene. Journal of Human Evolution. 32, 289–322.

Reynolds, S.C., Wilkinson, D.M., Marston, C.G., O’Regan, H.J., 2015. The “mosaic

habitat” concept in human evolution: past and present. Transactions of the Royal

Society of South Africa. 70, 57–69.

Sept, J.M., 1994. Beyond bones: archaeological sites, early hominid subsistence, and the

costs and benefits of exploiting wild plant foods in east African riverine

landscapes. Journal of Human Evolution. 27, 295–320.

Supp, S.R., Koons, D.N., Ernest, S.K.M., 2015. Using life history trade-offs to

understand core-transient structuring of a small mammal community. Ecosphere.

6, art187.

Werdelin, L., Lewis, M.E., 2013. Temporal Change in Functional Richness and Evenness

in the Eastern African Plio-Pleistocene Carnivoran Guild. PLoS ONE. 8, e57944.

Wiens, J.A., 1989. Spatial Scaling in Ecology. Functional Ecology. 3, 385–397.

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Winterhalder, B., 1980. Hominid paleoecology: The competitive exclusion principle and

determinants of niche relationships. American Journal of Physical Anthropology.

23, 43–63.

Wood, B., Strait, D., 2004. Patterns of resource use in early Homo and Paranthropus.

Journal of Human Evolution. 46, 119–162.

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Chapter 2: Applying the core-transient paradigm to large mammal paleo-communities in the Omo-Turkana Basin

Abstract

Recent research has shown that many modern ecological patterns can be successfully explained by the fact that communities are made up of two types of species:

1) core species that are temporally persistent, numerically abundant, dominant competitors, ecologically specialized, and well-adapted to local environmental conditions, and 2) transient species that show the opposite ecological patterns. I tested whether the same predictions made by modern core-transient theory can be applied to the

Pliocene-Pleistocene large mammal communities of the Koobi Fora, Nachukui, and

Shungura Formations in the Omo-Turkana Basin in eastern Africa. Once taphonomic biases are properly accounted for, this is in effect asking whether short-term core- transient dynamics can be extrapolated to fossil time scales. This has important implications for understanding the drivers of species persistence and extinction over evolutionary time scales.

Core species were defined for each formation as occupying more than 50% of the number of geological members that the most temporally persistent species. All other species were classified as transient. I used null probability models to compare the observed number of core species in each paleo-community to the expected number, and to see whether core species were significantly concentrated in particular taxonomic families. I then used logistic regression to see which ecological factors (abundance, body mass, diet) were associated with species being assigned to core membership. Results show the Koobi Fora and Shungura paleo-communities had an excess number of core

9 species compared to the null expectation, whereas the number of core species in the

Nachukui paleo-community was consistent with the null model. All three paleo- communities showed significant concentrations of core species in larger-bodied taxonomic families, though many other large-bodied families did not exhibit such concentrations. Finally, the logistic regression results showed that core species possessed on average higher abundances, which agrees with the predictions of core-transient theory.

Diet and body size showed mixed results regarding core-transient theory’s predictions.

The diversity of transient species has been shown to be driven more by regional, landscape-scale heterogeneity as opposed to local environmental attributes (Coyle et al.,

2013). If one assumes core-transient processes were active in these paleo-communities, paleoanthropologists may need to adopt a larger-scale perspective regarding the ecological drivers of hominin evolution. In conclusion, the partial agreement between the patterns found in these paleo-communities and those predicted by core-transient theory highlights the difficulty in bridging spatial and temporal scales across neo- and paleoecological systems. However, the similarities may offer a way to utilize modern studies of species persistence and macroevolutionary studies of species temporal duration and extinction risk in providing new perspectives on human evolution.

1. Introduction

Species persistence within a community is of interest to both neo- and paleoecologists because of its importance in understanding community temporal turnover, biodiversity maintenance and conservation, and evolutionary patterns and diversification on longer time scales (Gilinsky and Good, 1991; McKinney, 1997;

10

Magurran and Henderson, 2003). Persistence here is defined as the number of instances a species is observed over time throughout the duration of one’s study. Recent literature has shown that not all species in a modern community are equal when it comes to persistence. More specifically, species can be divided into two categories: 1) core species that are temporally persistent, numerically abundant, dominant competitors (i.e., they use a disproportionately large share of resources within a given community), ecologically specialized, and well-adapted to local environmental conditions, and 2) transient species

(also called occasional species) that show the opposite ecological patterns (Magurran and

Henderson, 2003; Supp et al. 2015). The core-transient species paradigm has been successful in explaining the shape of species abundance distributions (Magurran and

Henderson, 2003; Ulrich and Ollik, 2004; Dolan et al., 2009), local versus regional drivers of richness (Belmaker, 2009; Coyle et al., 2013), species’ population dynamics through time (Henderson and Magurran, 2014), and community life-history trade-offs in a modern small mammal community (Supp et al., 2015). It is reasonable then to see whether this theory may be used as a heuristic framework to interpret patterns we see in fossil communities.

It is well known that (paleo)ecological pattern and process change across spatial, temporal, and taxonomic scales (Wiens, 1989; Levin, 1992; Rosenzweig, 1995; Jablonski and Sepkoski, 1996; Maurer, 1999; Valentine, 2001; Pandolfi, 2002; Williams and

Jackson, 2007; McGill, 2010; Jackson and Blois, 2015). The large temporal (and usually spatial and taxonomic) scale discrepancy between modern and fossil studies presents an obstacle for the exchange of theory and method between the two fields. As a result, it is unclear what kind of predictions core-transient theory would make at large, geological

11 time scales given how scale-coarsening alters community patterns. Here, I take an exploratory approach and test whether the predictions core-transient theory makes on neo-ecological time scales are borne out on geological time-scales, given the patterns we see in paleo-communities. This type of inductive approach is not unusual and has been done before in paleoecological research on large macroevolutionary time scales. For example, Harnik and colleagues (2012) examined how different forms of rarity (cf.,

Rabinowitz, 1981) related to extinction risk, and multiple researchers have asked whether ecological interactions between clades are important on macroevolutionary time scales

(Rosenzweig and McCord, 1991; Sepkoski, 1996; Liow et al., 2015). If core-transient theory can be successfully applied to the fossil record, we can take advantage of many predictions based on this theory and more fully understand the ecological correlates of persistence and extinction. Moreover, understanding how fossil communities align with these predictions (or not) will give us a better understanding of how community patterns and dynamics change across vastly different temporal scales.

1.1. Area, time period, and taxonomic group of interest

For this study, the area of interest is the Omo-Turkana Basin, located on the

Kenyan-Ethiopian border, and the time period is the Pliocene-Pleistocene (specifically, 4 to 1 million years ago) (Figure 1). The taxonomic group studied here are large, terrestrial mammals (i.e., small-bodied orders, such as Rodentia and Lagomorpha were removed)

(Figure 2), since taphonomic bias is known to be inversely proportional to body size in terrestrial mammals (Behrensmeyer et al., 1979; Behrensmeyer and Dechant Boaz, 1980;

Miller et al., 2014). Taphonomic bias is particularly strong for small mammals versus

12 large because of the differences in collecting methods as well (e.g., surface survey vs. screen-washing).

The fossil assemblages of the Omo-Turkana Basin provide an ideal sample on which to test the predictions of core-transient theory. The Omo-Turkana fossil mammals have been extensively and meticulously collected and studied for decades (Harris et al.,

2006; Bobe, 2011; Leakey et al., 2011; Wood and Leakey, 2011). The mammalian record is temporally well-resolved given the detailed stratigraphic and chronological research there (Brown and McDougall, 2011; Feibel, 2011). The taxonomy of mammals is well worked out at the species level (Harris, 1983a, 1991a; Harris et al., 1988; Wood, 1991;

Jablonski and Leakey, 2008; Werdelin and Sanders, 2010; Werdelin and Lewis, 2013a), thereby making taxonomic scale comparable between this and neo-ecological studies.

Because data were originally collected at the specimen level, this enables the extraction of abundance data with their respective spatial and temporal contexts (Bobe, 2011).

Furthermore, the basin has three generally contemporaneous geological formations (i.e., the Koobi Fora, Nachukui, and Shungura Formations) during the target time period, which serve as three spatial replicates for exploring core-transient dynamics. Because of the recent geological age of these formations, the ancestors of many of the well-known, modern African savanna mammals are found in these deposits. This means the ecological traits (e.g., diet) of these fossil species can be easily inferred (e.g., Spencer, 1997;

Fortelius and Solounias, 2000; Cerling et al., 2015). Furthermore, recent research has shown functional traits of Kenyan living communities are captured with high fidelity in their respective skeletal assemblages (Miller et al., 2014). Finally, the spatial and temporal scales of these formations (spatial and temporal grain cf., Wiens, 1989 is 102-

13

103 km2 104-105 years, respectively) are more similar to those of modern core-transient studies than most other paleoecological studies, which are conducted at regional to continental spatial scales and on time scales of 106-107 years (e.g., Patzkowsky and

Holland 2003).

1.2. Defining a paleo-community

As in neo-ecology, the spatial (and temporal) delimitation of a community in the fossil record is ultimately arbitrary (Ricklefs, 2008) and dependent on the research question and data in hand. For this study, I operationally defined each geological formation (i.e., Koobi Fora, Nachukui, and Shungura) as a “paleo-community” in the broadest sense. In other words, I simply treat each paleo-community as an analytical unit and make no assumptions about whether the species actually overlapped in space and time (in fact, it is certain that the species in the oldest geological members did not overlap with the species in the youngest members). Species persistence is then measured as the number of total geological members occupied by a given species in each paleo- community/formation (Figure 1).

1.3. Research questions

To revisit the general research question, I am interested in whether predictions from core-transient theory are observed in the large mammal paleo-communities of the

Omo-Turkana Basin. I divide this overarching question into four sub-questions:

1) Is the observed number of core species in each geological formation consistent with what one would expect from random sampling processes?

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 Given a set of species in a geological formation, one would expect a

certain number to occupy many members (i.e., be a core species) simply

due to chance. In other words, if there is some probability of an event

happening, it will happen given enough opportunities to do so. Therefore,

can the observed number of core species in each formation (based on the

presence of a species in each member) be attributed parsimoniously to

random processes or was there something about these species that caused

them to occupy more or less members than expected by chance?

2) Are core species non-randomly concentrated in certain taxonomic families?

 Whether or not the number of observed core species falls within or differs

from expectations given a random sampling model (question 1), it would

be useful to see if core species are significantly concentrated in particular

taxonomic families. That is, does belonging to a particular family play a

role in whether a species is core vs. transient? This question addresses

whether there is a phylogenetic signal in the core-transient analysis, and

because many ecological attributes are non-randomly distributed across

families, this set of analyses also addresses whether there is an ecological

signal associated with being a core species (although no specific

ecological trait is explicitly studied here; see next question).

3) What ecological traits (diet, abundance, body mass) are associated with core species?

 This addresses the previous question on a finer level using actual species-

level ecological variables to see if they are associated with species being

core or transient. A functional trait is defined as a measurable trait that

15 influences performance and fitness in a given environment (McGill et al.,

2006). I looked at three functional traits: mean relative abundance, log10- transformed body mass, and diet. Neo-ecologists may not view abundance as a functional trait, but paleobiologists have long studied abundance as a species ecological attribute that is correlated with extinction risk (Simpson and Harnik, 2009). Because of this and the fact that modern core-transient theory makes explicit predictions about the relationship between core species and abundance (Magurran and Henderson, 2003), I include abundance here as a “functional trait,” even though it may not be one per se. Relative abundance of taxa in fossil assemblages is also known to be affected by taphonomic processes (Badgley, 1986), thus requiring additional analyses to test for taphonomic biases.

Core-transient theory can make predictions pertaining to each one of these traits: (1) core species, on average, will have higher abundances. (2)

Though defining ecological specialization is a less than straightforward exercise (Devictor et al., 2010), most researchers would agree that a specialized diet can be defined as one that is nested within another more generalized diet. With this in mind, transient species should be associated with an omnivorous diet, whereas core species are more likely to be carnivores. Within herbivores, transient species should be associated with a mixed grazer/browser diet within herbivores, while core species should be specialized grazers or browsers. (3) Core species should be associated

16

with larger body mass on average. Competitive dominance and ecological

specialization as it pertains to body mass is more ambiguous, but many

researchers have associated larger body size with these two characteristics

(Brown and Maurer, 1986; McKinney, 1997; Van Valkenburgh et al.,

2004).

4) How can the core-transient conceptual framework inform hominin paleoecology and evolution?

 Hominin paleoecology has traditionally consisted of paleoenvironmental

reconstructions (e.g., Bobe and Behrensmeyer, 2004; Levin et al., 2011;

Barr, 2015) followed by post hoc explanations for hominin adaptations to

those environments. This study takes a different approach and, once

hominins are established as either core or transient species, core-transient

theory can be used to predict a number of hominin ecological attributes,

which can then be tested with fossil data.

2. Materials and Methods

2.1. Omo-Turkana mammalian fossil data

In order to analyze the Pliocene-Pleistocene mammalian fauna of the Omo-

Turkana Basin, I accessed data from the Turkana Basin Institute Database (TBI DB) and the American Shungura Database (SDB). The TBI DB was kindly provided and is maintained by Mikael Fortelius and Meave Leakey. It includes all specimens from the

Turkana Database, supplemented with recently published specimens from the order

Carnivora (Werdelin and Lewis, 2013a) as well as unpublished collected material from

17 the field. I also entered recently published specimens from the order Tubulidentata

(Lehmann, 2008). Because number of geological members occupied was used as the criterion to distinguish core and transient species, I only analyzed data that could be unambiguously assigned to a member from the Koobi Fora and Nachukui Formations

(excluding specimens from Lothagam) for the TBI DB and the Shungura Formation for the SDB.

Because I was interested in species-level questions, only specimens that could be identified to species were kept for analysis. If a specimen could only be identified to the genus level (e.g., Potamochoerus sp.), it was retained only if there were no other specimens from the same genus that could be identified to species. This was done on a formation-by-formation basis (e.g., the existence of Potamochoerus porcus in the Koobi

Fora Fm. did not result in the discarding of Potamoporcus sp. from the Nachukui Fm.).

Specimens with genus and species modifiers such as “cf.” and “aff.” were retained in order to maximize sample size within each species. The only exception is aff.

Hippopotamus, which formerly belonged to the genus Hexaprotodon (Boisserie, 2005).

Subspecies (e.g., Elephas recki recki, Elephas recki atavus, etc.) were lumped (e.g.,

Elephas recki) and analyzed at the species level. As mentioned before, micromammals

(i.e., those specimens belonging to the Orders Rodentia and Lagomorpha) were removed due to differential taphonomic and collecting biases affecting micro- versus large mammals (Figure 2) (Behrensmeyer et al., 1979; Behrensmeyer and Dechant Boaz, 1980;

Miller et al., 2014).

Both surface collected materials and those derived from excavations were used, again to maximize sample size. This distinction is made explicitly only in the SDB,

18 where excavated material makes up 30% of the entire database. I analyzed number of individuals instead of raw number of specimens in order to prevent species with recovered partial skeletons from inflating abundance counts in analyses. This problem would be particularly noticeable in rare species or in members with few fossils.

Individuals are denoted in the TBI DB by shared specimen numbers with letter modifiers representing different skeletal elements within the same individual. The SDB explicitly notes which specimens are presumed to belong to the same individual (in the “Individual

Number” column), and this was used to extract data on individuals. See Table 1 for the final analytical dataset.

2.2. Core and transient species designations

I assigned species to core or transient categories based on the number of geological members occupied for each formation. Each member needed at least 10 species to be considered in my analyses. This only resulted in the exclusion of Member A from the Shungura Fm. Because the boundary between core and occasional species is ultimately arbitrary, previous work assigned species to each category in different ways.

Examples include a priori classification schemes (e.g., (Belmaker, 2009; Coyle et al.,

2013) or post hoc categorization, which is done by looking at the observed distribution of occupied time periods (e.g., Magurran and Henderson, 2003). I chose the former method and used an a priori cut-off of 50% occupation of the maximum number of members occupied by any one species. The 50% cut-off is for each species’ total number of occupied members regardless of whether the members are consecutive or not. The 50% number is scaled to the maximum number of members occupied by any one species instead of the total number of members in a formation. This accounts for members that

19 may not be particularly well-sampled by effectively scaling the core-transient threshold to only those members that produce an adequate number of fossils. Either way, scaling the 50% number to either total number of members in a formation or maximum number of members occupied by a species yields the same cut-off. For example, for the Koobi

Fora and Nachukui Fms., there are a total of eight and seven members, respectively, but the largest number of members ever occupied by a species in either formation is six.

Therefore, for both formations, core species are those that occupy four or more members

(not necessarily consecutively), and transient species occupy three or less. For the

Shungura Fm., there are 10 members analyzed but species occupy at most nine members, so the cut-off is five or more (not necessarily consecutive) members for core species and four or less for transients.

2.3. Functional traits

2.3.1. Mean relative abundance

Mean relative abundance was calculated on a per-member basis for each formation: each species’ abundance in a given member was divided by that member’s

푛푖 th total number of individuals (i.e., 푆 , where 푛푖 is the abundance of the i species in a ∑ 표푏푠 푖=1 푛푖 given member, and 푆표푏푠 is the number of species in that same member). A species’ relative abundance was then calculated as the mean of all non-zero relative abundances across all members within a formation. Mean and maximum relative abundance values were highly correlated for each formation (Koobi Fora Fm.: r = 0.976; Nachukui Fm.: r =

0.928; Shungura Fm.: r = 0.909), so either metric will work but I use mean here.

2.3.2. Species diet

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I used the following diet categories: carnivore (includes consumption of invertebrates and fish), omnivore, browser, mixed browser/grazer, and grazer. These dietary categories are relatively coarse, but they represent what is possible and credible given the available published data. Diets for most fossil ungulates were inferred from enamel stable isotope values published by Cerling and colleagues (2015). Where possible, specimens from Cerling et al.’s dataset were matched with those from the TBI

DB by specimen number, so isotope values could be assigned at the species level.

Otherwise, the enamel isotope value for a given species was estimated using its higher taxon’s values from the same geological formation. For example, the diet of Aepyceros melampus from the Koobi Fora Fm. was estimated using Koobi Fora Fm. Aeypcerotini values. This could result in some averaging of isotope values across different species and also introduces some non-independence of dietary information among closely related species (e.g., the diet of both Aepyceros melampus and Aepyceros shungurae are inferred using the same Aepycerotini values). This non-independence results in some pseudo- replication in the data, and analyses of diet with p-values that are borderline significant should be interpreted with caution (Hurlbert, 1984). An ungulate was labeled as a browser, mixed C3/C4 feeder, or a grazer if its median isotope was less than -8‰, between -8‰ and -1‰, and greater than -1‰, respectively. The same stable isotope criterion was used for Paranthropus (Cerling et al., 2011; Cerling et al., 2013b) and

Theropithecus (Cerling et al., 2013a) species. All other species’ inferred diets were gathered from the literature. If there was no published information on a fossil species’ diet, either the diets of modern conspecifics or congeners were used or the published inferred diet of a fossil congeneric species was used, though the latter case is rare. See the

21 final functional trait dataset (Supplementary Data Table) for more information on the basis for each species’ diet.

2.3.3. Species body mass estimates

Body masses were estimated for each species in the Koobi Fora, Nachukui, and

Shungura samples. Potential phyletic changes in body mass through time were ignored, and body mass is estimated for each species as an average across all geological members in each formation. This approach results in a single estimate for each species, which allows me to test whether a species’ core/transient membership is related to body mass.

Ordinary least squares regressions were used to predict each fossil specimen’s mass based on a given skeletal element measurement. Measurements for all ungulates were taken from the Evolution of Terrestrial Ecosystems Database

(http://naturalhistory.si.edu/ete/ETE_Database.html), which is a compilation of previously published measurements (Bovidae: Harris, 1991b; Camelidae: Harris, 1991c;

Giraffidae: Harris, 1991d; Hippopotamidae: Harris, 1991e; Suidae: Harris, 1983b;

Equidae: Eisenmann, 1983; Rhinocerotidae: Harris, 1983c; Deinotheriidae: Harris,

1983d; Elephantidae: Beden, 1983). All suid third molar measurements were discarded given their specialized morphology. Measurements for carnivorans and primates were obtained respectively from Werdelin and Lewis (2013) and Jablonski and Leakey (2008).

Published measurements from which body mass can be estimated were mostly based on teeth, but some were from the skull and postcrania (see Supplementary Data Table). All published measurements were in millimeters but were converted to centimeters when a regression’s reference measurements were recorded as such (i.e., Janis, 1990; Scott,

1990).

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All regressions were based on allometric relationships and therefore used a power law equation (log-log equation) to estimate body mass. Because a bias is introduced when taking the antilog of a predicted, log-transformed variable (Newman, 1993), I used the raw log10 body mass estimate from the log-log regression equations. For ungulate cranial or dental measurements, I used the regression equations from Janis (1990) because her reference sample dental measurements were taken at the occlusal surface, which is how the fossil measurements were also recorded. Regressions from Scott (1990) were used to estimate ungulate body masses from postcranial measurements on the humerus, radius, and tibia. For Damalborea sp. in the Shungura sample, body mass was estimated using the upper molar row length of the holotype Damalborea elisabethae (Gentry, 2010) and

Damuth’s (1990) equation for selenodont nonbrowsers. Because Damuth’s equations estimate body mass in log10 grams, this estimate was antilogged, transformed into kilograms, and log10-transformed again. The estimate is biased due to the antilog transformation, but this is unavoidable and the bias is likely very small.

For carnivorans, Van Valkenburgh’s (1990) equations were used for lower first molar length measurements, and Anyonge’s (1993) equations were used for femoral and humeral length and midshaft circumference measurements. Midshaft circumferences were calculated using a derived midshaft diameter measure: because Werdelin & Lewis

(2013) provide both the mediolateral and anteroposterior widths of long bone midshafts, midshaft diameter was calculated as the mean of these two published measures. This mean diameter was then multiplied by 휋 to get midshaft circumference. Anyonge also provides a regression equation for estimating body mass using the femur’s distal articular area (calculated as the anteroposterior length of the distal articular surface times the

23 mediolateral width of each condyle). However, Werdelin & Lewis (2013) only provide measurements for femur bicondylar width and femur distal anteroposterior length. That is, their width is calculated as the maximum dimension across both condyles instead of adding the width of each condyle separately as in Anyonge (Anyonge, 1993). As a result, the calculation of distal femur area using Werdelin & Lewis’s measurements is overestimated relative to Anyonge’s, but the body estimate should still be approximately of the same order of magnitude. I used this equation for species where only the distal femur is preserved (i.e., Agriotherium sp.).

Regressions from Delson et al. (2000) were used to estimate primate body masses on dental and a few postcranial measurements. Because Delson et al.’s (2000) reference sample measured body mass in grams, their regression equations estimate body mass in log-transformed grams (they used natural logarithms). However, they provide a mean squared error estimate for each regression equation, so an unbiased estimate of antilogged body mass can be obtained. This is done using the equation:

푏1 휀 푦푖 = 푏0푎푥푖 푒

th where 푦푖 is the body mass of the 푖 individual in grams, 푏0푎 is the antilog (i.e.,

th exponentiated) of the intercept, 푥푖 is the relevant measurement of the 푖 individual, 푏1 is the slope estimate, 푒 is the natural logarithm base (i.e., 2.71), and 휀 is the error term. 푒휀 can be calculated as:

푀푆퐸 푒휀 = 푒 2

24 where MSE is the mean squared error. Estimated primate body masses were then converted from grams to kilograms and log10 transformed, in keeping with the log10 kg estimates of all other species in my analyses.

A single fossilized individual can potentially have multiple estimated body masses. For example, an individual may have associated cranial and postcranial elements, all of which can be used to estimate body mass. Likewise, a single element, such as the molar, can provide numerous body mass estimates, depending on whether the length, width, or area is used. Lastly, several appropriate regression equations may exist for a given measurement, e.g., body mass can be estimated from a bovid’s first lower molar length using a regression model calibrated on a reference sample of all ungulates, ruminants only, or bovids only (Janis, 1990). Rather than averaging all possible body masses for each fossil individual, I decided to use the regression equation that yielded the lowest mean prediction error (calculated and provided by the authors) since the goal here is, in fact, to predict body mass. Mean prediction error gives the mean percent difference between actual and predicted body masses and is calculated as a percent. The formula

(Smith, 1984; Van Valkenburgh, 1990) is:

푛 1 |푦 − 푦̂| ∑ 푖 푖 ×100 푛 푦̂푖 푖=1

th where 푦푖 is the observed body mass of the 푖 individual in the reference sample, 푦̂푖 is the body mass of the 푖th individual predicted from the linear regression, and 푛 is the number of total individuals in the reference sample. Because Delson et al. (2000) provide body mass equations for each primate subfamily as well as each sex, I used the most specific regression possible for each fossil primate individual. Where sex could not be determined

25 for a fossil individual, I used the combined male and female regression equations. The lowest mean prediction error criterion was then applied to all candidate primate regressions after this initial filter. The only exception to this criterion is with the Order

Proboscidea (i.e., all deinotheres and elephants) because all published ungulate regressions were calibrated on species far smaller than proboscideans. Estimating body mass for this Order requires extrapolation to at least an order of magnitude larger than the reference sample. Indeed, estimated body masses for proboscideans appear far too large.

For example, body mass for the modern African elephant (Loxodonta africana) is 3940 kg (Smith et al., 2003), but the estimated body masses for all fossil proboscidean species are consistently an order of magnitude larger. Thus, instead of using the regression equation with the lowest mean prediction error, I use the regression equation that provides the smallest body mass estimate for each proboscidean species, regardless of mean prediction error.

Once body mass was estimated for each fossil individual, individual body masses for a given species were averaged to get mean body mass for each species. Because the individual body mass estimates were log10 transformed, taking the arithmetic mean of these values is equal to log-transforming the geometric mean of the unlogged body masses. For fossil species where body mass could not be estimated because the appropriate elements were not preserved, measurements were either taken from the literature (e.g., Grabowski et al., 2015 for hominins), the NOW New and Old Worlds fossil mammal database (i.e., Gazella janenschi, Plesiogulo sp., and Viverra leakeyi), or the MOM mammal body mass database for species with modern conspecifics or congenerics (Smith et al., 2003). As a last resort, body masses for some species were

26 estimated as averages across the already estimated body masses of congenerics. This introduces some non-independence among data points, but the main goal here is to approximate the order of magnitude of each species, so this method is justified. As in the diet dataset, this results in some pseudo-replication in the data, so analyses of body mass with p-values that are borderline significant should again be interpreted with caution

(Hurlbert, 1984). The final functional trait dataset (Supplementary Data Table) can be consulted to see how body mass was estimated for each species.

2.4. Data analysis

2.4.1. Does the observed number of core species differ from what one would expect given a random binomial model?

To address this question, I used a binomial probability model to generate an expectation for the number of core species in each formation. This was done by first calculating a per-member occupation probability averaged across all species. If 푀푖 is the

th number of members occupied by the i species, 푀퐹푚is the number of members in the formation of interest, 푆표푏푠 is the number of observed species in the formation, and

푆푢푛푠푒푒푛̂ is the estimated number of species believed to have existed during the deposition of the formation but not recovered (i.e., taphonomically destroyed or not collected), then the mean per-member occupation probability (푝̅̅푀푏푟̅̅̅̅) is calculated as:

푆표푏푠 ∑푖=1 푀푖 푝̅̅푀푏푟̅̅̅̅ = 푀퐹푚(푆표푏푠 + 푆푢푛푠푒푒푛̂ )

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The denominator represents the total number of members that could potentially have been occupied over all species. The number of unseen species is estimated using the Chao1 estimator (Chao et al., 2009):

2 (푛 − 1) 푓1 푆푢푛푠푒푒푛̂ = , if 푓2 > 0 푛 2푓2

(푛 − 1) 푓1(푓1 − 1) 푆푢푛푠푒푒푛̂ = , if 푓2 = 0 푛 2(푓2 + 1)

where 푛 is the total number of individuals, 푓1 is the number of singleton species (i.e., species with one individual), and 푓2 is the number of doubletons (i.e., species with two individuals).

Once I calculated the mean species per-member occupation probability, I used the binomial cumulative distribution function to calculate the probability that a species belongs to the core category:

푘 푀퐹푚 1 − 푃(푋 ≤ 푘) = 1 − ∑ ( ) 푝̅̅̅̅̅̅ 푖 (1 − 푝̅̅̅̅̅̅)푀퐹푚−푖 푖 푀푏푟 푀푏푟 푖=0

where again 푀퐹푚is the number of members in the formation of interest, 푝̅̅푀푏푟̅̅̅̅̅ is the mean species per-member occupation probability, and 푘 is the number of occupied members cut-off for core species membership. This equation first calculates the cumulative probability of a species occupying 푘 or less members. Using the Koobi Fora Fm. as an example, species occupying three or less members is designated as transient, so 푘 here is three. Thus, 푃(푋 ≤ 푘) actually gives the total cumulative probability that a species is transient (i.e., occupies one, two, or three members in the Koobi Fora example). 1 −

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푃(푋 ≤ 푘) then gives the probability a species is core (i.e., occupies four, five, six, seven, or eight members). This can be easily calculated in R using the pbinom() function: 1 –

pbinom(k, size = 푀퐹푚, prob = p̅̅Mbr̅̅̅̅ ), using the notation above. The pbinom() function along with all other R probability density functions (which I refer to below) are from the

“stats” package (R Core Team, 2015).

The expected number of core species in each formation is simply the product of the total number of species (both seen and unseen) and the probability of being a core species (i.e., 퐸(푆푐표푟푒) = (푆표푏푠 + 푆푢푛푠푒푒푛̂ )푝푐표푟푒 ). Calculating 95% confidence intervals is trickier given the central limit theorem does not necessarily produce a symmetrical normal distribution for binomial variables, especially if the probability of “success” is near zero or one. Therefore, I used the inverse cumulative distribution function (AKA the quantile function) to estimate the 95% confidence interval for a two-tailed test (i.e., observed number of core species could be significantly less or greater than expected).

This was done using the qbinom() function in R: qbinom(p = c(0.025, 0.975), size =

푆표푏푠 + 푆푢푛푠푒푒푛̂ , prob = 푝푐표푟푒 ). This was repeated for each of the three formations (i.e.,

Koobi Fora, Nachukui, and Shungura Fms.). The pbinom() R function was used to assess statistical significance: pbinom(q = # observed core species, size = 푆표푏푠 + 푆푢푛푠푒푒푛̂ , prob

= 푝푐표푟푒 ). Probability values less than 0.025 or greater than 0.975 were considered significant (two-tailed test; p < 0.05).

This method assumes each species has the same mean species per-member occupation probability, and any deviation from this mean on a species-by-species basis is due to random variation one would expect given a binomial sampling process. This assumption may be wrong given the differences in live abundance and taphonomic filters

29 across species, but it serves as a useful simplifying assumption. Thus, I am making the implicit statement here that a species’ per-member occupation probability is so complex and determined by a myriad of factors that I am willing to treat per-member occupation probability as an emergent, random process (Gotelli and Ellison, 2013). If the observed number of core species falls within expectations of a random binomial process, then the results are consistent with, but do not necessarily prove, that stochastic processes determined the number of observed core species. Conversely, sample size may not be large enough, so there is not enough statistical power to falsify the null binomial model.

If the observed number of core species is greater or less than expected given a binomial process, one can then ask whether there is something ecologically special about these species that causes them to be in more or fewer members than expected by chance.

2.4.2. Are the identities of core species randomly distributed across families?

To quantitatively address this question, I used a hypergeometric model (Ross,

2014) to see if core species are non-randomly distributed across families. This is effectively asking how the observed distribution compares to a random distribution generated by reshuffling (i.e., without replacement) core species across families. To do this, I compared the observed number of core species in each family to the expected value derived using the hypergeometric model. As in the binomial model analyses, 95% confidence intervals can be calculated using the quantile function. This was done in R using the qhyper() function: qhyper(p = 0.025, m = total # core species, n = total # transient species, k = vector of # species in each family). This is the lower tail of the 95% hypergeometric confidence interval. The code was run again setting p = 0.975 to get the upper tail. These confidence intervals provide the expected range of number of core

30 species for each family if core species were randomly distributed across families.

Confidence intervals were calculated for each family and compared with its respective observed number of core species (two-tailed test). The phyper() function in R was used to assess which families had significantly more or less core species than expected: phyper(q

= vector of # core species in each family, m = total # core species, n = total # transient species, k = vector of # species in each family). Probability values less than 0.025 or greater than 0.975 were considered significant (two-tailed test). Those values less than

0.05 or greater than 0.95 (the equivalent of a two-tailed test where p < 0.1) were considered marginally significant but still of interest.

2.4.3. What functional traits are associated with core species membership?

I used multiple logistic regression to address this question, where the dependent variable was whether a species was core or transient (coded as 1 and 0, respectively), and each of the functional traits was an independent variable. Mean relative abundance was first log10 transformed to minimize the influence of outliers as well as to normalize the data distribution. Normalization was important because this variable, along with log10 body mass which was already normally distributed, were transformed into standard deviation units (which are more interpretable when the variable is normally distributed) prior to analysis. Both continuous variables are in different units, so standardizing the variables to mean = 0 and variance = 1 enables these two variables to be compared on the same scale. Diet, being a categorical trait, was coded as a factor with grazer fixed as the baseline reference level. Because diet is a categorical variable that could not be standardized, its results must be interpreted separately from that of the continuous independent variables.

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The estimation of multiple logistic regression coefficients can be confounded if there is strong collinearity among the independent variables. To check this, I ran linear models with each pairwise combination of the three functional traits as dependent and independent variables and extracted R2 estimates for each formation. The largest R2 estimate is 0.306, estimated from regressing Nachukui mean relative abundance on diet.

Only very high levels of collinearity (R2 = 0.8 or more) pose serious problems (Menard,

2002), so collinearity is not an issue here and the coefficient estimates are sound.

Regarding body mass, ecological specialization and competition for resources might make more sense within restricted body mass classes. For example, one might not expect a large-bodied elephant to compete for resources with a small-bodied jackal. Thus,

I re-ran the multiple logistic regression but within body mass classes (<10kg, >10kg and

<100kg, >100kg and <1000kg, and >1000kg), where competition might be expected to be more marked.

All analyses were done in R version 3.3.1. (R Core Team, 2015).

3. Results

See Table 1 for the final analytical dataset, showing the total number of individuals and species (core and transient) in all three geological formations. Table 2 shows the identity of the core species in each formation. Figure 6-Figure 8 show the observed distribution of species across members within each formation.

3.1. Comparing the observed number of core species with what one would expect given a random binomial model

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The purpose of the binomial null model analysis was to generate an expectation for how many core species should be expected given some total number of species in a formation. Though all three formations have more core species than would be expected given a random binomial process, only Koobi Fora and Shungura are significantly so

(Figure 9). The deviation of the number of core species in these two formations from a binomial process can be most parsimoniously attributed to the fact that the per-member sampling probability is not constant across species. Therefore, it seems there is potentially something ecologically unique about the core species in these two formations that contributed to their persistence. Only the Nachukui Fm.’s observed number of core species falls within the binomial 95% confidence interval (Figure 9), i.e., the spread of observed per-member sampling probabilities among species is consistent with binomial variation derived from a single mean sampling probability. As a result, the number of core species in the Nachukui Fm. is consistent with what would be expected if stochastic processes determined species’ member occupations and core-transient designations, but it does not necessarily prove it.

3.2. Hypergeometric model results investigating whether core species are randomly distributed across families

The hypergeometric analysis asked whether core species were significantly concentrated in certain taxonomic families. Results show that in all three formations, most families’ observed number of core species falls within what is expected of the model (Figure 10-Figure 12). This means most families have the expected number of core species given the number of species in each family and the number of core species throughout the entire formation. However, there are several families where the observed

33 number of core species is significantly greater than what would be expected given the hypergeometric null model. In the Koobi Fora Fm., Deinotheriidae and Giraffidae have more core species than expected (p < 0.05), and the same is true for Hippopotamidae at p

< 0.10 (Figure 10). Likewise, Deinotheriidae, Equidae, and Rhinocerotidae (p < 0.05) and

Elephantidae and Giraffidae (p < 0.10) in the Nachukui Fm. have more core species than expected (Figure 11). The same is true for Deinotheriidae, Equidae, Giraffidae,

Hippopotamidae, and Rhinocerotidae (all p < 0.05) in the Shungura Fm. (Figure 12).

3.3. Logistic regression results examining which functional traits are associated with core species membership

The logistic regression analysis specifically asked whether there were certain functional traits (i.e., diet, abundance, and body mass) that were associated with a species belonging to the core category. Figure 13 and Table 3 show the estimated coefficients with ± one standard error. Comparing the different dietary levels to abundance and body mass is difficult because only the latter variables are standardized, so I will only compare the diet coefficient estimates (i.e., effect sizes) to each other first. Grazer is the baseline diet level (i.e., the intercept) and is interpreted as the log odds1 a species with scale(log10(abundance)) = 0 and scale(log10(body mass)) = 0 is core. Because the two continuous variables are centered and scaled, their means are zero. This means the intercept is interpreted as the log odds that a grazer species with an average abundance and body mass is a core species. The intercept estimate for all three formations is

1 Odds are defined as 푝/(1 − 푝). For example, a 50-50 event has an odds of 1, while an event with 0.8 probability of success has an odds of 4, meaning success is four times as likely on average as failure. Odds range from zero to infinity, so log-transformed odds (i.e., the log odds or logit transformation) go from negative to positive infinity, making it ideal in regression when dealing with bounded (and problematic) binomial probabilities.

34 negative, so a grazer is more likely to be transient than core on average (Figure 13). The log odds estimate can be exponentiated to get the odds a grazer species with mean abundance and body mass is core (Table 3). For example, the odds for the Koobi Fora

Fm. is 0.186 (i.e., exp(-1.682)), meaning that a grazer species with mean abundance and body mass selected at random from this paleocommunity has a 16% probability of being core (using the inverse logit transformation). If the same exercise is carried out for

Nachukui and Shungura, we see that grazers have an estimated 9% (0.099 odds) and 14% chance (0.161 odds) of being a core species, respectively.

The coefficient estimates for the other dietary categories are each interpreted as the change in log odds as one goes from grazer to the other dietary category of interest while holding abundance and body mass constant. For example, if we look at herbivorous mixed feeders (mixed browse and graze diet) in the Koobi Fora Fm., we see the coefficient estimate is -0.469 (Table 3). This means a mixed feeder on average has a log odds 0.469 less than a grazer while accounting for abundance and body mass. When exponentiated, this translates to an odds ratio of 0.625 (Table 3), which is interpreted as a

60% increase in the odds of being a transient species. One can also interpret the change in log odds relative to the grazer intercept estimate in order to get absolute odds (via exponentiating) and probability statements (via inverse logit transformation) as before.

Sticking with the mixed feeder example, the log odds of a mixed feeder being a core species at average abundance and body mass estimates (i.e., when these coefficients are set to zero) is -2.151 (-1.682 [the grazer intercept] plus -0.469). Thus, the odds a mixed feeder at Koobi Fora is core on average is 0.116, and the probability that a mixed feeder with mean body mass and abundance is core is 10.4%, on average.

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Interpreting the diet coefficients as a whole, all categories for the most part show an increase in log odds for being a core species relative to grazer species (Figure 13;

Table 3). The largest increase in seen in omnivores. Nachukui omnivores exhibit the largest increase in log odds (1.93) with Shungura close behind (1.50) (Table 3). This translates to a 589% increase in odds on average in the Nachukui sample relative to grazers, and a 349% increase in Shungura. For those species of mean abundance and body mass, Nachukui omnivores have a 41% probability of being core, while the probability is 42% for Shungura omnivores. The exception is in the Koobi Fora Fm.; no recorded core species are omnivores, and the calculated likelihood of an omnivore being a core species is interpreted as being very low.

Browsers possess the second highest coefficient estimate in all three formations followed by mixed browser/grazers (Figure 13; Table 3). Between the three formations, mixed feeders show a mixed signal: Shungura has a moderate, positive effect size,

Nachukui has one that is positive but weaker, and Koobi Fora has a negative effect size.

Carnivores have a near zero effect size in Koobi Fora and Shungura and a very large negative effect size in Nachukui due to that formation having zero carnivore core species.

It should be noted that the grazer intercept estimate is so strongly negative that for any species with mean abundance and body size, the log odds for any other diet type is still negative on average (obtained from adding intercept with any diet coefficient; Table

3). This may be more intuitively understood if the coefficient estimates are transformed into probability estimates (Table 3). For all three formations, all species of all dietary types with mean abundance and body mass have less than a 50% probability of being core on average. Omnivorous species from the Shungura Fm. have the highest probability

36 at 42% (Table 3). In order for a species to have a probability of being core greater than

50%, their abundance and/or body mass needs to increase. However, it is still interesting to see the relative increase in odds and probability of being a core species when abundance and body mass are held constant.

All diet coefficients (except for the grazer intercept) are quite noisy with large standard errors. This is reflected in the lack of statistical significance in these coefficient estimates (although browser is marginally significant in the Koobi Fora paleocommunity). Nevertheless, it is still useful to interpret the coefficient point estimate and think about the average effect of diet coefficients on the odds of a species being core.

The continuous variable coefficients (i.e., log10 abundance and log10 body mass) are interpreted similarly to the different dietary categories. The coefficients are the change in log odds of being a core species for every one standard deviation increase (due to centering and scaling) in whatever the independent variable of interest is while holding all other independent variables constant. For example, the coefficient estimate for log10 abundance in the Koobi Fora Fm. is 1.150 (Table 3). That means for every unit standard deviation increase in log10 abundance, the log odds of being a core species increases by

1.150 when all other variables are held constant. This translates to an odds ratio of 3.159

(Table 3), meaning there is a 216% increase in odds of being a core species for every standard deviation increase in log10 abundance. Therefore, the effect size here is actually quite large. When looking within body mass classes, however, the coefficients drop markedly, with a third of them even becoming negative (Table 4). All the coefficients are noisy with large standard errors and non-significant p-values. As with the categorical

37 dietary variable, absolute odds and probability estimates can be obtained for a given abundance, body mass, and dietary value.

Looking at the log10 abundance coefficients as a whole, Shungura has the largest effect size by far (there is a 514% increase in the odds of being a core species with a one standard deviation increase in log10 abundance). Koobi Fora and Nachukui have comparable effect sizes that are nearly 50% that of Shungura (216% and 198%, respectively). The difference in log10 body mass effect size among the three formations is smaller, but Shungura still possesses the largest one (166% increase in odds). This is approximately twice as large as that of Koobi Fora, which has the smallest log10 body mass effect size (68% increase in odds). Nachukui is intermediate with a 121% increase in odds. All of these coefficients have relatively large signal to noise ratios as exhibited by their statistical significance. Comparing the effects of log10 abundance and log10 body mass on the odds of being a core species, one can see that the effect size of abundance is always larger than that of body mass in each formation. The smallest difference is seen in Nachukui (the odds ratio associated with abundance is 1.35 times larger than that associated with body mass), while Shungura exhibits the largest difference (2.31 times larger), and Koobi Fora is intermediate (1.88 times larger).

4. Discussion

The excess of observed core species relative to that expected from the binomial null model in the Koobi Fora and Shungura Fms. (Figure 9) reflects the fact that core species on average have a higher per-member sampling probability than predicted from

38 random binomial processes. This suggests there is something non-random and unique about these core species that allows them to occupy an unusually large number of members. The observed number of Nachukui core species is consistent with a binomial process (Figure 9), but it does not necessarily prove that species’ distribution of per- member sampling probabilities was generated by emergent random processes.

All three formations have non-random concentrations of core species within a few families (Figure 10-Figure 12). What these families have in common for each formation is not readily apparent. Each group includes a mix of grazing and browsing families, with one family (i.e., Rhinocerotidae) possessing both grazing and browsing genera (i.e.,

Ceratotherium and Diceros, respectively). One possible unifying theme is body size.

These are all large-bodied families (e.g., Deinotheriidae, Elephantidae, Equidae,

Giraffidae, Rhinocerotidae), though in every formation, there are certain large-bodied families that do not have significant concentration of core species (i.e., Camelidae,

Chalicotheriidae, Hippopotamidae, Stegodontidae, and Ursidae). So while this pattern may be somewhat influenced by a body size-related taphonomic bias, the overall results indicate that there is an ecological signal as well.

One can investigate the effect of body size on a species being core more explicitly from the logistic regression results (Figure 13; Table 3). In all three formations, body size has a positive, not insubstantial relationship with the odds of being a core species. If one views large body size as a form of competitive dominance and ecological specialization

(Brown and Maurer, 1986; McKinney, 1997; Van Valkenburgh et al., 2004), this agrees with predictions from modern core-transient studies. That is, the species that are more ecologically specialized and adapted to the local habitat are the ones that persist and are

39 more abundant (Magurran and Henderson, 2003; Coyle et al., 2013; Supp et al., 2015).

However, when one looks at the effect of body mass within size classes (which might be more appropriate regarding interspecific competition for resources), the pronounced result disappears (Table 4). This suggests that perhaps ecological specialization and interspecific competition via body size is not operating within these paleo-communities.

The stronger effect of body mass on persistence across all size classes may then be a taphonomic effect (to be discussed later) or driven by some other ecological factor that is related to body size (e.g., geographic range size; Harnik, 2011).

Intriguingly, some paleobiologists have found that body size is positively correlated with extinction risk in mammals (Van Valkenburgh et al., 2004; Liow et al.,

2008), while others have found the opposite (Flynn et al., 1995) or no relationship

(Viranta, 2003; Casanovas-Vilar et al., 2010; Raia et al., 2012; Tomiya, 2013; Smits,

2015). I should reiterate that persistence, in my case, is defined as number of occupied geological members, and this may not be correlated with temporal duration (date of last occurrence minus date of first occurrence) or extinction risk. If a species’ ecological strategy is to emigrate rather than to stay put during times of ecological stress (e.g., environmental change, competition, etc.), then that species’ persistence will be low, but the species may very well endure in the larger metacommunity. This phenomenon has been found in some fossil mammal studies (Casanovas-Vilar et al., 2010; Raia et al.,

2012). Persistence and temporal duration are highly correlated in this dataset (Koobi

Fora: r = 0.95; Nachukui: r = 0.85; Shungura: r = 0.87), however, and this study may serve as a theoretical and empirical bridge between the finer-scaled, neoecological and coarser-scaled, macroevolutionary studies. My measures of persistence and duration are

40 measured in three paleocommunities within the same basin over seven to ten time intervals. Ideally, one addresses the problem of persistence and temporal duration by examining persistence in a local community (as in neoecological studies) compared with regional or global taxonomic duration (as in macroevolutionary studies).

There is a strong, non-linear relationship between abundance and number of members occupied in all three formations (Figure 3; Figure 13; Table 3), which matches observations of modern core-transient patterns. The proposed reason for this pattern in modern settings is that those species most well-adapted to the local habitat and most competitively dominant are the ones that will take up most of the resources in the system and produce the highest abundance and biomass. A recent study adds a layer of complexity to this picture: McGill (2012) found that tree species are rarely most abundant where they grow best and instead are outcompeted by other more dominant species in areas where they would have grown best. Thus, the distribution of core and transient individuals and species may have just as much to do with competition and priority effects

(or even more so) than with habitat filtering.

Whatever the reason for the positive abundance-persistence relationship, we see it in all three formations, and it is not entirely generated by sampling and preservational biases (see “Sampling and preservation biases?” below; Figure 14). One can test the habitat filtering hypothesis by matching up the known paleoenvironmental conditions of the three formations with the diet logistic regression coefficients. It is now well known from previous studies that on average, Nachukui had the driest and grassiest environment, whereas Shungura was the wettest and most wooded, and Koobi Fora was somewhere in between (Bobe, 2011; Levin et al., 2011; Fortelius et al., 2016). Therefore, one would

41 expect browsers to have the highest coefficient in Shungura, while grazers should have the highest in Nachukui. It is unclear which diet should be more associated with core membership in the Koobi Fora Fm. This prediction is borne out for the Shungura Fm., but we see the opposite expected signal in Nachukui (Figure 13; Table 3). Browsers have the highest positive effect size in Koobi Fora. Therefore, the results are ambiguous relative to expectations from modern core-transient theory. This may have more to do with the fact that grasslands do not become dominant (at least in the Koobi Fora & Nachukui Fms.) until 2 million years ago (Bobe, 2011; Thure E. Cerling et al., 2011). Therefore, at the scale of the entire geological formation, all three communities might be considered wooded or mixed woodland/grassland communities.

The diet results from the logistic regression analysis seem to show the opposite of what would be predicted by core-transient theory. Core-transient theory predicts that specialists are the species most likely to be core. Contrary to expectations, the logistic regression results show generalists (omnivores, in this case) are generally associated with a higher probability of being a core species, at least in the Nachukui and Shungura Fms.

(Figure 13; Table 3). In Koobi Fora, there are no omnivorous core species, so this relationship is in the opposite direction of that observed in the two other formations.

Therefore, as before with comparing diets to local habitats, the results are ambiguous

(i.e., two formations exhibit one pattern while the third shows the opposite).

Within herbivores, mixed browser/grazer feeders may be considered generalists, while grazers and browsers are each considered specialists. From core-transient theory, one would predict that browsers and grazers are correlated with higher probabilities of being core, whereas the opposite is true of mixed feeders. One can see from Figure 13

42 that this is not the case. Browsers do indeed have a higher likelihood of being core than mixed feeders, but grazers have lower odds of being core in Nachukui and Shungura.

Interestingly, Koobi Fora shows the opposite relationship: mixed feeders have a negative effect size, which is what one would predict from core-transient theory. As with the previous diet discussion, the results are mixed. Two formations (i.e., Nachukui and

Shungura) show the opposite of what one would expect from modern core-transient studies, but Koobi Fora’s diet results align with these predictions. The agreement of

Koobi Fora’s diet results with core-transient theory may be due to chance, some other non-related phenomenon, or theoretical core-transient dynamics (at least regarding diet) are only operating in Koobi Fora. However, as I mentioned in the previous paragraph, these three paleocommunities might be considered wooded or mixed woodland/grassland habitats at the scale of my analysis. Therefore, the larger effect size of “specialized” browsers compared to grazers and mixed feeders may actually suggest the operation of core-transient dynamics in these systems.

The diet categories I use are relatively coarse, which may affect the results if the meaningful adaptations are not grazer or browser, for example, but more specific dietary requirements within these categories. At this time, however, I cannot parse diet into finer categories and still retain meaningful sample sizes given the available data. Future research might use different methods that are able to infer diet at finer categories (Pineda-

Munoz et al., 2016), and this may yield results more congruous with modern studies.

Conversely, some other ecological trait can be measured that better reflects ecological specialization (a concept that itself is fraught [Devictor et al., 2010]), but such a trait is currently undiscovered.

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It is unlikely that a species persisted continuously in the same geological region for millions of years. It seems more reasonable that species migrated in and out of the paleocommunity and persisted in the larger metacommunity. It is unclear how core- transient processes behave on larger time scales and interact with these proposed spatial dynamics. Do species switch core and transient species identities through time and across space? Regarding space, (Supp et al., 2015) describe a category of “source-sink” transients which may be transient at a focal site but core elsewhere. Similarly, Magurran and Henderson (2003) hypothesized that if local conditions are significantly altered, new core species will be drawn from the larger pool of available transient species. Therefore, there may be a switching of core and transient identities among species with spatiotemporal environmental shifts. However, there is a core species pattern in the Omo-

Turkana data, at least with respect to abundance and perhaps diet. There are species that persist through many members, and these species are typically abundant and therefore unlikely to be transient species (by the modern definition). So it may be that these species were transient for a small fraction of the time, but their dominant roles as core species overwhelm these minor transient periods.

4.2. Possible confounding factors

4.2.1. Taxonomic scale?

There may be a taxonomic-scale bias regarding which species are core or not.

Some species are included in our sample but were only identified to the genus level (e.g.,

Potamochoerus sp.) and therefore may actually represent more than one species. The longevity of this “species” may then actually be attributed to one transient species’ temporal range following the other, so the species is not actually core. If this bias actually

44 exists, one would expect core species to have a disproportionate number of species that could only be identified to the genus level. This is not the case. The Koobi Fora Fm. only has one such core species (Homotherium sp.), while there are 23 species that could only be identified to genus in the transient sample (3.6% and 23.5% of their respective samples). For the Nachukui Fm., there are two such core species (11.8%), and eight transient species (11.1%). And lastly, the Shungura Fm. has five core species only identified to genus (16.7%) and 18 such transient species (29.5%). Because the core species percentage is either less than or approximately equal to the transient species percentage, I conclude that this potential taxonomic-scale bias is not an issue.

Another possibility is that the families with more core species than expected from the hypergeometric analyses (Figure 10-Figure 12) are taxonomically conservative and lump species relative to the other families. This issue cannot be resolved at this time, but

I see no a priori reason why these families should have more lumped species than others.

4.2.2. Sampling and preservation biases?

The existence of a positive linear relationship between persistence (i.e., number of occupied members) and log-abundance (i.e., mean relative abundance) may indeed indicate that core-transient dynamics operated in time-averaged paleo-communities.

However, critics may argue that this relationship is indicative of sampling and preservation effects: if a species is better preserved and/or was more intensively sampled, it will have more fossils and is therefore more likely to be sampled in multiple members.

This should only be a problem if all species occupied approximately the same number of members and the “rarer” species were under-sampled and found to be in a smaller number of members.

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A subsampling analysis of the more common species could be used to see if the number of occupied members drops with declining abundance. However, any subsampling analysis would need to choose an arbitrary number of individuals to subsample, which would likely be too small (e.g., the smallest number of individuals in the Koobi Fora Fm. is one). Instead, I estimate the evenness of species’ non-zero abundances across all members within a given formation to see if there is a relationship with abundance. The idea here is that subsampling will only substantially decrease the number of members occupied by a species if that species’ abundances are distributed unevenly across members. For example, if a common species’ abundances are distributed unevenly across members, then there are some members for which that species has very few individuals. Those individuals may be removed during the subsampling procedure and therefore those members are no longer occupied by the species in question.

Conversely, a fairly even distribution of abundances across members should consistently yield the same number of members after subsampling until a prohibitively low abundance threshold is reached. Using this logic, if sampling biases are generating the positive abundance-persistence relationship, one would expect a strong negative relationship between abundance and evenness. Using the Probability of Interspecific Encounter index to estimate evenness (Hurlbert, 1971), we can see from Figure 14 that this is not the case.

There is indeed a negative relationship, as one would predict given the scenario above, but it is a weak one. As a result, I assume the positive log-linear relationship between abundance and number of occupied members to be ecologically “real” and not significantly attributable to taphonomic biases.

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An alternative explanation is that larger-bodied species possess larger fossils that are more durable and less susceptible to being destroyed by taphonomic processes. The fact that core species are found in more members means that they must have existed during the deposition of those members along with the smaller-bodied “transient” species, but the latter’s remains were subsequently destroyed. This is possible given the odds ratio of the body mass coefficients. That is, for every standard deviation increase in log10 body mass, a species’s odds of being core increases by 68% in the Koobi Fora Fm.,

120% in the Nachukui Fm., and 166% in the Shungura Fm. (Table 3). It is unfortunate from the standpoint of testing ecological patterns that the same positive relationship between body size and core membership is predicted by both core-transient theory and taphonomic biases. As demonstrated by the hypergeometric models, many of the core species are indeed non-randomly concentrated in larger-bodied families, but there also are plenty of larger-bodied families that do not have such concentrations. In Figure 15, I used the Amboseli live-dead data (Western and Behrensmeyer, 2009) to show that body size is not a strong pre-burial biasing factor in whether a taxon is present in the surface assemblage. Other taphonomic biases conceivably could increase representation of taxa with larger, more durable, skeletal parts (e.g., via destruction of smaller skeletal remains in fluvial systems), but these issues cannot be addressed at this time.

4.3. Possible influence of paleoenvironmental context

All else held equal, browsing species are more likely to be core than grazers or mixed browsers/grazers (Figure 13; Table 3). This suggests that trees and bushes must have been a stable resource during the entirety of each formation. There is some empirical support for this given what we know about the basin structure and

47 paleogeography of the Omo-Turkana drainage systems. The continued presence of the ancestral Omo River would have provided a stable wooded environment through time in the Shungura Fm. (Bobe, 2011; Feibel, 2011; Levin et al., 2011). For the Nachukui and

Koobi Fora Fms., river systems draining the basin margins would have supported riparian woodlands. Increased water could have led to the spread of woodlands and decreases in grassland in these systems, but even during periods of decreased water availability, trees and shrubs would have persisted along the watercourses (especially along the ancestral

Omo River). As a result, any species well-suited to ecologically take advantage of this temporally stable resource would have been able to persist as a core species.

4.4. What does the core-transient paradigm mean for human evolution?

It is clear from this study that hominins (or many other primates for that matter) were not core species in the areas in question. The one exception might be Paranthropus aethiopicus in the Shungura Fm., which occupies four members (one below the cut-off for core membership). There are specimens in Member G, which are only identifiable to the Paranthropus genus and may actually be P. aethiopicus specimens. However, the basal age for Member G is 2.27 Ma, which is right around the time this species goes extinct (Wood and Boyle, 2016), so it is unlikely those specimens belong to P. aethiopicus. The median fitted probability for being a core species for all hominins in all formations given their abundance, body mass, and diet is 17% (min < 0.001; max = 59%

[Homo erectus in Shungura]). This establishes an empirical baseline for examining one important measure of the ecological role of hominins in other places and time intervals.

Because core and transient species are associated with a number of life history traits, we can begin to characterize and predict what the hominin ecological condition might have

48 looked like if we accept there is a strong core-transient signal in these paleo- communities. According to core-transient theory, hominins would have been generalists that were not competitively or numerically dominant. Hominins as generalists (relative to the rest of the mammal paleocommunity) is an idea that has been developed many times in the literature and has some empirical support (Teaford and Ungar, 2000; Wood and

Strait, 2004; Scott et al., 2005; Elton, 2006). Although ecological specialization and

“competitive dominance” is not well defined by paleoanthropology researchers, there is a rising consensus that hominins played a large ecological role in their communities, at least by the time of the appearance of Homo erectus. This idea mainly stems from H. erectus acquiring an increasing amount of large mammal prey into its diet, thereby outcompeting certain carnivoran species and driving them to extinction (Werdelin and

Lewis, 2013b) and creating a trophic cascade (resulting in the release and proliferation of herbivore species) (Fortelius et al., 2016). However, this would have occurred in the latter 15% of the time period studied here and therefore may not produce a detectable signature.

Regarding abundance, it is well established that hominins were rare in their communities (Bobe and Leakey, 2009). Supp and others (2015) split rare transient species into two more categories: source-sink transient and nomadic transient, each with its own set of life history correlates. Source-sink transients are transients that are rare in the focal community but are numerically dominant elsewhere. This model has been used successfully to mechanistically generate many of the macroecological patterns we see in large-scale assemblages (McGill and Collins, 2003). Nomadic transients are those species

49 that are generally rare everywhere and are optimal colonizers who seek out their optimal niche as habitats shift.

In terms of empirical support from the hominin record, hominins are relatively rare everywhere except possibly for Hadar (Johanson, 2004). If hominins are source-sink transients, then a fixed suite of life history traits cannot be appended to an entire species, and their life history traits will shift relative to the ecological context of the local community. For example, wherever a hominin species’ source community is, the hominin population residing there will be numerically abundant, ecologically specialized, well- adapted to their local habitat (but see McGill, 2012 for an alternative explanation), competitively dominant, and possess high survival rates (Supp et al., 2015). The opposite is true for those contemporaneous hominin populations in sink communities. If hominins are nomadic transients, then they would have been strong colonizers, ecological generalists, rare everywhere, easily outcompeted (perhaps preventing establishment at a given site), and they would have had lower survival and higher fecundity rates. Coyle and others (2013) showed that landscape-scale heterogeneity better explains transient species richness, whereas the local habitat conditions better explained core species richness. This means the reconstructed local habitat should not be used to explain hominin diversity, and possibly also their physical and behavioral adaptations. The only instance where this would be acceptable is in a hominin species’ source community (e.g., possibly Hadar).

Therefore, in reconstructing hominin ecology and resource use, it may be more informative to study large-scale habitat variance and metacommunities rather than smaller-scale averages of paleoenvironmental variables (e.g., the proportions of C3 and

C4 vegetation).

50

As I have shown, there are numerous species that persist in each of the three formations in the Omo-Turkana Basin, but hominins are not one of them. Instead of persisting as individual species, the evolutionary “coping strategy” for hominin lineages and clades may have been to evolve and diversify against a backdrop of climatic and environmental change (Bobe et al., 2002; Potts, 2013). It is interesting that source-sink transients are predicted to have relatively low gene flow among populations, while nomadic transients have intermediate to high gene flow among populations (Supp et al.,

2015). The large (and growing) number of species in the hominin clade (Haile-Selassie et al., 2016; Wood and Boyle, 2016) is consistent with low gene flow, speciation, and hominins being source-sink transients. These alternatives and predictions can also be explored and tested against other species which were identified as transients.

5. Conclusions

Core-transient theory predicts core species in a community will be temporally persistent, numerically abundant, dominant competitors, ecological specialized, and well- adapted to the local environment. I set out to test whether these predictions were borne out in three paleo-communities in the Pliocene-Pleistocene Omo-Turkana Basin. After categorizing species as core or transient based on their persistence patterns, I found:

1. The Koobi Fora and Shungura paleo-communities had an excess of

core species relative to what would be expected from a random binomial sampling

process. This suggests there is something special about these core species which

enabled them to have higher per-member occupation probabilities than transient

51 species. Nachukui’s observed number of species matched that predicted by the binomial model.

2. All three paleo-communities had core species that were non- randomly concentrated in certain taxonomic families. The common ecological theme seemed to be these were larger bodied families, but there were also larger- bodied families without significant concentrations of core species.

3. Core membership was associated with higher abundances and larger body masses when considering all body size classes. The former is predicted by core-transient theory, but the latter is not if one views body size through the lens of ecological specialization and interspecific competition. Diet showed ambiguous results regarding the degree of specialization, but there seems to be some correspondence between diet and known paleoenvironmental reconstructions as predicted by core-transient theory.

4. If one assumes that core-transient processes were operating in these paleo-communities, one can produce a number of ecological expectations given that hominins are transient species. Several predictions already accord with the fact that hominins were rare and seemingly ecological generalists. Other predictions include competitive inferiority (at least for the majority of the time period studied here), regional landscape heterogeneity driving biodiversity, and low gene flow which may explain the plurality of species that co-existed at any given time.

The three paleo-communities in this study showed moderate support regarding the

52 predictions of core-transient theory from neo-ecology. This may be due in part to the large discrepancy in spatial and temporal scales between this study and those of modern communities, which suggests different sets of processes are acting at these large scales.

Future analyses can attempt to subdivide members into sub-members, thereby decreasing temporal scale, but this would still be a far-cry from the time scales observed in modern studies. It may also be that the traits measured on each fossil species were inappropriate for describing the desired ecological process (i.e., regarding ecological specialization, body mass may not have been an appropriate proxy, at least on these time scales).

Nevertheless, there is some agreement between my paleo-community patterns and those predicted by core-transient theory (i.e., abundance and perhaps diet), which suggest there may be some processes that do operate across scale, though this requires further testing. It is likely that the same processes in the broad sense are driving species persistence on both modern and fossil time scales. That is, modern species may move in and out of a site seasonally but persist in the larger metacommunity on an annual scale, and fossil species may move in and out of a site on a 104-5 year time scale but persist in the larger metacommunty on a 106 year time scale. In both cases, dispersal is the key process facilitating persistence. Therefore, it is important to specify the spatiotemporal scale of one’s analysis and make sure it is commensurate with the data and question at hand. In conclusion, analyzing fossil patterns using modern ecological frameworks is a useful heuristic exercise, and serves here as a conceptual bridge between neo-ecological studies studying species persistence and macroevolutionary studies that examine species temporal duration and extinction risk.

53

Figures

Figure 1. A) Map of the Turkana Basin, showing the location of the three geological formations studied here (from Bobe 2011). B) Ages of analyzed geological members for the three formations considered in our study. Age data are from McDougall (1985),

Feibel et al. (1989), McDougall & Brown (2006), Brown & McDougall (2011), and

McDougall et al. (2012).

54

Figure 2. Log10-transformed body size distributions (kg) of all large mammal species for each formation, showing similar distributions for the fossil taxa from the three different formations (communities). The lack of a second peak less than 1kg (Kelt and Meyer,

2009) is due to the removal of smaller-bodied Orders (i.e., Lagomorpha and Rodentia).

55

Figure 3. Observed relationship between number of occupied members versus mean relative abundance for each species. Note the y-axis is logged. A positive, log-linear relationship between these two variables is what one would expect in a core-transient system, where core species are abundant and persistent because they are well adapted to the area being sampled.

56

Figure 4. Observed species frequency distribution of number of occupied members for each formation. Zero number of occupied members is estimated using a Chao1 estimator

(Chao et al., 2009). These are species that are inferred to have existed but were not observed in a formation because they were destroyed prior to sampling or simply were not sampled.

57

Figure 5. Observed per-member sampling probability for each species in a given formation. A species’ observed per-member sampling probability is calculated as the number of occupied members divided by the number of members in that formation. Zero per-member sampling probabilities are estimated using a Chao1 estimator (Chao et al.,

2009) as in Figure 4. The mean and median estimates are similar, so the mean is used for the binomial null model. The only exception is the Shungura Fm. However, a smaller median than mean per-member sampling probability should result in lower expected number of core species for the null model. Because the observed number of core species is larger than that predicted by the null model, using the mean is conservative.

58

Figure 6. Observed species ranges and member occupancies (represented by dots) in the

Koobi Fora Formation. Core species are marked with red ranges. Species are ordered from left to right by family and then by decreasing abundance within each family.

Different families are demarcated by alternating white and gray shading and, from left to right, are Bovidae, Camelidae, Giraffidae, Hippopotamidae, Suidae, Canidae, Felidae,

Hyaenidae, Mustelidae, Ursidae, Viverridae, Equidae, Rhinocerotidae, Cercopithecidae,

Hominidae, Deinotheriidae, Elephantidae, and Orycteropodidae.

59

Figure 7. Same as Figure 6 but for the Nachukui Formation. Families from left to right are Bovidae, Camelidae, Giraffidae, Hippopotamidae, Suidae, Canidae, Felidae,

Herpestidae, Hyaenidae, Viverridae, Equidae, Rhinocerotidae, Cercopithecidae,

Hominidae, Deinotheriidae, and Elephantidae.

60

Figure 8. Same as Figure 6 and Figure 7 but for the Shungura Formation. Families from left to right are Bovidae, Camelidae, Girafidae, Hippopotamidae, Suidae,

Felidae,Herpestidae, Hyaenidae, Mustelidae, Viverridae, Procaviidae, Chalicotheriidae,

Equidae, Rhinocerotidae, Cercopithecidae, Hominidae, Deinotheriidae, Elephantidae, and

Orycteropodidae.

61

Figure 9. Comparison of observed number of core species versus that expected from the binomial null model. Error bars denote 95% confidence intervals. Those points and error bars in red denote significance (two-tailed, p < 0.05).

62

Figure 10. Observed vs. expected number of core species within each taxonomic family calculated using a hypergeometric null model for the Koobi Fora Fm. Points denote observed number of core species, while error bars represent 95% confidence intervals.

Points and error bars in red signify significant results, whereas those in purple represent marginally significant results (two-tailed; p < 0.05 & 0.1, respectively).

63

Figure 11. Observed vs. expected number of core species within each taxonomic family calculated using a hypergeometric null model for the Nachukui Fm. Points, error bars, and colors as in Figure 10.

64

Figure 12. Observed vs. expected number of core species within each taxonomic family calculated using a hypergeometric null model for the Nachukui Fm. Points, error bars, and colors as in Figure 10.

65

Figure 13. Logistic regression coefficient estimates with ± one standard error for all three formations. The dependent variable, in this case, is whether a species is core or transient. The two continuous independent variables (i.e., abundance and body mass) were centered and scaled to have mean = 0 and variance = 1. All continuous variable coefficient estimates are located to the right of the vertical dashed line. This means an increase in these variables is associated with an increased probability of a species being classified as core. Diet is a discrete variable (with five different categories), so it was not standardized. Different symbols in the diet portion of the graph denote different dietary levels. Grazer is set as the baseline level and therefore is the intercept to which all other dietary levels are compared. All estimates to the right of the vertical dashed line are associated with an increased probability of being core relative to the grazer diet category.

Arrows next to points signify coefficient estimates of dietary categories that have no observed core species. Therefore, they are ultimately arbitrary and should be interpreted as associated with very, very low probabilities of being core. Significance levels can be seen in Table 3.

66

Figure 14. Relationship between absolute abundance and evenness (estimated using the

Probability of Interspecific Encounter index [Hurlbert, 1971]) for the three formations.

Each point is represented by a species, where abundance is its total abundance summed across all members, and evenness is calculated on abundances also across all members.

Note the x-axis is logged. As discussed in the main text, one would predict a strong negative relationship between these two measures if sampling and preservational biases are artificially generating the core-transient signal. There is a negative but very weak relationship, so sampling and preservational biases are discounted as driving the observed core-transient signal.

67

Figure 15. Comparison between observed log-transformed relative abundance and predicted “live” log-transformed relative abundance from the Koobi Fora Formation.

Predicted “live” abundance was estimated by fitting a multiple regression model to the

Amboseli live-dead data (Western and Behrensmeyer, 2009) which were summed across all time bins, where log10(live relative abundance) was modeled as a function of log10(dead relative abundance) plus log10(body mass)). Then, observed Koobi Fora log10(relative abundance) and log10(body mass) were input into the model to get predicted log10(live relative abundance). It is clearly seen that the points cluster tightly around the 1:1 line. The slight bias towards large observed relative abundances (more points below the line) demonstrates there is indeed a body size bias, but it does not play a huge role in the pre-burial taphonomic process, assuming that this was similar to those operating in Amboseli.

68

Tables Table 1. Number of individuals and species of large mammals (core and transient) found in each Pliocene-Pleistocene geological formation in the Omo-Turkana Basin.

Formation Total number Total number Number of Number of of individuals of species core species transient species Koobi Fora 4282 126 28 98 Nachukui 1026 89 17 72 Shungura 4482 91 30 61

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Table 2. List of large mammal core species for each formation. Order of species is alphabetical within families, and the order of families follows Figure 10-Figure 12.

Koobi Fora Nachukui Shungura Antidorcas recki Aepyceros melampus Aepyceros shungurae Connochaetes gentryi Antidorcas recki Kobus ancystrocera Damaliscus eppsi Megalotragus sp. Kobus kob Gazella praethomsoni Tragelaphus nakuae Kobus sigmoidalis Kobus kob Tragelaphus strepsiceros Menelikia lyrocera Kobus sigmoidalis Sivatherium maurusium Tragelaphus gaudryi Menelikia lyrocera Hippopotamus gorgops Tragelaphus nakuae Pelorovis turkanensis Kolpochoerus limnetes Giraffa gracilis Tragelaphus nakuae Metridiochoerus andrewsi Giraffa jumae Giraffa jumae Notochoerus scotti Giraffa pygmaea Giraffa pygmaea Hyaena hyaena Sivatherium sp. Giraffa stillei Equus sp. aff. Hippopotamus Sivatherium maurusium Eurygnathohippus protamphibius aff. Hippopotamus ethiopicum Kolpochoerus limnetes protamphibius Ceratotherium simum Kolpochoerus olduvaiensis Hippopotamus gorgops Diceros bicornis Metriodiochoerus Kolpochoerus limnetes Deinotherium bozasi compactus Metridiochoerus andrewsi Elephas recki Metriodiochoerus jacksoni Metridiochoerus hopwoodi Megantereon sp. Homotherium sp. Hyaena sp. Crocuta ultra Equus oldowayensis Enhydriodon afman Eurygnathohippus libycum Eurygnathohippus Eurygnathohippus sitifense ethiopicum Ceratotherium simum Eurygnathohippus Diceros bicornis hasumense Papio sp. Cercopithecoides kimeui Paracolobus mutiwa Rhinocolobus turkanaensis Rhinocolobus turkanaensis Theropithecus oswaldi Small Papionini B Deinotherium bozasi Theropithecus brumpti Elephas recki Deinotherium bozasi Elephas recki

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Table 3. Raw, exponentiated, and inverse logit transformed logistic regression coefficients for all three formations. Regression was done using whether a species was core as the dependent variable and diet, abundance, and body mass as independent variables. Diet is categorical, while the other two variables are continuous. The continuous variables were log10 transformed and then scaled to have mean = 0 and variance = 1. The inverse logit transformation was applied to the baseline dietary category (i.e., the intercept, which is grazer), and each of the other diet coefficient estimates added to the intercept (e.g., for Koobi Fora mixed feeders, -1.682 + -0.469).

This gives probability estimates that a given species is core on average, at mean abundance and body mass values.

Inverse logit transformed Raw estimated coefficients (log Exponentiated coefficients (odds coefficients (probability of odds ratio) ratio) being core at mean abundance Coefficient and body mass) Koobi Koobi Koobi Nachukui Shungura Nachukui Shungura Nachukui Shungura Fora Fora Fora Grazer (intercept) -1.682**** -2.309**** -1.827*** 0.186 0.099 0.161 15.69% 9.03% 13.86% Mixed -0.469 0.333 0.684 0.625 1.396 1.982 10.42% 12.17% 24.18% Browser 1.219* 0.864 1.014 3.384 2.373 2.757 38.64% 19.07% 30.73% Omnivore -16.794† 1.93 1.502 0.000† 6.891 4.492 0.000%† 40.63% 41.95% Carnivore -0.19 -15.361† -0.023 0.827 0.000† 0.977 13.34% 0.000%† 13.58% scale(log10(abundance)) 1.150**** 1.093** 1.814**** 3.159 2.984 6.138 NA NA NA scale(log10(body mass)) 0.517* 0.791** 0.978** 1.677 2.205 2.659 NA NA NA †coefficient estimates for dietary levels that have no core species. As a result, these are arbitrary estimates produced by R and should simply be interpreted as very, very low.

Statistical significance is only noted for the raw coefficients, but their respective transformed coefficients are significant as well. Significance is coded as: **** < 0.001 <

*** < 0.01 < ** < 0.05 < * < 0.1.

71

Table 4. Raw body mass coefficients estimated using multiple logistic regression (as in

Table 3) but this time within body mass classes. Coefficient estimates ± one standard error and sample size in parentheses are shown for each formation. “No core species” denotes body mass classes that have all transient species, meaning no meaningful coefficient estimates could be obtained. “Overfit” indicates those body mass classes that have too low of a sample size, resulting in overfit models and nonsensical coefficient estimates. None of the coefficient estimates are statistically significant at p < 0.05.

Body mass class Koobi Fora Nachukui Shungura (kg) < 10 No core species No core species (2) No core species (11) (10) 10-100 0.283 ± 0.502 (59) -1.296 ± 0.855 (42) 1.012 ± 0.817 (39) 100-1000 -0.826 ± 0.489 (45) -0.185 ± 0.527 (34) 0.401 ± 0.661 (31) > 1000 0.021 ± 0.941 (12) 0.767 ± 0.975 (11) Overfit (9)

72

References

Anyonge, W., 1993. Body mass in large extant and extinct carnivores. Journal of

Zoology. 231, 339–350.

Badgley, C., 1986. Counting Individuals in Mammalian Fossil Assemblages from Fluvial

Environments. PALAIOS. 1, 328–338.

Barr, W.A., 2015. Paleoenvironments of the Shungura Formation (Plio-Pleistocene:

Ethiopia) based on ecomorphology of the bovid astragalus. Journal of Human

Evolution. 88, 97–107.

Beden, M., 1983. Family Elephantidae. In: Harris, J.M. (Ed.), The Fossil Ungulates:

Proboscidea, Perissodactyla, and Suidae, Koobi Fora Research Project. Clarendon

Press, Oxford, pp. 40–129.

Behrensmeyer, A.K., Dechant Boaz, D., 1980. The recent bones of Amboseli Park Kenya

in relation to East African paleoecology. In: Fossils in the Making: Vertebrate

Taphonomy and Paleoecology. University of Chicago Press, Chicago, pp. 72–92.

Behrensmeyer, A.K., Western, D., Boaz, D.E.D., 1979. New Perspectives in Vertebrate

Paleoecology from a Recent Bone Assemblage. Paleobiology. 5, 12–21.

Belmaker, J., 2009. Species richness of resident and transient coral-dwelling fish

responds differentially to regional diversity. Global Ecology and Biogeography.

18, 426–436.

Bobe, R., 2011. Fossil Mammals and Paleoenvironments in the Omo-Turkana Basin.

Evolutionary Anthropology: Issues, News, and Reviews. 20, 254–263.

73

Bobe, R., Behrensmeyer, A.K., 2004. The expansion of grassland ecosystems in Africa in

relation to mammalian evolution and the origin of the genus Homo.

Palaeogeography, Palaeoclimatology, Palaeoecology. 207, 399–420.

Bobe, R., Behrensmeyer, A.K., Chapman, R.E., 2002. Faunal change, environmental

variability and late Pliocene hominin evolution. Journal of Human Evolution. 42,

475–497.

Bobe, R., Leakey, M.G., 2009. Ecology of Plio-Pleistocene Mammals in the Omo—

Turkana Basin and the Emergence of Homo. In: Grine, F.E., Fleagle, J.G.,

Leakey, R.E. (Eds.), The First Humans – Origin and Early Evolution of the Genus

Homo, Vertebrate Paleobiology and Paleoanthropology. Springer Netherlands,

pp. 173–184.

Boisserie, J.-R., 2005. The phylogeny and taxonomy of Hippopotamidae (Mammalia:

Artiodactyla): a review based on morphology and cladistic analysis. Zoological

Journal of the Linnean Society. 143, 1–26.

Brown, F.H., McDougall, I., 2011. Geochronology of the Turkana Depression of

Northern Kenya and Southern Ethiopia. Evolutionary Anthropology: Issues,

News, and Reviews. 20, 217–227.

Brown, J.H., Maurer, B.A., 1986. Body size, ecological dominance and Cope’s rule.

Nature. 324, 248–250.

Casanovas-Vilar, I., García-Paredes, I., Alba, D.M., Van Den Hoek Ostende, L.W.,

Moyà-Solà, S., 2010. The European Far West: Miocene mammal isolation,

diversity and turnover in the Iberian Peninsula: Miocene mammals of the Iberian

Peninsula. Journal of Biogeography. 37, 1079–1093.

74

Cerling, T.E., Andanje, S.A., Blumenthal, S.A., Brown, F.H., Chritz, K.L., Harris, J.M.,

Hart, J.A., Kirera, F.M., Kaleme, P., Leakey, L.N., Leakey, M.G., Levin, N.E.,

Manthi, F.K., Passey, B.H., Uno, K.T., 2015. Dietary changes of large herbivores

in the Turkana Basin, Kenya from 4 to 1 Ma. Proceedings of the National

Academy of Sciences. 112, 11467–11472.

Cerling, T.E., Chritz, K.L., Jablonski, N.G., Leakey, M.G., Manthi, F.K., 2013a. Diet of

Theropithecus from 4 to 1 Ma in Kenya. Proceedings of the National Academy of

Sciences. 110, 10507–10512.

Cerling, T.E., Manthi, F.K., Mbua, E.N., Leakey, L.N., Leakey, M.G., Leakey, R.E.,

Brown, F.H., Grine, F.E., Hart, J.A., Kaleme, P., Roche, H., Uno, K.T., Wood,

B.A., 2013b. Stable isotope-based diet reconstructions of Turkana Basin

hominins. Proceedings of the National Academy of Sciences. 110, 10501–10506.

Cerling, T.E., Mbua, E., Kirera, F.M., Manthi, F.K., Grine, F.E., Leakey, M.G.,

Sponheimer, M., Uno, K.T., 2011. Diet of Paranthropus boisei in the early

Pleistocene of East Africa. Proceedings of the National Academy of Sciences.

108, 9337–9341.

Cerling, T.E., Wynn, J.G., Andanje, S.A., Bird, M.I., Korir, D.K., Levin, N.E., Mace, W.,

Macharia, A.N., Quade, J., Remien, C.H., 2011. Woody cover and hominin

environments in the past 6 million years. Nature. 476, 51–56.

Chao, A., Colwell, R.K., Lin, C.-W., Gotelli, N.J., 2009. Sufficient sampling for

asymptotic minimum species richness estimators. Ecology. 90, 1125–1133.

75

Coyle, J.R., Hurlbert, A.H., White, E.P., 2013. Opposing Mechanisms Drive Richness

Patterns of Core and Transient Bird Species. The American Naturalist. 181, E83–

E90.

Damuth, J., 1990. Problems in estimating body masses of archaic ungulates using dental

measurements. In: Damuth, J.D., MacFadden, B.J. (Eds.), Body Size in

Mammalian Paleobiology: Estimation and Biological Implications. Cambridge

University Press, Cambridge ; New York, pp. 229–254.

Delson, E., Terranova, C.J., Jungers, W.L., Sargis, E.J., Jablonski, N.G., Dechow, P.C.,

2000. Body mass in Cercopithecidae (Primates, Mammalia): estimation and

scaling in extinct and extant taxa. Anthropological Papers of the American

Museum of Natural History. 1–159.

Devictor, V., Clavel, J., Julliard, R., Lavergne, S., Mouillot, D., Thuiller, W., Venail, P.,

Villéger, S., Mouquet, N., 2010. Defining and measuring ecological

specialization. Journal of Applied Ecology. 47, 15–25.

Dolan, J.R., Ritchie, M.E., Tunin-Ley, A., Pizay, M.-D., 2009. Dynamics of core and

occasional species in the marine plankton: tintinnid ciliates in the north-west

Mediterranean Sea. Journal of Biogeography. 36, 887–895.

Eisenmann, V., 1983. Family Equidae. In: Harris, J.M. (Ed.), The Fossil Ungulates:

Proboscidea, Perissodactyla, and Suidae, Koobi Fora Research Project. Clarendon

Press, Oxford, pp. 156–214.

Elton, S., 2006. Forty years on and still going strong: the use of hominin-cercopithecid

comparisons in palaeoanthropology. Journal of the Royal Anthropological

Institute. 12, 19–38.

76

Feibel, C.S., 2011. A Geological History of the Turkana Basin. Evolutionary

Anthropology: Issues, News, and Reviews. 20, 206–216.

Feibel, C.S., Brown, F.H., McDougall, I., 1989. Stratigraphic context of fossil hominids

from the Omo Group deposits: northern Turkana Basin, Kenya and Ethiopia.

American Journal of Physical Anthropology. 78, 595-622.

Flynn, L.J., Barry, J.C., Morgan, M.E., Pilbeam, D., Jacobs, L.L., Lindsay, E.H., 1995.

Neogene Siwalik mammalian lineages: Species longevities, rates of change, and

modes of speciation. Palaeogeography, Palaeoclimatology, Palaeoecology. 115,

249–264.

Fortelius, M., Solounias, N., 2000. Functional Characterization of Ungulate Molars Using

the Abrasion-Attrition Wear Gradient: A New Method for Reconstructing

Paleodiets. American Museum Novitates. 3301, 1–36.

Fortelius, M., Žliobaitė, I., Kaya, F., Bibi, F., Bobe, R., Leakey, L., Leakey, M.,

Patterson, D., Rannikko, J., Werdelin, L., 2016. An ecometric analysis of the

fossil mammal record of the Turkana Basin. Philosophical Transactions of the

Royal Society B: Biological Sciences. 371, 20150232.

Gentry, A.W., 2010. Bovidae. In: Werdelin, L., Sanders, W.J. (Eds.), Cenozoic Mammals

of Africa. University of California Press, Berkeley, pp. 741–796.

Gilinsky, N.L., Good, I.J., 1991. Probabilities of origination, persistence, and extinction

of families of marine invertebrate life. Paleobiology. 17, 145–166.

Gotelli, N.J., Ellison, A.M., 2013. A primer of ecological statistics, Second edition. ed.

Sinauer Associates, Inc., Publishers, Sunderland, Massachusetts.

77

Grabowski, M., Hatala, K.G., Jungers, W.L., Richmond, B.G., 2015. Body mass

estimates of hominin fossils and the evolution of human body size. Journal of

Human Evolution. 85, 75–93.

Haile-Selassie, Y., Melillo, S.M., Su, D.F., 2016. The Pliocene hominin diversity

conundrum: Do more fossils mean less clarity? Proceedings of the National

Academy of Sciences. 113, 6364–6371.

Harnik, P.G., 2011. Direct and indirect effects of biological factors on extinction risk in

fossil bivalves. Proceedings of the National Academy of Sciences. 108, 13594–

13599.

Harnik, P.G., Simpson, C., Payne, J.L., 2012. Long-term differences in extinction risk

among the seven forms of rarity. Proceedings of the Royal Society B: Biological

Sciences. 279, 4969–4976.

Harris, J.M. (Ed.), 1983a. The Fossil Ungulates: Proboscidea, Perissodactyla, and Suidae,

Koobi Fora Research Project. Clarendon Press, Oxford.

Harris, J.M., 1983b. Family Suidae. In: Harris, J.M. (Ed.), The Fossil Ungulates:

Proboscidea, Perissodactyla, and Suidae, Koobi Fora Research Project. Clarendon

Press, Oxford, pp. 215–302.

Harris, J.M., 1983c. Family Rhinocerotidae. In: Harris, J.M. (Ed.), The Fossil Ungulates:

Proboscidea, Perissodactyla, and Suidae, Koobi Fora Research Project. Clarendon

Press, Oxford, pp. 130–155.

Harris, J.M., 1983d. Family Deinotheriidae. In: Harris, J.M. (Ed.), The Fossil Ungulates:

Proboscidea, Perissodactyla, and Suidae, Koobi Fora Research Project. Clarendon

Press, Oxford, pp. 22–39.

78

Harris, J.M. (Ed.), 1991a. The Fossil Ungulates: Geology, Fossil Artiodactylas, and

Palaeoenvironments, Koobi Fora Research Project. Clarendon Press, Oxford.

Harris, J.M., 1991b. Family Bovidae. In: Harris, J.M. (Ed.), The Fossil Ungulates:

Geology, Fossil Artiodactylas, and Palaeoenvironments, Koobi Fora Research

Project. Clarendon Press, Oxford, pp. 139–320.

Harris, J.M., 1991c. Family Camelidae. In: Harris, J.M. (Ed.), The Fossil Ungulates:

Geology, Fossil Artiodactylas, and Palaeoenvironments, Koobi Fora Research

Project. Clarendon Press, Oxford, pp. 86–92.

Harris, J.M., 1991d. Family Giraffidae. In: Harris, J.M. (Ed.), The Fossil Ungulates:

Geology, Fossil Artiodactylas, and Palaeoenvironments, Koobi Fora Research

Project. Clarendon Press, Oxford, pp. 93–138.

Harris, J.M., 1991e. Family Hippopotamidae. In: Harris, J.M. (Ed.), The Fossil

Ungulates: Geology, Fossil Artiodactylas, and Palaeoenvironments, Koobi Fora

Research Project. Clarendon Press, Oxford, pp. 31–85.

Harris, J.M., Leakey, M.G., Brown, F.H., 1988. Stratigraphy and Paleontology of

Pliocene and Pleistocene Localities West of Lake Turkana, Kenya, Contributions

in Science. Natural History Museum of Los Angeles County, Los Angeles.

Harris, J.M., Leakey, M.G., Brown, F.H., 2006. A Brief History of Research at Koobi

Fora, Northern Kenya. Ethnohistory. 53, 35–69.

Henderson, P.A., Magurran, A.E., 2014. Direct evidence that density-dependent

regulation underpins the temporal stability of abundant species in a diverse animal

community. Proceedings of the Royal Society B: Biological Sciences. 281,

20141336–20141336.

79

Hurlbert, S.H., 1971. The Nonconcept of Species Diversity: A Critique and Alternative

Parameters. Ecology. 52, 577–586.

Hurlbert, S.H., 1984. Pseudoreplication and the Design of Ecological Field Experiments.

Ecological Monographs. 54, 187–211.

Jablonski, D., Sepkoski, J.J., 1996. Paleobiology, Community Ecology, and Scales of

Ecological Pattern. Ecology. 77, 1367–1378.

Jablonski, N.G., Leakey, M.G. (Eds.), 2008. The Fossil Monkeys, Koobi Fora Research

Project. California Academy of Sciences, San Francisco.

Jackson, S.T., Blois, J.L., 2015. Community ecology in a changing environment:

Perspectives from the Quaternary. Proceedings of the National Academy of

Sciences. 112, 4915–4921.

Janis, C.M., 1990. Correlation of cranial and dental variables with body size in ungulates

and macropodoids. In: Damuth, J.D., MacFadden, B.J. (Eds.), Body Size in

Mammalian Paleobiology: Estimation and Biological Implications. Cambridge

University Press, Cambridge ; New York, pp. 255–300.

Johanson, D.C., 2004. Lucy, Thirty Years Later: An Expanded View of Australopithecus

afarensis. Journal of Anthropological Research. 60, 465–486.

Kelt, D.A., Meyer, M.D., 2009. Body size frequency distributions in African mammals

are bimodal at all spatial scales. Global Ecology and Biogeography. 18, 19–29.

Leakey, M., Grossman, A., Gutiérrez, M., Fleagle, J.G., 2011. Faunal Change in the

Turkana Basin during the Late Oligocene and Miocene. Evolutionary

Anthropology: Issues, News, and Reviews. 20, 238–253.

80

Lehmann, T., 2008. Plio-Pleistocene aardvarks (Mammalia, Tubulidentata) from East

Africa. Fossil Record. 11, 67–81.

Levin, N.E., Brown, F.H., Behrensmeyer, A.K., Bobe, R., Cerling, T.E., 2011. Paleosol

carbonates from the Omo Group: Isotopic records of local and regional

environmental change in East Africa. Palaeogeography, Palaeoclimatology,

Palaeoecology. 307, 75–89.

Levin, S.A., 1992. The Problem of Pattern and Scale in Ecology: The Robert H.

MacArthur Award Lecture. Ecology. 73, 1943–1967.

Liow, L.H., Fortelius, M., Bingham, E., Lintulaakso, K., Mannila, H., Flynn, L., Stenseth,

N.C., 2008. Higher origination and extinction rates in larger mammals.

Proceedings of the National Academy of Sciences. 105, 6097–6102.

Liow, L.H., Reitan, T., Harnik, P.G., 2015. Ecological interactions on macroevolutionary

time scales: clams and brachiopods are more than ships that pass in the night.

Ecology Letters. 18, 1030–1039.

Magurran, A.E., Henderson, P.A., 2003. Explaining the excess of rare species in natural

species abundance distributions. Nature. 422, 714–716.

Maurer, B.A., 1999. Untangling ecological complexity: the macroscopic perspective.

University of Chicago Press, Chicago, Ill.

McDougall, I., 1985. K-Ar and 40Ar/39Ar dating of the hominid-bearing Pliocene-

Pleistocene sequence at Koobi Fora, Lake Turkana, northern Kenya. Geological

Society of America Bulletin. 96, 159-175.

81

McDougall, I., Brown, F.H., 2006. Precise 40Ar/39Ar geochronology for the upper

Koobi Fora Formation, Turkana Basin, northern Kenya. Journal of the Geological

Society, London. 163, 205-220.

McDougall, I., Brown, F.H., Vasconcelos, P.M., Cohen, B.E., Thiede, D.S., Buchanan,

M.J., 2012. New single crystal 40Ar/39Ar ages improve time scale for deposition

of the Omo Group, Omo-Turkana Basin, East Africa. Journal of the Geological

Society, London. 169, 213-226.

McGill, B., Collins, C., 2003. A unified theory for macroecology based on spatial

patterns of abundance. Evolutionary Ecology Research. 5, 469–492.

McGill, B.J., 2010. Matters of Scale. Science. 328, 575–576.

McGill, B.J., 2012. Trees are rarely most abundant where they grow best. Journal of Plant

Ecology. 5, 46–51.

McGill, B.J., Enquist, B., Weiher, E., Westoby, M., 2006. Rebuilding community

ecology from functional traits. Trends in Ecology & Evolution. 21, 178–185.

McKinney, M.L., 1997. Extinction Vulnerability and Selectivity: Combining Ecological

and Paleontological Views. Annual Review of Ecology and Systematics. 28, 495–

516.

Menard, S.W., 2002. Applied logistic regression analysis, 2nd ed. ed, Sage university

papers. Quantitative applications in the social sciences. Sage Publications,

Thousand Oaks, Calif.

Miller, J.H., Behrensmeyer, A.K., Du, A., Lyons, S.K., Patterson, D., Tóth, A.,

Villaseñor, A., Kanga, E., Reed, D., 2014. Ecological fidelity of functional traits

82

based on species presence-absence in a modern mammalian bone assemblage

(Amboseli, Kenya). Paleobiology. 40, 560–583.

Newman, M.C., 1993. Regression analysis of log-transformed data: Statistical bias and its

correction. Environmental Toxicology and Chemistry. 12, 1129–1133.

Pandolfi, J., 2002. Coral community dynamics at multiple scales. Coral Reefs. 21, 13–23.

Patzkowsky, M.E., Holland, S.M., 2003. Lack of community saturation at the beginning

of the Paleozoic plateau: the dominance of regional over local processes.

Paleobiology. 29, 545-560.

Pineda-Munoz, S., Lazagabaster, I.A., Alroy, J., Evans, A.R., 2016. Inferring diet from

dental morphology in terrestrial mammals. Methods in Ecology and Evolution.

Potts, R., 2013. Hominin evolution in settings of strong environmental variability.

Quaternary Science Reviews. 73, 1–13.

Rabinowitz, D., 1981. Seven forms of rarity. In: Synge, H. (Ed.), The Biological Aspects

of Rare Plant Conservation. Riley, pp. 205–217.

R Core Team, 2015. R: A Language and Environment for Statistical Computing. R

Foundation for Statistical Computing, Vienna, Austria.

Raia, P., Passaro, F., Fulgione, D., Carotenuto, F., 2012. Habitat tracking, stasis and

survival in Neogene large mammals. Biology Letters. 8, 64–66.

Ricklefs, R.E., 2008. Disintegration of the Ecological Community: American Society of

Naturalists Sewall Wright Award Winner Address. The American Naturalist. 172,

741–750.

Rosenzweig, M.L., 1995. Species Diversity in Space and Time. Cambridge University

Press, Cambridge, United Kingdom.

83

Rosenzweig, M.L., McCord, R.D., 1991. Incumbent Replacement: Evidence for Long-

Term Evolutionary Progress. Paleobiology. 17, 202–213.

Ross, S.M., 2014. Introduction to Probability Models, Eleventh Edition, 11th ed.

Academic Press, Amsterdam.

Scott, K.M., 1990. Postcranial dimensions of ungulates as predictors of body mass. In:

Damuth, J.D., MacFadden, B.J. (Eds.), Body Size in Mammalian Paleobiology:

Estimation and Biological Implications. Cambridge University Press, Cambridge ;

New York, pp. 301–336.

Scott, R.S., Ungar, P.S., Bergstrom, T.S., Brown, C.A., Grine, F.E., Teaford, M.F.,

Walker, A., 2005. Dental microwear texture analysis shows within-species diet

variability in fossil hominins. Nature. 436, 693–695.

Sepkoski, J.J., 1996. Competition in macroevolution: the double wedge revisited. In:

Evolutionary Paleobiology. University of Chicago Press, Chicago, pp. 211–255.

Simpson, C., Harnik, P.G., 2009. Assessing the role of abundance in marine bivalve

extinction over the post-Paleozoic. Paleobiology. 35, 631–647.

Smith, F.A., Lyons, S.K., Ernest, S.K.M., Jones, K.E., Kaufman, D.M., Dayan, T.,

Marquet, P.A., Brown, J.H., Haskell, J.P., 2003. Body mass of Late Quaternary

mammals: Ecological Archives E084-094. Ecology. 84, 3403–3403.

Smith, R.J., 1984. Allometric scaling in comparative biology: problems of concept and

method. American Journal of Physiology - Regulatory, Integrative and

Comparative Physiology. 246, R152.

Smits, P.D., 2015. Expected time-invariant effects of biological traits on mammal species

duration. Proceedings of the National Academy of Sciences. 112, 13015–13020.

84

Spencer, L.M., 1997. Dietary adaptations of Plio-Pleistocene Bovidae: implications for

hominid habitat use. Journal of Human Evolution. 32, 201–228.

Supp, S.R., Koons, D.N., Ernest, S.K.M., 2015. Using life history trade-offs to

understand core-transient structuring of a small mammal community. Ecosphere.

6, art187.

Teaford, M.F., Ungar, P.S., 2000. Diet and the evolution of the earliest human ancestors.

Proceedings of the National Academy of Sciences. 97, 13506–13511.

Tomiya, S., 2013. Body Size and Extinction Risk in Terrestrial Mammals Above the

Species Level. The American Naturalist. 182, E196–E214.

Ulrich, W., Ollik, M., 2004. Frequent and occasional species and the shape of relative-

abundance distributions. Diversity and Distributions. 10, 263–269.

Valentine, J.W., 2001. Scaling is everything: Brief comments on evolutionary

paleoecology. In: Allmon, W.D., Bottjer, D.J. (Eds.), Evolutionary Paleoecology:

The Ecological Context of Macroevolutionary Change. Columbia University

Press, New York, p. 357.

Van Valkenburgh, B., 1990. Skeletal and dental predictors of body mass in carnivores.

In: Damuth, J.D., MacFadden, B.J. (Eds.), Body Size in Mammalian

Paleobiology: Estimation and Biological Implications. Cambridge University

Press, Cambridge ; New York, pp. 181–206.

Van Valkenburgh, B., Wang, X., Damuth, J., 2004. Cope’s Rule, hypercarnivory, and

extinction in North American canids. Science. 306, 101–104.

Viranta, S., 2003. Geographic and temporal ranges of Middle and Late Miocene

carnivores. Journal of Mammalogy. 84, 1267–1278.

85

Werdelin, L., Lewis, M.E., 2013a. The Carnivora, Koobi Fora Research Project.

California Academy of Sciences, San Francisco.

Werdelin, L., Lewis, M.E., 2013b. Temporal Change in Functional Richness and

Evenness in the Eastern African Plio-Pleistocene Carnivoran Guild. PLoS ONE.

8, e57944.

Werdelin, L., Sanders, W.J. (Eds.), 2010. Cenozoic mammals of Africa. University of

California Press, Berkeley.

Western, D., Behrensmeyer, A.K., 2009. Bone Assemblages Track Animal Community

Structure over 40 Years in an African Savanna Ecosystem. Science. 324, 1061–

1064.

Wiens, J.A., 1989. Spatial Scaling in Ecology. Functional Ecology. 3, 385–397.

Williams, J.W., Jackson, S.T., 2007. Novel climates, no-analog communities, and

ecological surprises. Frontiers in Ecology and the Environment. 5, 475–482.

Wood, B., 1991. Hominid Cranial Remains, Koobi Fora Research Project. Clarendon

Press, Oxford.

Wood, B., Boyle, E.K., 2016. Hominin taxic diversity: Fact or fantasy? American Journal

of Physical Anthropology. 159, 37–78.

Wood, B., Leakey, M., 2011. The Omo-Turkana Basin Fossil Hominins and Their

Contribution to Our Understanding of Human Evolution in Africa. Evolutionary

Anthropology: Issues, News, and Reviews. 20, 264–292.

Wood, B., Strait, D., 2004. Patterns of resource use in early Homo and Paranthropus.

Journal of Human Evolution. 46, 119–162.

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Chapter 3: Spatial, temporal, and taxonomic scaling of richness in the skeletal assemblage of a modern East African large mammal community

Abstract

It is well known that ecological pattern and process change across spatial, temporal, and taxonomic scales. This hinders our ability to compare modern and fossil communities, which exist on very different scales, especially temporal ones. Researchers may be tempted to use the scaling relationship between time and richness to account for the differences in temporal scale, but recent research has shown that the rate of richness accumulation with time decreases as a function of increasing area, i.e., the species-time- area relationship, or STAR (Adler and Lauenroth, 2003; Adler et al., 2005). Conversely, the rate of species accumulation with area decreases as a function of increasing time.

Moreover, most modern ecological studies are carried out at the species-level, whereas fossil studies often are conducted at the genus-level or above, so there is a taxonomic scale discrepancy between the two as well. Here, I create a STAR model for describing how species richness scales as a function of time and area in the large mammal skeletal assemblage of Amboseli National Park, Kenya. I then analyze how the model coefficients change at different taxonomic scales (i.e., genus, family, order). I also estimate at what spatial and temporal scales richness turnover rates are equivalent (i.e., “scales of time- area equivlance” sensu Adler and colleagues (2005) in order to understand the relationship between increasing spatial scale and increasing temporal scale. In agreement with previous studies, I find species richness scales positively with time and area but with a negative interaction between the two. Rates of richness turnover decrease as one increases taxonomic scale. I hypothesize that decreasing rates of turnover with increasing

87 spatial or temporal scale is caused by progressive sampling of a relatively static species pool. Continued sampling of the species pool leads to a larger proportion of sampled rare species, which are typically associated with regional correlates of diversity. This means that increased time-averaging of communities results in a more spatially-averaged ecological signal, which can be calibrated by estimating scales of time-area equivalence.

In this study, the rate of species turnover over one year is equivalent to turnover over 0.09 km2, and turnover over 10,000 years is equivalent to turnover over 895 km2. In conclusion, the STAR presents a framework for extrapolating and comparing richness between small-scale modern and large-scale fossil communities, as well as a means to understand the mechanisms involved with changing scale.

1. Introduction

Neo- and paleoecological research are complementary and have a lot to offer each other. For example, many paleoecological studies use modern ecological models as an interpretive framework for inferring process from fossil patterns (e.g., Sepkoski, 1978;

Patzkowsky and Holland, 2003; DiMichele et al., 2004; Harnik et al., 2012; Liow et al.,

2015; Saupe et al., 2015). Likewise, modern ecologists are beginning to appreciate the historical and large-scale perspectives that fossil assemblages can offer (Ricklefs and

Schluter, 1993; Brown, 1995; Enquist et al., 1995; Rosenzweig, 1995; Brown et al., 2001;

McGill et al., 2005; Svenning and Skov, 2007). More recently, researchers have analyzed combined neo- and paleoecological datasets to see if community assembly processes differed in the past compared to the present (Lyons et al., 2016). However, the appropriateness of this cross-field exchange of ideas and data between neo- and

88 paleoecology is contingent upon their commensurability across different scales.

Unfortunately, it is well established now that ecological pattern and process change across spatial, temporal, and taxonomic scales (Bell, 1989; Wiens, 1989; Levin, 1992;

Jablonski and Sepkoski, 1996; McGill et al., 2015). This poses a challenge for studying ecological communities across scales that differ by orders of magnitude, as is done when comparing modern and fossil communities.

One way to assess the comparability of ecological phenomena across orders of magnitude of scale is to study scaling relationships in ecological patterns (Brown et al.,

2002; White, 2007). One of the oldest such studies in ecology is the species-area relationship (SAR) (Arrhenius, 1921; Rosenzweig, 1995), which analyzes how species richness (the dependent variable) scales with increasing area (the independent variable).

The rate of species accumulation as a function of area has been shown to be related to the rate of species turnover (i.e., species replacement) (Harte and Kinzig, 1997; Harte et al.,

1999; Lennon et al., 2001; Koleff et al., 2003), and the two concepts are treated interchangeably here. Across many orders of magnitude, the SAR has been partitioned into three phases (i.e., “triphasic”), where each phase is defined by a dominant process acting at a particular scale: sampling, ecological, and evolutionary (Williams, 1943;

Preston, 1960; Brown, 1995; Rosenzweig, 1995; He and Legendre, 1996; Hubbell, 2001).

That is, at small spatial scales on a log-log plot, the relationship is convex-up and is driven solely by sampling processes (cf., Gotelli and Colwell, 2001). This is borne out by random placement models (Coleman, 1981), which adequately predict richness at small spatial scales (Plotkin et al., 2000). At intermediate scales, the log-log relationship is linear and is caused by ecological processes such as habitat heterogeneity and species

89 dispersal. At the largest scale, richness turnover is driven by sampling regions with different evolutionary histories, causing an increased rate of species accumulation and a concave-up relationship (Allen and White, 2003). Given the SAR’s rich intellectual history, it is not surprising that it has been studied in a number of fossil assemblages

(Sepkoski, 1976; Rosenzweig, 1998; Hadly and Maurer, 2001; Barnosky et al., 2005;

Raia et al., 2011; Sclafani and Holland, 2013).

Preston (1960) first proposed that the processes influencing species accumulation across space can be transposed to describe species accumulation through time. By analogy, he called this relationship the species-time relationship (STR). As in the SAR,

Preston claimed the three processes – sampling, ecological turnover, and evolutionary turnover – characterize the STR pattern over many orders of temporal magnitude

(Preston, 1960; McKinney and Frederick, 1999; White, 2007). At small temporal scales, more time spent sampling means discovering the rarer, harder-to-sample species and increased uncovering of the underlying community (cf., Gotelli and Colwell, 2001). At intermediate time scales, temporal habitat changes and chance colonization events by invasive and/or sink species (i.e., those species populations that are non-viable without immigration from neighboring communities) contribute to species turnover (Grinnell,

1922). At long enough time scales, in situ speciation or geologically infrequent migration events across biogeographic provinces (i.e., the Great American Biotic Interchange) cause species accumulation. Though not as well studied as the SAR, empirical studies have demonstrated similar functional forms between the SAR and STR (Preston, 1960;

Hadly and Maurer, 2001; Adler and Lauenroth, 2003; White, 2004; White et al., 2006).

Like the SAR, multiple researchers have studied the STR in fossil systems (Preston,

90

1960; Rosenzweig, 1995, 1998; McKinney and Frederick, 1999; Hadly and Maurer,

2001; Tomašových and Kidwell, 2010a; Raia et al., 2011).

Recently, the SAR and STR were unified into a single interaction model called the species-time-area relationship (STAR) (Adler and Lauenroth, 2003; Adler et al.,

2005). The area-by-time interaction term is consistently negative (Adler and Lauenroth,

2003; Adler et al., 2005; McGlinn and Palmer, 2009; Raia et al., 2011; but see

Jacquemyn et al., 2001) and suggests similar processes underlying community assembly across space and through time. A negative interaction term indicates the rate of species accumulation across space decreases as a function of time and vice versa.

The discovery of the STAR has important implications for scaling richness in order to compare neo- and paleoecological studies. One cannot only extrapolate the time span of sampling but must also take into account sampling area. To this end, I created a

STAR model using the large mammal skeletal assemblage of the Amboseli ecosystem.

Amboseli National Park is a semiarid savanna ecosystem located in southern Kenya just north of the Tanzanian border (2° S) (Figure 16). The study covers an area of 600 km2 and includes a habitat mosaic of dense and open woodland, swamp, bushland, lake margin, and open plains (Western, 2007). It is home to a diverse plant and mammal community which has been extensively studied for the last 40+ years (Western, 2007;

Western and Behrensmeyer, 2009). Study of the modern bone assemblage was initiated to understand how well it represented the living mammal community (Behrensmeyer et al.,

1979; Behrensmeyer and Dechant Boaz, 1980). Subsequent studies have demonstrated high fidelity between the living and skeletal assemblage in terms of species richness

(Behrensmeyer et al., 1979; Behrensmeyer, 1993), relative abundance (Western and

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Behrensmeyer, 2009), and functional diversity (Miller et al., 2014).

The Amboseli data are ideal for addressing these questions because 1) its large spatial extent enables the construction of SARs and also encompasses a number of different habitats, which are each occupied by different suites of species (Behrensmeyer et al., 1979; Western, 2007); 2) the skeletal data cover 50+ years from the late 1960s through 2010 (enabling the creation of time series and STRs), during which Amboseli has experienced extensive habitat change (Western, 2007), which has likely occurred in any time-averaged fossil assemblage; 3) species turnover in charismatic East African large mammals has been understudied, particularly at the spatiotemporal scale of this study; 4) previous studies have shown high compositional fidelity between the living community and the skeletal assemblage as mentioned before (Behrensmeyer et al., 1979;

Behrensmeyer and Dechant Boaz, 1980; Western and Behrensmeyer, 2009; Miller et al.,

2014); and 5) the time-averaged skeletal nature of these data – along with the fact that many of Amboseli’s congeners and ancestors are found in East African fossil assemblages (Bobe, 2011) – facilitates direct comparisons with the fossil record.

I believe the STAR can be used as an effective tool for enabling comparisons between modern and fossil communities across spatiotemporal scales which differ by orders of magnitude. I first fit multiple STAR models to the Amboseli data and use model selection techniques in order to characterize the functional form of the STAR. I then describe how the STAR model coefficients change as a function of taxonomic scale to investigate how the latter interacts with space and time to influence richness. This is especially relevant since many paleoecological studies are conducted at the genus-level or higher (e.g., Patzkowsky and Holland, 2003; Bobe, 2011). I next estimate scales of

92 time-area equivalence (Adler et al., 2005), which are the spatial and temporal scales at which richness turnover rates are equal, in order to understand the relationship between increasing spatial scale and increasing temporal scale. Finally, I hypothesize what processes might be driving the STAR pattern in order to understand, from a mechanistic basis, how changing spatiotemporal scales influences our interpretation of ecological dynamics. It is my hope that this contribution will convince neo- and paleoecological researchers alike to think more explicitly about scale as a means to conceptually bridge the two fields.

2. Materials and Methods

2.1. Sampling of the Amboseli bone assemblage

2.1.1. Sampling across space

Data on all terrestrial mammal bones analyzed in this study were recorded using

103 noncontiguous transects, which sampled a total area of 8.26 km2. Transects were spaced between 0.07 to 2.29 km apart (median=0.88 km). This amount of spacing is far less than the home range size of the large mammals in this study, so the estimated rate of spatial turnover should be largely unaffected. Transect lengths varied from 0.1 to 6.47 km

(median=0.80 km), while their widths ranged from 0.01 to 0.2 km (median=0.1 km).

Area sampled for each transect was calculated as the product between the two measures

(range=0.002-0.281 km2, median=0.07 km2). Some transects were sampled repeatedly through time but did so using different lengths and widths. To simplify the analyses, I calculated the geometric mean across each transect’s temporal replicates, so there was only one area estimate for each transect. For each transect, observers recorded all bone

93 specimens along with their species identity and whether the bones belonged to one individual or not (Behrensmeyer et al., 1979; Behrensmeyer and Dechant Boaz, 1980).

2.1.2. Sampling through time

The Amboseli bone data were collected intermittently at the end of the long dry season (August-October) (Behrensmeyer, 2007) from 1975 to 2010 (Table 5). To establish a time series, data were binned according to year surveyed as well as the weathering stage of the bones in question (Behrensmeyer, 1978). Weathering stages were first developed to estimate time since death of an individual by visual inspection of the bone’s physical traits (e.g., cracking, flaking) as it progressively weathers and breaks down. Though widely used in many other modern and fossil bone studies (e.g., Miller et al., 2013), weathering stages were originally calibrated on large mammal bones in the

Amboseli ecosystem (Behrensmeyer, 1978), so these age-since-death estimates should be accurate for these analyses. Bones with weathering stages 0-2 are estimated to range from

0 to 6 years since the individual’s death, while weathering stages 3-5 encompass 4-15+ years from death (Behrensmeyer, 1978). Thus, weathering stages allow approximate estimates for when individuals died and what time bins those individuals should be assigned to. Given the variation in time since death in weathering stages (Behrensmeyer,

1978; Lyman and Fox, 1989), binning seemed to be the most appropriate method for establishing robust time groups. Some individuals with long-lasting identifiable skeletal parts (e.g., elephants) may occur in consecutive time bins, but this is unlikely to affect the results in any substantial way. The compilation of weathering stage data resulted in seven time bins, which were more or less contiguous except for the gap between 1976 and

1982. This allowed for the creation of time series that could be used to examine the

94 effects of time and space on species richness. See Table 5 for the time bins used, their respective years surveyed, and the number of transects and area covered in each bin.

2.2. Data treatment and generating area, time, and species richness estimates

Only mammals that could be identified to species were analyzed, though tentative identifications were retained to increase sample size. The only exceptions were those specimens that could not be differentiated between sheep (Ovis aries) and goat (Capra hircus). The rationale for this exception was that these two species often could not be distinguished based on their skeletal features. Moreover, this lumping increases comparability between this and paleoecological studies since these two species are commonly indistinguishable in the fossil record (Zeder and Pilaar, 2010). Small mammal data (<1kg) were excluded because of the empirical size-related bias against their recovery in the Amboseli bone assemblage (Behrensmeyer et al., 1979; Behrensmeyer and Dechant Boaz, 1980; Miller et al., 2014). Only specimens that could be confidently attributed to distinct individuals were retained to prevent double-counting and to ensure comparability between this study and other individual-based STAR studies.

Given the unbalanced nature of this dataset (i.e., different-sized transects which were not uniformly sampled across space and through time), it was necessary to take an iterative approach in the construction of STARs. To this end, SARs were first constructed in each time bin by sequentially aggregating transects. This involved selecting one transect at random and recording the number of species in it and the area of that transect.

Next, the geographically closest transect was added to the original transect, and the number of species and the new aggregated area were again recorded. It was necessary to choose the nearest transect to minimize overestimation of spatial turnover given the large

95 extent and habitat heterogeneity of Amboseli. This process was continued until all possible transects within a time bin were finally aggregated. This entire procedure was repeated n times (where n equals the number of transects in the time bin in question) with a new starting transect each time in order to obtain all possible area combinations along with their species richness estimates. This is similar to the Type IIIA sampling scheme of

Scheiner (2003), except quadrats are not equal-sized.

Once this procedure was done for each individual time bin, I repeated the process using a moving window approach while iteratively increasing the window length by one bin (Adler and Lauenroth, 2003; Adler et al., 2005). For example, for a window of two time bins, I started off by analyzing the 1964-1968 and 1969-1976 bins together and noted which transects sampled both those bins. The iterative SAR procedure from the previous paragraph was then carried out for this two-bin window. The window was then iteratively moved forward by one bin (e.g., 1969-1976 and 1982-1987), each time executing the SAR procedure, which resulted in six replicates for windows of two-bin width. I then increased window width to three bins resulting in five replicates, four bins resulting in four replicates, and so on until I attained one replicate that included all seven time bins. This is the “complete-nested” sampling scheme described by Carey and colleagues (2007), and it emphasizes average scaling of richness with time as opposed to any directional changes in richness, colonization rate, etc. Because I required transects to sample all time bins for a given window size, the number of sampled transects (and thus sampled area) may actually decrease as window size is increased.

These methods resulted in a final dataset with area estimates ranging from one to the total number of transects in each time window, number of year estimates ranging

96 from one time bin to including all seven, and their respective species richness estimates.

For all repeated combinations of area and time, I calculated the geometric mean of species richness, so each unique combination of area and time only had one corresponding richness estimate. Given the method of iterative aggregation both in time and space, these data are non-independent, which violates one of the assumptions of ordinary least squares regression (Draper and Smith, 1998). However, non-independence only affects the calculation of parameter standard error estimates and p-values; the parameter estimates themselves are less efficient but remain unbiased (Draper and Smith,

1998).

2.3. Fitting and comparing different models of spatiotemporal turnover

Following Adler and colleagues (2005), I assessed four models of increasing complexity describing how species accumulate with increasing area and time. The simplest model can be considered a null model where species are shuffled (without replacement) across time bins and transects, and the previously described iterative procedure is carried out for each shuffled iteration. The geometric mean of species richness was calculated for all repeated combinations of area and time, resulting in a single vector of expected species richness. This was repeated 200 times. This random placement model tested whether species accumulation is simply a function of increasing number of individuals with area and time and does not involve non-random (presumably ecological) distributions of individuals across space and/or time.

I also tested three power-law models (Adler et al., 2005), which were fit using ordinary least squares (OLS) with log10-transformed dependent and independent variables. Fitting a power function to SARs, STRs, and STARs is common practice

97

(Williamson, 1988; Rosenzweig, 1995, 1998; McKinney and Frederick, 1999; Hadly and

Maurer, 2001; Adler and Lauenroth, 2003; Adler et al., 2005; White et al., 2006; Raia et al., 2011), and a power scaling relationship is also expected for theoretical reasons

(Preston, 1962a, 1962b; May, 1975; Harte et al., 1999; Ostling et al., 2003; Sizling and

Storch, 2004; Martín and Goldenfeld, 2006). Power functions have also been found to provide optimal fits to SARs (Adler and Lauenroth, 2003; Fridley et al., 2005; Dengler,

2009) and many STRs (Adler and Lauenroth, 2003; White et al., 2006). Furthermore, by following the model-fitting methods of previous researchers, the estimated model coefficients from this study can be directly compared to published ones (Adler et al.,

2005; McGlinn and Palmer, 2009; Raia et al., 2011).

The simplest power-law model is 푙표푔10푆 = 푙표푔10푐 + 푧 푙표푔10퐴푇, where c is an estimated constant, z is the estimated slope (i.e., a measure of turnover [Harte and Kinzig,

1997; Harte et al., 1999; Lennon et al., 2001; Koleff et al., 2003]), A is area, and T is time. This model treats species accumulation as a function of an area x time “volume,” where area and time are assumed to have identical, non-interactive effects on species richness. The next model is 푙표푔10푆 = 푙표푔10푐 + 푧 푙표푔10퐴 + 푤 푙표푔10푇, where z is the species richness rate of increase with area, and w is the rate of increase with time. This model stipulates that area and time have independent, non-interactive effects on richness.

The final, most complex model is one where area and time have independent and interactive effects on richness: 푙표푔10푆 = 푙표푔10푐 + 푧1 푙표푔10퐴 + 푤1 푙표푔10푇 +

푢 (푙표푔10퐴)(푙표푔10푇). z1 is the time-independent rate of richness increase with area at unit time (i.e., one year), w1 is the area-independent rate of increase with time at unit area (i.e., one km2), and u is the interaction parameter. This interactive model is the one that is best

98 supported in a number of taxonomic groups (Jacquemyn et al., 2001; Adler and

Lauenroth, 2003; Adler et al., 2005; McGlinn and Palmer, 2009) and even fossil assemblages (Raia et al., 2011).

To evaluate the fit of each model to the data, I used the Akaike Information

Criterion (AIC). However, because of the non-independent nature of the data, AIC here only served as an ad hoc way to assess model fit and penalize for complexity (i.e., number of parameters) (Adler et al., 2005). To estimate AIC for all models, I first calculated residual sum of squares using the observed and expected richness values from each model. I then calculated AIC assuming a least squares model, where 퐴퐼퐶 =

푅푆푆 푛 ln ( ) + 2퐾, where n equals the total number of data points, RSS equals the residual 푛 sum of squares, and K equals the number of estimated model parameters (Burnham and

Anderson, 2002).

2.4. Spatiotemporal scaling of richness across taxonomic scales

All previously published STAR models were originally fit to species-level data

(as the “S” in “STAR” stands for species). To see how spatiotemporal scaling of richness changes as a function of taxonomic scale, I repeated the moving temporal window and spatial aggregation procedure outlined in “Data treatment” at the genus-, family-, and order-level. Despite the change in taxonomic scale, I keep the STAR acronym for simplicity’s sake. I then fit the best-fit STAR model (previously assessed using AIC) to each dataset. Finally, I compared the estimated model coefficients to see how rates of spatiotemporal turnover vary as a function of taxonomic scale.

2.5. Calculating scales of time-area equivalence

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I calculated scales of time-area equivalence for all four taxonomic scales following Adler and colleagues (Adler et al., 2005). Scales of equivalence are defined as the combination of sampled area and time span where rates turnover are equivalent.

Turnover rates here are relative and not dependent on the unit of measurement. Scales of equivalence are usually presented as ratios and using the estimated parameters from the interaction STAR model, they are calculated as (Adler et al., 2005):

퐴 푧1−푤1 = 10 푢 푇

As an example, a ratio of 4 km2/year implies that the rate of relative temporal turnover in an area of 4 km2 is equivalent to the rate of relative spatial turnover over a one-year period. These ratios enable the comparison of rates of spatial and temporal turnover in a

STAR model while accounting for the interaction term (Adler et al., 2005). They also have obvious implications for the interpretation of time-averaged fossil assemblages.

Knowing the spatial scale at which temporal turnover equals spatial turnover in a time- averaged assemblage informs the relationship between time- and spatial-averaging. This sheds quantitative light on a long-standing issue in paleoecology, i.e., how time- averaging impacts interpretation of species richness measures.

All analyses were done in R version 3.3.1. (R Core Team, 2015).

3. Results

The final analytical dataset includes a total of 3,181 individuals and 35 species.

Each transect within a given time bin records a median of eight individuals and four species. 97 transects were sampled in more than one time bin, and 53 were sampled in at

100 least four (Figure 17). Time window sizes range from 5 to 44 years (median=19 years), and area spans 0.002 to 7.164 km2 (median=2.111 km2). There are 14,717 unique time by area combinations and respective richness estimates (i.e., there are 14,717 data points in all fitted models). Figure 18 shows how each variable is distributed and how they relate to each other.

3.1. Which STAR model fits best?

I fit and evaluated four models of spatiotemporal turnover of species richness

(Table 6). However, determining which model fit the data best is less than straightforward. Unexpectedly, the null random placement model has the best AIC score

(Table 6). This implies that species richness accumulation is merely a function of increasing number of individuals as one expands the temporal and spatial scope of sampling. In other words, the distribution of species across the landscape and through time is random and not due to ecological factors of interest (e.g., habitat filtering, dispersal limitation, etc.).

There are a number of reasons why the null model is expected to fit the data poorly. Previous research has shown that the transition from the sampling to ecological phase in STRs is quite quick and occurs within 1-4 years (White, 2004, 2007; White et al., 2006), an order of magnitude shorter than the time span of this study. Moreover, it has been documented that Amboseli possesses multiple distinct habitats, and these changed dramatically over the bone-sampling period (Western, 2007). Furthermore, the skeletal assemblage was able to faithfully record these temporal changes (Western and

Behrensmeyer, 2009), so my analyses should have been able to detect these ecological shifts. One possible reason for this result is that averaging richness over all possible

101 combinations of area and time can effectively smooth out and dampen the effects of habitat heterogeneity across space and through time (Carey et al., 2007; Harte et al.,

2009).

From a statistical standpoint, the large AIC difference between the random placement and interaction models (the next best-fit model) can be attributed to the large number of data points in the analytical dataset (14,717 points). This large sample size overemphasizes a very small difference in R2 between the two models (Table 6; though the interaction model does have four more free parameters). This is akin to a large- sampled, over-powered statistical test exploiting a small effect size to obtain a significant p-value. Moreover, the lower R2 in the interaction model can be attributed to a mismatch between observed and predicted richness for those data points where observed richness is less than or equal to five species (Figure 19). However, we know from theory (Preston,

1962a, 1962b; May, 1975; Harte et al., 2009) and empirical examples (Williams, 1943;

Preston, 1960; Rosenzweig, 1995, 1998; White, 2004; Fridley et al., 2006) that the SAR and STR are convex-up over very small areas, which can cause richness to be over- predicted at these small scales when using a linear model. Removal of these points by excluding data associated with single time bin windows increases R2 to be greater than that of the random placement model, and coefficient estimates are not appreciably altered

(Table 7). Future analyses should consider using segmented regression models to distinguish the sampling and ecological phases of the STAR (White, 2004; White et al.,

2006).

What is perhaps more telling is the comparison of observed richness to predicted richness from the random placement model (Figure 19). Predicted richness is for the most

102 part consistently greater than observed richness (Figure 19). This is to be expected when observed species exhibit high spatial and/or temporal autocorrelation (i.e., high degree of intraspecific clumping of individuals) (Plotkin et al., 2000; He and Legendre, 2002;

White and Gilchrist, 2007; McGill, 2011). This is because clumping will increase the likelihood that any point in space and time will be comprised of relatively few species, so alpha diversity is low. As a result, richness is over-predicted by a model that assumes no autocorrelation (i.e., random placement).

As a final test of the random sampling model, we can use Fisher’s alpha (Fisher et al., 1943) as a measure of species diversity instead of richness (Rosenzweig, 1995, 1998).

Because Fisher’s alpha is robust to sample size effects (Taylor et al., 1976; Rosenzweig,

1995), alpha is expected to have a negligible increase with area and time if species increased only as a function of number of individuals (i.e., species were randomly distributed across space and time). We can see from Table 7 that this is not the case and that there is “real” ecological spatiotemporal turnover in the Amboseli ecosystem.

Knowing all of this and the fact that the interaction STAR model was the best fit for a number of taxonomically disparate communities (Adler and Lauenroth, 2003; Adler et al., 2005; McGlinn and Palmer, 2009; Raia et al., 2011), I designate the interaction model as the one that best describes the Amboseli data.

3.2. STAR interaction model coefficients

See Table 7 for the estimated coefficients using the full interaction model.

Species-level z1 is greater than w1, and both estimates are within the range found in other communities (Adler and Lauenroth, 2003; Adler et al., 2005; Raia et al., 2011). However, it should be noted that these coefficients are dependent on the units used to measure area

103 and time. The interaction term is negative, a result consistently found in other modern and fossil studies which span many taxonomic groups (Adler and Lauenroth, 2003; Adler et al., 2005; McGlinn and Palmer, 2009; Raia et al., 2011; contra Jacquemyn et al.,

2001). This means the rate of species accumulation with area decreases as the sampling time span increases, and the rate of accumulation with time decreases as the sampling area increases (Figure 20). This is also seen in Figure 21, where z (the rate of spatial species accumulation) as a function of time has the same negative estimate (i.e., -0.14) as w (the temporal rate of species accumulation) as a function of area (i.e., -0.15). This is, by definition, an interaction effect (McGlinn and Palmer, 2009).

Figure 22 and Table 7 show how the interaction model’s coefficient estimates change as a function of taxonomic scale. The intercept (mean log10 richness accumulated

2 over one year and one km ) and z1 (i.e., rate of richness increase as a function of area in a one year time span) monotonically decrease as taxonomic scale increases. A plateau is

2 seen in w1 (i.e., rate of richness increase as a function of time in a one km sampling area) from the species- to family-level, but a noticeable decrease is seen at the order-level. And finally, the magnitude of u (i.e., the interaction term) also steadily decreases as taxonomic scale increases, though the family- and order-level estimates are quite similar.

Figure 23 presents an intuitive way to interpret the effects of sampling area and time on richness. Because of the universal negative interaction term at all taxonomic scales, predicted richness as a function of area and time is always saddle-shaped. That is, richness only monotonically increases as a function of area at smaller time spans and vice versa. An increase in both area and time results in initial richness increases followed by decreases due to the negative interaction term.

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3.3. Ratios of scales of time-area equivalence

Table 7 shows the calculated scales of time-area equivalence ratios for all four taxonomic levels. At the species-level, the ratio is 0.089 km2 per year, which means temporal turnover in 0.089 km2 of space is equal to spatial turnover measured over a single year. One can multiply the ratio by 1,000 to see at what spatial scale temporal turnover is equal to spatial turnover measured over 1,000 years (i.e., the amount of time over which a minimally time-averaged fossil large mammal assemblage is deposited

[Behrensmeyer et al., 2000]). This is equal to 89.5 km2, and 10,000 years of time- averaging is equivalent to 895 km2 (i.e., 1.5 times the study area of Amboseli). This provides some idea of how time-averaging translates into spatial averaging and the scales at which processes across space and through time are analogous (cf., space-for-time substitution studies [Blois et al., 2013]).

The scales of equivalence ratios seem generally to increase as taxonomic scale is increased (Table 7). This means that for a given time span and its respective turnover rate, spatial scale needs to be increased to match said rate as taxonomic scale is increased.

In other words, time-averaging equals greater degrees of spatial averaging as one moves up the taxonomic hierarchy. The only outlier is the family-level ratio which is far higher than what would be expected given the pattern seen in the other three. This is primarily due to the small difference between its z1 and w1 coefficients, which is ultimately attributable to its unusually large w1 coefficient (Figure 22).

4. Discussion

4.1. What mechanisms generate the STAR pattern?

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It has recently been demonstrated that the interactive STAR model and its negative interaction term characterize a number of taxonomically disparate communities, ranging from algae to invertebrates to small mammals (Adler and Lauenroth, 2003; Adler et al., 2005; McGlinn and Palmer, 2009) and even large fossil mammals (Raia et al.,

2011). Now, the large mammal community from Amboseli’s skeletal assemblage can be added to the list. The generality of these STAR patterns is impressive and suggests a common, underlying phenomenon.

The key question is what causes a decrease in the rate of spatial (or temporal) turnover as time (or area) increases? Recalling the form of the triphasic SAR/STR

(explained in Introduction), the first two phases exhibit a convex-up then linear relationship in log-log space (Brown, 1995; Rosenzweig, 1995; White, 2004). Given a

(relatively) static species pool, this functional form is exactly what one would expect: as sampled richness approaches the size of the species pool by increasing either spatial or temporal scale, the rate of species accumulation decreases (Preston, 1960; Lennon et al.,

2001; Fridley et al., 2006; White, 2007; Harte et al., 2009) due to a diminishing supply of species from the pool (Figure 9A; McGlinn and Palmer, 2009; Tomašových and Kidwell,

2010a). More precisely, the relative rate of turnover decreases: a smaller percentage of new species is being discovered relative to the growing number of sampled species

(White, 2007). This phenomenon may also explain why the relative rate of species accumulation decreases as local richness increases (Rosenzweig, 1995; Lyons and Willig,

2002; Ulrich, 2006; White et al., 2006; White, 2007).

These patterns suggest that space and time have analogous effects on how richness accumulates (for example, see Fig. 3 in McKinney and Frederick, 1999). A

106 researcher can either increase area to sample new species, or because species move across the landscape, sample for a longer period and wait for the species to arrive at the sampling site. This is akin to how geologists think about depositional facies in time and space. If one focuses on a given site, the lateral movement over time of depositional environments across that site leads to the deposition of a vertical succession of facies that corresponds to laterally adjacent environments, i.e., Walther’s Law (Middleton, 1973).

This is virtually identical to how Preston introduced his reasoning for equating the dynamics of the STR to that of the SAR (Preston, 1960; McKinney and Frederick, 1999).

Furthermore, species that occasionally disperse into a site over time are viewed as being ill-adapted to that site and not being able to sustain viable populations there (i.e., transient or occasional species sensu Magurran and Henderson, 2003). These patterns also describe sink species, which migrate from a source community (where they are presumably well- adapted to the environment and where they have positive population growth rates) to a sink community, where they exhibit long-term, negative growth rates (Pulliam, 1988).

Therefore, one would predict increased regional heterogeneity would create more source communities, from which sink species can migrate into a focal site causing increased temporal turnover (White et al., 2010). This has important implications for the maintenance of biodiversity in the present (and future), which is experiencing a trend towards increased homogenization (McKinney and Lockwood, 1999; Rahel, 2000; La

Sorte and Boecklen, 2005; Tóth et al., 2014). That these two temporal and spatial paradigms are essentially describing the same process further demonstrates a link between space and time (White et al., 2010; Supp et al., 2015). Therefore, spatial and temporal species accumulation do not only have to decrease as a function of time and

107 space, respectively. Because decreasing accumulation rates are driven by increasing scale and a relatively static species pool, spatial (or temporal) accumulation rates can also decrease as a function of increasing area (or time) (Harte et al., 2009). This, again, describes the shape of the first two phases of the triphasic SAR (and presumably, STR).

Knowing all this, it is then worth exploring how species are distributed across space and through time to see which species are being sampled and in what order.

Most species in a community are numerically rare (McGill et al., 2007). Species abundance is positively correlated with both temporal (Williams, 1964; Guo et al., 2000;

Magurran and Henderson, 2003; Magurran, 2007; Dolan et al., 2009) and spatial occupancy (as well as geographic range size) (Hanski, 1982; Brown, 1984; Gaston et al.,

2000; Guo et al., 2000; Yu and Dobson, 2000; Gaston and He, 2011). Occupancy is here defined as the number of time periods or spatial sites in a study that a species occupies

(Hercos et al., 2013). In addition, it has been shown that temporal and spatial occupancy are themselves correlated (Guo et al., 2000; Hadly and Maurer, 2001; Hercos et al.,

2013). In other words, common species are common across space and through time and vice versa for rare species (McGill, 2011). Moreover, the distribution of species in spatial and temporal “sites” is nested (Hadly and Maurer, 2001). That is, those “sites” with low richness are dominated by widespread species, whereas species-rich “sites” include both widespread and restricted species (Atmar and Patterson, 1993). The similarity of these macroecological patterns in time and space again emphasize how the two have similar effects on species diversity (Preston, 1960; McKinney and Frederick, 1999; Magurran,

2007). This similarity may permit the use of spatial stochastic geometric models (McGill,

2010) to predict diversity accumulation with increasing temporal scale. Or, a temporal

108 dimension may be added to these spatial models in order to predict diversity across a wide range of spatiotemporal scales.

Following from these patterns, species accumulation through time and space proceeds by first sampling the most common species in the species pool, followed by progressively rarer species as the scale of analysis is increased (Preston, 1948). After taking iteratively larger, nested (i.e., autocorrelated) samples at larger scales, the rare species tail of a sampled species abundance distribution is inflated, thus increasing community evenness (McGill, 2003; Tomašových and Kidwell, 2010a, 2010b). This is ecologically interesting because ecological traits are non-randomly distributed across abundance classes. As alluded to previously, abundant and temporally persistent species are more adapted to the local habitat, maintain viable populations there, and experience density-dependent regulation (i.e., the core-transient paradigm; Magurran and Henderson,

2003; Coyle et al., 2013; Henderson and Magurran, 2014; Supp et al., 2015). Conversely, rare and temporally intermittent species’ diversity is controlled by regional environmental heterogeneity and subsequent dispersal to the focal site (Coyle et al., 2013). The same patterns are seen across space where large-ranged species’ richness is driven by productivity, whereas narrow-ranged species’ richness is better explained by habitat and topographic heterogeneity (Jetz and Rahbek, 2002; Ruggiero and Kitzberger, 2004; Kreft et al., 2006; Rahbek et al., 2007). Similarly, Ulrich and Zalewski (2006) have found that the distribution of beetle species with high spatial occupancy values is driven by interspecific interactions and niche division (i.e., density-dependent processes), whereas the distribution of species with low occupancy values is determined by random dispersal.

In sum, because rare species are more influenced by regional factors and dispersal and

109 are preferentially accumulated with increasing scale, larger-scale communities will exhibit a stronger regional ecological signal. This is borne out by studies which show regional drivers have a stronger effect on richness when time scale is increased (White and Hurlbert, 2010). Moreover, community patterns will approach that of the regional species pool with increased amounts of time-averaging (Tomašových and Kidwell, 2009,

2010a, 2010b).

The negative interaction term in the Amboseli STAR model suggests these processes might be occurring in the Amboseli ecosystem. One way to test this hypothesis is to test each of the independent predictions put forth (Rosenzweig and Abramsky,

1997). For example, is species abundance correlated with spatial and temporal occupancy in Amboseli, and are these two measures themselves correlated? Is the distribution of species across space and through time significantly nested? One can also see whether the order of species accumulation reflects a progression towards rarer species, and if common and rare species have different ecological correlates of richness.

4.2. Implications of taxonomic averaging

Taxonomic averaging (i.e., moving up the taxonomic hierarchy) also decreases richness turnover but for different reasons (Flessa, 1975; McGill et al., 2005). Instead of uncovering more of the species pool, taxonomic-averaging aggregates taxa due to the nested nature of the taxonomic hierarchy. This effectively decreases the number of taxa in any given sample and in the “species” pool, and the rate at which new taxa are encountered correspondingly decreases as time and/or area is increased (Figure 24). As a result, mean richness (i.e., the intercept) and turnover rate at unit time and area (z1 and w1, respectively) decrease with increased taxonomic-averaging (Table 7; Figure 22;

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Figure 24). The interaction term at all taxonomic levels is still negative because more of the taxon pool is still being sampled as scale increases. The magnitude of the negative interaction term decreases with increasing taxonomic scale (Table 7; Figure 22) because rates of richness accumulation decrease and the size of the taxon pool is reduced (due to the aggregation of taxonomic units) (Figure 24). So even though taxonomic averaging causes turnover rates to decrease for a different reason than increasing spatial or temporal scale, the effects are still the same, and this must be kept in mind when specifying the scales of one’s study.

This has important implications for paleoecological studies, since most are done at the genus-level or higher, including those studies that look at SARs and STRs in the fossil record (e.g., Sclafani and Holland, 2013). Given the effects of taxonomic-averaging on estimates of richness turnover rates, these results should not be compared to those of modern SAR/STR studies unless the latter are conducted at the same taxonomic scale.

4.3. Spatiotemporal scaling of richness in fossil assemblages

Time-averaging roughly corresponds to spatial averaging of ecological communities. Because all fossil communities exhibit some degree of time-averaging, this becomes problematic when trying to infer small-scale patterns and processes using fossil assemblages (e.g., ancient habitat reconstruction, interspecific interactions, etc., though the same can be said of modern species lists, which are accumulated over many years, if not decades). Fossil patterns other than diversity must be studied in order to address these smaller-scale questions (e.g., individual-based proxies such as stable isotope analyses and dental wear, though these data can become time-averaged as well if non-

111 contemporaneous samples are combined). Alternatively, modeling of small-scale processes can be up-scaled to match the time scales observed in the fossil record

On the other hand, it is still useful to think about these smaller-scale questions in terms of larger-scale averages. For example, it is informative to know whether ancient hominins were more abundant in one time-averaged environment that was on average more arid than another. In fact, a first-order explanation for the preponderance of hominin environments being classified as “mosaic” (Reynolds et al., 2015) is likely due to time-averaged fossil assemblages spatially averaging multiple habitats. Furthermore, time-averaged fossil assemblages allow researchers to ask questions that may not be easily addressed with modern community studies (e.g., regional scale processes, metacommunity turnover). Understanding the amount of spatial averaging involved in a time-averaged fossil assemblage can be accomplished by calculating scales of time-area equivalence (Adler et al., 2005). These scales of equivalence identify the spatial and temporal scales at which rates of turnover are roughly equivalent. See Table 7 for the scales of equivalence calculated using the Amboseli data at different taxonomic scales.

In modern ecology, one assumes a static species pool, which is not unreasonable given the short time scale of these studies. Nevertheless, I have proposed that the negative interaction term in the STAR model is primarily caused by diminishing returns as one continuously samples a static species pool. On longer time scales, however, one needs to account for the fact that the species pool is likely evolving and responding to large-scale climatic shifts. Depending on rates of speciation and climatic change, one might assume that the rate of species pool turnover is proportional to or exceeds the rate at which it is sampled due to increasing scale (Figure 24). As a result, the relationship

112 between scale and richness would be linear or concave-up, much like the third phase of the SAR (Preston, 1960; Rosenzweig, 1998). This is a ripe area for future research.

4.4. Predictions of richness in fossil assemblages

It is clear that taxonomic richness is sensitive to the scale at which it is measured.

One cannot only account for differences in area, time span, or taxonomic level, but must bear in mind all three. The present study attempts to do so by using the time-averaged

Amboseli skeletal assemblage as a “scale-bridge” to connect small scales in modern communities to large scales found in the fossil record. Researchers can take the observed spatiotemporal and taxonomic scales characterizing a fossil assemblage and extrapolate the interactive STAR model to see how predicted richness compares to observed richness

(e.g., Figure 23) (assuming that taphonomic biases affecting taxonomic representation are adequately accounted for). However, scale extrapolation should not be too extreme since the negative interaction term ensures richness will decrease at very large spatiotemporal scales, which is counterintuitive (Figure 8; White et al., 2010). Otherwise, if fossil richness is under-predicted by the STAR model, this would parsimoniously suggest that the current model does not take into account richness generated on evolutionary time scales (and inter-provincial spatial scales if the fossil study’s spatial scale is large enough). This may be informative, however, as the deficit between predicted and observed richness may tell us something about the rate at which evolutionary processes generate richness given the temporal scale of one’s fossil study (i.e., the shape of the third phase of the STR). Future research should attempt to build STAR models at biogeographic spatial and evolutionary time scales. An alternative explanation for under- predicted richness is that the rate of spatial and/or temporal ecological turnover in the

113 past was higher than it is today. Over-predicted richness would suggest the opposite.

Either way, this would indicate that the past was different in terms of spatial and temporal controls on species richness. Agreement between observed and predicted research would suggest spatiotemporal turnover is the same today as it was in the past (but it does not necessarily prove it). Thus, the STAR model presents an informative baseline to which richness of fossil communities can be compared.

5. Conclusions

It has been previously established across a wide range of ecosystems that the rate of species accumulation across space and through time decreases as a function of increasing temporal and spatial scale, respectively. Species turnover rates in the

Amboseli skeletal assemblage show the same pattern with model coefficient estimates in the range of published ones. The interactive species-time-area model demonstrates that space and time have analogous, complementary effects on how richness accumulates with growing scale. It is hypothesized that decreasing rates of turnover with increasing (spatial or temporal) scale is caused by progressive sampling of a relatively static species pool.

Rarer species become incorporated into one’s sample as the pool is more completely sampled with increasing scale. And because the richness of spatially and temporally rare species seems to be driven by more regional factors, large-scale communities will mostly exhibit a coarse, regional-scale ecological signal. This may seem redundant and intuitive for spatially large communities, but it has implications for using time-averaged fossil assemblages to address local-scale ecological questions (e.g., ancient habitat reconstructions and interspecific interactions). The relationship of space and time to each

114 other and their joint effect on diversity need more research to understand how the latter is affected mechanistically by the former. Increasing taxonomic scale also results in corresponding decreases in richness turnover rates, although this has less to do with increased sampling of the taxon pool and more to do with aggregating lower-level taxonomic units into coarser, higher-level ones. Nevertheless, the effect is analogous to increasing spatial and/or temporal scale, so researchers must be cognizant of all three types of scales when studying biodiversity patterns. By fitting a species-time-area model to describe how richness scales as a function of space and time, we can quantify the scales of our datasets and compare modern and fossil communities that differ across orders of magnitude of scale. This will enable exchange of theory and method between the two fields to enable a more comprehensive study of ecology at all scales.

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Figures

Figure 16. Map of the Kenyan-Tanzanian border showing the location of Amboseli

National Park (black polygon) and surrounding basin (solid line). From Miller and colleagues (2014).

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Figure 17. Number of sampled transects for each time window length. For example, 12 transects sample all seven time bins.

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Figure 18. Summary scatterplot matrix of the variables in the main analytical dataset.

Numbers in the upper triangle are Pearson correlation coefficients. Area is in km2, and time is in years. “# sp.” is species richness, and “# ind.” is number of individuals.

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Figure 19. Scatterplots showing model fits for each of the four different STAR models

(see Table 6). Predicted richness from the OLS models are plotted as a function of observed richness. The solid red lines represent the line of unity. Note that both axes are log-transformed.

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Figure 20. A) Species richness as a function of time with points color-coded by binned area estimates. Points are jittered, but there is still plenty of over-plotting due to the discrete nature of the independent variable (i.e., time). B) Species richness as a function of area with points color-coded by binned time estimates. The four regression lines in each plot are model fits from the interaction STAR model. Note how the regression lines’ intercepts and slopes increase and decrease, respectively, as the third variable (area in (A) and time in (B)) increases.

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Figure 21. A) z power-law coefficients plotted as a function of sampling time span. Each z coefficient was calculated using OLS where log10 species richness was modeled as a function of log10 area for each unique sampling time span. B) w power-law coefficients plotted as a function of area. Each w coefficient was calculated using OLS where log10 species richness was modeled as a function of log10 time for each unique area estimate.

Because area is a continuous variable, data were aggregated into discrete area estimates for plotting purposes only. Note the logarithmic x-axes for both plots.

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Figure 22. The interaction STAR model’s coefficient estimates as a function of taxonomic scale. See Table 7 for exact coefficient estimates. z1 is the rate at which log10 species richness scales with log10 area at the unit time span (when log10(time) = 0, i.e., 1 year). w1 is the rate at which log10 species richness scales with log10 time at unit area

2 (when log10(area) = 0, i.e., 1 km ). u is the interaction term between log10 area and log10 time.

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Figure 23. Contour plots showing predicted richness as a function of area and time at different taxonomic scales. The dotted red box in each plot represents the spatial and temporal scales at which the Amboseli data were collected. Note both axes are log- transformed.

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Figure 24. Schematic diagrams illustrating how progressive sampling of the species pool results in the coefficients seen in the STAR model. Even though richness is plotted here as a function of area with time as the third variable, the same logic would apply to a plot of richness as a function of time with area as the third variable. Progressively darker shades of gray represent an increase in scale of the third variable (which here is time). A)

The static species pool (large black dot) provides a hard limit on the number of species that can be accumulated in a sample with increasing scale (area or time). At the smallest quadrat size (represented by the small dots), an increase in time span results in a greater

124 number of species (i.e., the w1 coefficient is positive), which in turn displaces the starting point upwards on the plot. A line connecting a higher starting point to a fixed point on the right (i.e., the species pool) will result in a line with a shallower slope. In other words, the rate of richness increase decreases (i.e., the STAR interaction term is negative). B) The same plot but at a higher taxonomic level (which here is family). Due to the aggregation of taxa as taxonomic scale is coarsened, there are less unique taxa that can be recorded in any given sample. Comparing Figure 24B to 9A, this results in an overall downward shift of starting points (smaller intercept values), and smaller upward displacements as time is increased (smaller w1 coefficients). The latter can be visually seen as the starting points are vertically closer together in Figure 24B compared to Figure 24A. Because of this and a smaller family pool compared to the species pool (again due to taxonomic aggregation), the rate at which the line shallows as time increases is reduced compared to the species- level STAR. This results in a smaller-magnitude, negative interaction term. C) The interaction term between time and area may be zero or positive if the species pool is turning over due to speciation, large-scale climatic shifts, and/or other rare, large- magnitude events (e.g., the formation of a land bridge connecting two evolutionarily isolated regions). This is similar to the third phase of the SAR and STR where the rate of richness accumulation with area (or time) increases as sampled area (or time) increases.

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Table 5. Summary table of the time bins used in this study along with information on their respective areal coverage. “Back-censusing” using bone weathering stages provides samples for the time bins prior to 1975, when bone surveys began (Behrensmeyer, 1978;

Western and Behrensmeyer, 2009).

Time bins Years surveyed Number of Area covered by transects transects (km2) 1964-1968 1975, 1976, 1977 81 7.12 1969-1976 1975, 1976, 1977 88 7.16 1982-1987 1990, 1993 32 2.45 1988-1993 1990, 1993 34 2.54 1993-1998 2002, 2003, 2004 44 2.68 1999-2006 2002, 2003, 2004, 2010 53 3.34 2006-2010 2010 29 1.75

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Table 6. The four STAR models analyzed in this study. K is number of parameters in each model. ΔAIC is the difference in AIC scores between the model in question and the best fit model. The best fit model has a ΔAIC of zero, and progressively worse models have higher ΔAIC scores.

Model Formula K ΔAIC Multiple R2 Random NA 0 0.000 0.777 sampling model “Volume” 푙표푔10푆 = 푙표푔10푐 + 푧 푙표푔10퐴푇 2 751.605 0.765 model No interaction 푙표푔10푆 = 푙표푔10푐 + 푧 푙표푔10퐴 + 푤 푙표푔10푇 3 740.133 0.766 model Interaction 푙표푔10푆 = 푙표푔10푐 + 푧1 푙표푔10퐴 + 푤1 푙표푔10푇 4 229.134 0.774 model + 푢 (푙표푔10퐴)(푙표푔10푇)

127

Table 7. Number of taxa, model coefficient estimates, and calculated scales of equivalence for the interaction STAR model at different taxonomic levels. The rationale for including variants of the species-level models is explained in the main text. z1 is the rate at which log10 species richness scales with log10 area at the unit time span (when log10(time) = 0, i.e., 1 year). w1 is the rate at which log10 species richness scales with

2 log10 time at unit area (when log10(area) = 0, i.e., 1 km ). u is the interaction term between log10 area and log10 time.

Taxonomic scale Number Intercept z1 w1 u Multiple Ratios of of taxa R2 scales of equivalence (km2/year) Species 35 0.835 0.495 0.328 -0.159 0.774 0.089 Species (without 35 0.823 0.467 0.349 -0.126 0.781 0.115 single time bin points) Species (using 35 3.721 1.271 0.418 -0.396 0.178 NA Fisher’s alpha) Genus 30 0.792 0.456 0.329 -0.132 0.754 0.108 Family 14 0.523 0.379 0.348 -0.082 0.637 0.422 Order 6 0.406 0.268 0.205 -0.077 0.569 0.150

128

References

Adler, P.B., Lauenroth, W.K., 2003. The power of time: spatiotemporal scaling of species

diversity. Ecology Letters. 6, 749–756.

Adler, P.B., White, E.P., Lauenroth, W.K., Kaufman, D.M., Rassweiler, A., Rusak, J.A.,

2005. Evidence for a general species-time-area relationship. Ecology. 86, 2032–

2039.

Allen, A.P., White, E.P., 2003. Effects of range size on species–area relationships.

Evolutionary Ecology Research. 5, 493–499.

Arrhenius, O., 1921. Species and Area. Journal of Ecology. 9, 95–99.

Atmar, W., Patterson, B.D., 1993. The measure of order and disorder in the distribution

of species in fragmented habitat. Oecologia. 96, 373–382.

Barnosky, A.D., Carrasco, M.A., Davis, E.B., 2005. The Impact of the Species–Area

Relationship on Estimates of Paleodiversity. PLoS Biology. 3, e266.

Behrensmeyer, A., 1993. The bones of Amboseli: bone assemblages and ecological

change in a modern African ecosystem. National Geographic Research. 9, 402–

421.

Behrensmeyer, A.K., 1978. Taphonomic and ecologic information from bone weathering.

Paleobiology. 150–162.

Behrensmeyer, A.K., 2007. Changes through time in carcass survival in the Amboseli

ecosystem, southern Kenya. In: Pickering, T.R., Schick, K., Toth, N. (Eds.),

Breathing Life into Fossils: Taphonomic Studies in Honor of CK (Bob) Brain,

Stone Age Institute Publication Series. Stone Age Institute Press, Gosport,

Indiana, pp. 135–160.

129

Behrensmeyer, A.K., Dechant Boaz, D., 1980. The recent bones of Amboseli Park Kenya

in relation to East African paleoecology. In: Fossils in the Making: Vertebrate

Taphonomy and Paleoecology. University of Chicago Press, Chicago, pp. 72–92.

Behrensmeyer, A.K., Kidwell, S.M., Gastaldo, R.A., 2000. Taphonomy and

Paleobiology. Paleobiology. 26, 103–147.

Behrensmeyer, A.K., Western, D., Boaz, D.E.D., 1979. New Perspectives in Vertebrate

Paleoecology from a Recent Bone Assemblage. Paleobiology. 5, 12–21.

Bell, G., 1989. A Comparative Method. The American Naturalist. 133, 553–571.

Blois, J.L., Williams, J.W., Fitzpatrick, M.C., Jackson, S.T., Ferrier, S., 2013. Space can

substitute for time in predicting climate-change effects on biodiversity.

Proceedings of the National Academy of Sciences. 110, 9374–9379.

Bobe, R., 2011. Fossil Mammals and Paleoenvironments in the Omo-Turkana Basin.

Evolutionary Anthropology: Issues, News, and Reviews. 20, 254–263.

Brown, J.H., 1984. On the relationship between abundance and distribution of species.

American Naturalist. 124, 255–279.

Brown, J.H., 1995. Macroecology. University of Chicago Press, Chicago.

Brown, J.H., Ernest, S.K.M., Parody, J.M., Haskell, J.P., 2001. Regulation of diversity:

maintenance of species richness in changing environments. Oecologia. 126, 321–

332.

Brown, J.H., Gupta, V.K., Li, B.-L., Milne, B.T., Restrepo, C., West, G.B., 2002. The

fractal nature of nature: power laws, ecological complexity and biodiversity.

Philosophical Transactions of the Royal Society B: Biological Sciences. 357,

619–626.

130

Burnham, K.P., Anderson, D.R., 2002. Model selection and multimodel inference: a

practical information-theoretic approach, 2nd ed. ed. Springer, New York.

Carey, S., Ostling, A., Harte, J., Moral, R. del, 2007. Impact of curve construction and

community dynamics on the species-time relationship. Ecology. 88, 2145–2153.

Coleman, B.D., 1981. On random placement and species-area relations. Mathematical

Biosciences. 54, 191–215.

Coyle, J.R., Hurlbert, A.H., White, E.P., 2013. Opposing Mechanisms Drive Richness

Patterns of Core and Transient Bird Species. The American Naturalist. 181, E83–

E90.

Dengler, J., 2009. Which function describes the species–area relationship best? A review

and empirical evaluation. Journal of Biogeography. 36, 728–744.

DiMichele, W.A., Behrensmeyer, A.K., Olszewski, T.D., Labandeira, C.C., Pandolfi,

J.M., Wing, S.L., Bobe, R., 2004. Long-Term Stasis in Ecological Assemblages:

Evidence from the Fossil Record*. Annual Review of Ecology, Evolution, and

Systematics. 35, 285–322.

Dolan, J.R., Ritchie, M.E., Tunin-Ley, A., Pizay, M.-D., 2009. Dynamics of core and

occasional species in the marine plankton: tintinnid ciliates in the north-west

Mediterranean Sea. Journal of Biogeography. 36, 887–895.

Draper, N.R., Smith, H., 1998. Applied regression analysis, 3rd ed. ed, Wiley series in

probability and statistics. Wiley, New York.

Enquist, B.J., Jordan, M.A., Brown, J.H., 1995. Connections between ecology,

biogeography, and paleobiology: Relationship between local abundance and

131

geographic distribution in fossil and recent molluscs. Evolutionary Ecology. 9,

586–604.

Fisher, R.A., Corbet, A.S., Williams, C.B., 1943. The relation between the number of

species and the number of individuals in a random sample of an animal

population. The Journal of Animal Ecology. 42–58.

Flessa, K.W., 1975. Area, Continental Drift and Mammalian Diversity. Paleobiology. 1,

189–194.

Fridley, J.D., Peet, R.K., van der Maarel, E., Willems, J.H., Flather, A.E.C.H., Losos,

E.J.B., 2006. Integration of Local and Regional Species‐Area Relationships from

Space‐Time Species Accumulation. The American Naturalist. 168, 133–143.

Fridley, J.D., Peet, R.K., Wentworth, T.R., White, P.S., 2005. Connecting Fine- and

Broad-Scale Species–Area Relationships of Southeastern U.s. Flora. Ecology. 86,

1172–1177.

Gaston, K.J., Blackburn, T.M., Greenwood, J.J.D., Gregory, R.D., Quinn, R.M., Lawton,

J.H., 2000. Abundance-occupancy relationships. Journal of Applied Ecology. 37,

39–59.

Gaston, K.J., He, F., 2011. Species occurrence and occupancy. In: Maguran, A.E.,

McGill, B.J. (Eds.), Biological Diversity: Frontiers in Measurement and

Assessment. Oxford University Press, Oxford, UK, pp. 141–151.

Gotelli, N.J., Colwell, R.K., 2001. Quantifying biodiversity: procedures and pitfalls in the

measurement and comparison of species richness. Ecology Letters. 4, 379–391.

Grinnell, J., 1922. The Role of The “Accidental.” The Auk. 39, 373–380.

Guo, Q., Brown, J.H., Valone, & T.J., 2000. Abundance and distribution of desert

132 annuals: are spatial and temporal patterns related? Journal of Ecology. 88, 551–560.

Hadly, E.A., Maurer, B.A., 2001. Spatial and temporal patterns of species diversity in

montane mammal communities of western North America. Evolutionary Ecology

Research. 3, 449–463.

Hanski, I., 1982. Dynamics of Regional Distribution: The Core and Satellite Species

Hypothesis. Oikos. 38, 210–221.

Harnik, P.G., Simpson, C., Payne, J.L., 2012. Long-term differences in extinction risk

among the seven forms of rarity. Proceedings of the Royal Society B: Biological

Sciences. 279, 4969–4976.

Harte, J., Kinzig, A.P., 1997. On the Implications of Species-Area Relationships for

Endemism, Spatial Turnover, and Food Web Patterns. Oikos. 80, 417.

Harte, J., McCarthy, S., Taylor, K., Kinzig, A., Fischer, M.L., 1999. Estimating Species-

Area Relationships from Plot to Landscape Scale Using Species Spatial-Turnover

Data. Oikos. 86, 45.

Harte, J., Smith, A.B., Storch, D., 2009. Biodiversity scales from plots to biomes with a

universal species-area curve. Ecology Letters. 12, 789–797.

He, F., Legendre, P., 1996. On Species-Area Relations. The American Naturalist. 148,

719–737.

He, F., Legendre, P., 2002. Species Diversity Patterns Derived from Species–Area

Models. Ecology. 83, 1185–1198.

Henderson, P.A., Magurran, A.E., 2014. Direct evidence that density-dependent

regulation underpins the temporal stability of abundant species in a diverse animal

133

community. Proceedings of the Royal Society B: Biological Sciences. 281,

20141336–20141336.

Hercos, A.P., Sobansky, M., Queiroz, H.L., Magurran, A.E., 2013. Local and regional

rarity in a diverse tropical fish assemblage. Proc. R. Soc. B. 280, 20122076.

Hubbell, S.P., 2001. The unified neutral theory of biodiversity and biogeography,

Monographs in Population Biology. Princeton University Press, Princeton.

Jablonski, D., Sepkoski, J.J., 1996. Paleobiology, Community Ecology, and Scales of

Ecological Pattern. Ecology. 77, 1367–1378.

Jacquemyn, H., Butaye, J., Hermy, M., 2001. Forest plant species richness in small,

fragmented mixed deciduous forest patches: the role of area, time and dispersal

limitation: Plant species richness in small, fragmented forests. Journal of

Biogeography. 28, 801–812.

Jetz, W., Rahbek, C., 2002. Geographic Range Size and Determinants of Avian Species

Richness. Science. 297, 1548–1551.

Koleff, P., Gaston, K.J., Lennon, J.J., 2003. Measuring beta diversity for presence-

absence data. Journal of Animal Ecology. 72, 367–382.

Kreft, H., Sommer, J.H., Barthlott, W., 2006. The significance of geographic range size

for spatial diversity patterns in Neotropical palms. Ecography. 29, 21–30.

La Sorte, F.A., Boecklen, W.J., 2005. Temporal turnover of common species in avian

assemblages in North America. Journal of Biogeography. 32, 1151–1160.

Lennon, J.J., Koleff, P., Greenwood, J.J.D., Gaston, K.J., 2001. The geographical

structure of British bird distributions: diversity, spatial turnover and scale. Journal

of Animal Ecology. 70, 966–979.

134

Levin, S.A., 1992. The Problem of Pattern and Scale in Ecology: The Robert H.

MacArthur Award Lecture. Ecology. 73, 1943–1967.

Liow, L.H., Reitan, T., Harnik, P.G., 2015. Ecological interactions on macroevolutionary

time scales: clams and brachiopods are more than ships that pass in the night.

Ecology Letters. 18, 1030–1039.

Lyman, R.L., Fox, G.L., 1989. A critical evaluation of bone weathering as an indication

of bone assemblage formation. Journal of Archaeological Science. 16, 293–317.

Lyons, S.K., Amatangelo, K.L., Behrensmeyer, A.K., Bercovici, A., Blois, J.L., Davis,

M., DiMichele, W.A., Du, A., Eronen, J.T., Tyler Faith, J., Graves, G.R., Jud, N.,

Labandeira, C., Looy, C.V., McGill, B., Miller, J.H., Patterson, D., Pineda-

Munoz, S., Potts, R., Riddle, B., Terry, R., Tóth, A., Ulrich, W., Villaseñor, A.,

Wing, S., Anderson, H., Anderson, J., Waller, D., Gotelli, N.J., 2016. Holocene

shifts in the assembly of plant and animal communities implicate human impacts.

Nature. 529, 80–83.

Lyons, S.K., Willig, M.R., 2002. Species Richness, Latitude, and Scale-Sensitivity.

Ecology. 83, 47–58.

Magurran, A.E., 2007. Species abundance distributions over time. Ecology Letters. 10,

347–354.

Magurran, A.E., Henderson, P.A., 2003. Explaining the excess of rare species in natural

species abundance distributions. Nature. 422, 714–716.

Martín, H.G., Goldenfeld, N., 2006. On the origin and robustness of power-law species–

area relationships in ecology. Proceedings of the National Academy of Sciences.

103, 10310–10315.

135

May, R.M., 1975. Patterns of species abundance and diversity. In: Cody, M.L., Diamond,

J.M. (Eds.), Ecology and Evolution of Communities. Harvard University Press,

Cambridge, pp. 81–120.

McGill, B.J., 2003. Does Mother Nature really prefer rare species or are log-left-skewed

SADs a sampling artefact? Ecology Letters. 6, 766–773.

McGill, B.J., 2010. Towards a unification of unified theories of biodiversity: Towards a

unified unified theory. Ecology Letters. 13, 627–642.

McGill, B.J., 2011. Linking biodiversity patterns by autocorrelated random sampling.

American Journal of Botany. 98, 481–502.

McGill, B.J., Dornelas, M., Gotelli, N.J., Magurran, A.E., 2015. Fifteen forms of

biodiversity trend in the Anthropocene. Trends in Ecology & Evolution. 30, 104–

113.

McGill, B.J., Etienne, R.S., Gray, J.S., Alonso, D., Anderson, M.J., Benecha, H.K.,

Dornelas, M., Enquist, B.J., Green, J.L., He, F., Hurlbert, A.H., Magurran, A.E.,

Marquet, P.A., Maurer, B.A., Ostling, A., Soykan, C.U., Ugland, K.I., White,

E.P., 2007. Species abundance distributions: moving beyond single prediction

theories to integration within an ecological framework. Ecology Letters. 10, 995–

1015.

McGill, B.J., Hadly, E.A., Maurer, B.A., 2005. Community inertia of Quaternary small

mammal assemblages in North America. Proceedings of the National Academy of

Sciences. 102, 16701–16706.

McGlinn, D.J., Palmer, M.W., 2009. Modeling the sampling effect in the species–time–

area relationship. Ecology. 90, 836–846.

136

McKinney, M.L., Frederick, D.L., 1999. Species–time curves and population extremes:

ecological patterns in the fossil record. Evolutionary Ecology Research. 1, 641–

650.

McKinney, M.L., Lockwood, J.L., 1999. Biotic homogenization: a few winners replacing

many losers in the next mass extinction. Trends in Ecology & Evolution. 14, 450–

453.

Middleton, G.V., 1973. Johannes Walther’s law of the correlation of facies. Geological

Society of America Bulletin. 84, 979–988.

Miller, J.H., Behrensmeyer, A.K., Du, A., Lyons, S.K., Patterson, D., Tóth, A.,

Villaseñor, A., Kanga, E., Reed, D., 2014. Ecological fidelity of functional traits

based on species presence-absence in a modern mammalian bone assemblage

(Amboseli, Kenya). Paleobiology. 40, 560–583.

Miller, J.H., Druckenmiller, P., Bahn, V., 2013. Antlers on the Arctic Refuge: capturing

multi-generational patterns of calving ground use from bones on the landscape.

Proceedings of the Royal Society B: Biological Sciences. 280, 20130275–

20130275.

Ostling, A., Harte, J., Green, J. l., Kinzig, A. p., 2003. A community-level fractal

property produces power-law species-area relationships. Oikos. 103, 218–224.

Patzkowsky, M.E., Holland, S.M., 2003. Lack of community saturation at the beginning

of the Paleozoic plateau: the dominance of regional over local processes.

Paleobiology. 29, 545–560.

137

Plotkin, J.B., Potts, M.D., Leslie, N., Manokaran, N., Lafrankie, J., Ashton, P.S., 2000.

Species-area Curves, Spatial Aggregation, and Habitat Specialization in Tropical

Forests. Journal of Theoretical Biology. 207, 81–99.

Preston, F.W., 1948. The Commonness, And Rarity, of Species. Ecology. 29, 254–283.

Preston, F.W., 1960. Time and Space and the Variation of Species. Ecology. 41, 611–

627.

Preston, F.W., 1962a. The Canonical Distribution of Commonness and Rarity: Part I.

Ecology. 43, 185.

Preston, F.W., 1962b. The Canonical Distribution of Commonness and Rarity: Part II.

Ecology. 43, 410–432.

Pulliam, H.R., 1988. Sources, Sinks, and Population Regulation. The American

Naturalist. 132, 652–661.

R Core Team, 2015. R: A Language and Environment for Statistical Computing. R

Foundation for Statistical Computing, Vienna, Austria.

Rahbek, C., Gotelli, N.J., Colwell, R.K., Entsminger, G.L., Rangel, T.F.L.V.B., Graves,

G.R., 2007. Predicting continental-scale patterns of bird species richness with

spatially explicit models. Proceedings of the Royal Society of London B:

Biological Sciences. 274, 165–174.

Rahel, F.J., 2000. Homogenization of Fish Faunas Across the United States. Science.

288, 854–856.

Raia, P., Carotenuto, F., Meloro, C., Piras, P., Barbera, C., 2011. Species accumulation

over space and time in European Plio-Holocene mammals. Evolutionary Ecology.

25, 171–188.

138

Reynolds, S.C., Wilkinson, D.M., Marston, C.G., O’Regan, H.J., 2015. The “mosaic

habitat” concept in human evolution: past and present. Transactions of the Royal

Society of South Africa. 70, 57–69.

Ricklefs, R.E., Schluter, D., 1993. Species diversity in ecological communities: historical

and geographical perspectives. University of Chicago Press, Chicago.

Rosenzweig, M.L., 1995. Species Diversity in Space and Time. Cambridge University

Press, Cambridge, United Kingdom.

Rosenzweig, M.L., 1998. Preston’s ergodic conjecture: the accumulation of species in

space and time. In: Biodiversity Dynamics: Turnover of Populations, Taxa, and

Communities. Columbia University Press, New York, pp. 311–348.

Rosenzweig, M.L., Abramsky, Z., 1997. Two gerbils of the Negev: A long-term

investigation of optimal habitat selection and its consequences. Evolutionary

Ecology. 11, 733–756.

Ruggiero, A., Kitzberger, T., 2004. Environmental correlates of mammal species richness

in South America: effects of spatial structure, taxonomy and geographic range.

Ecography. 27, 401–417.

Saupe, E.E., Qiao, H., Hendricks, J.R., Portell, R.W., Hunter, S.J., Soberón, J.,

Lieberman, B.S., 2015. Niche breadth and geographic range size as determinants

of species survival on geological time scales. Global Ecology and Biogeography.

24, 1159–1169.

Scheiner, S.M., 2003. Six types of species-area curves. Global Ecology and

Biogeography. 12, 441–447.

139

Sclafani, J., Holland, S., 2013. The Species-Area Relationship in the Late Ordovician: A

Test Using Neutral Theory. Diversity. 5, 240–262.

Sepkoski, J.J., 1976. Species diversity in the Phanerozoic: species-area effects.

Paleobiology. 2, 298–303.

Sepkoski, J.J., 1978. A kinetic model of Phanerozoic taxonomic diversity I. Analysis of

marine orders. Paleobiology. 4, 223–251.

Sizling, A.L., Storch, D., 2004. Power-law species-area relationships and self-similar

species distributions within finite areas. Ecology Letters. 7, 60–68.

Supp, S.R., Koons, D.N., Ernest, S.K.M., 2015. Using life history trade-offs to

understand core-transient structuring of a small mammal community. Ecosphere.

6, art187.

Svenning, J.-C., Skov, F., 2007. Could the tree diversity pattern in Europe be generated

by postglacial dispersal limitation? Ecology Letters. 10, 453–460.

Taylor, L.R., Kempton, R.A., Woiwod, I.P., 1976. Diversity Statistics and the Log-Series

Model. Journal of Animal Ecology. 45, 255–272.

Tomašových, A., Kidwell, S.M., 2009. Fidelity of variation in species composition and

diversity partitioning by death assemblages: time-averaging transfers diversity

from beta to alpha levels. Paleobiology. 35, 94–118.

Tomašových, A., Kidwell, S.M., 2010a. The Effects of Temporal Resolution on Species

Turnover and on Testing Metacommunity Models. The American Naturalist. 175,

587–606.

140

Tomašových, A., Kidwell, S.M., 2010b. Predicting the effects of increasing temporal

scale on species composition, diversity, and rank-abundance distributions.

Paleobiology. 36, 672–695.

Tóth, A.B., Lyons, S.K., Behrensmeyer, A.K., 2014. A Century of Change in Kenya’s

Mammal Communities: Increased Richness and Decreased Uniqueness in Six

Protected Areas. PLoS ONE. 9, e93092.

Ulrich, W., 2006. Decomposing the process of species accumulation into area dependent

and time dependent parts. Ecological Research. 21, 578–585.

Ulrich, W., Zalewski, M., 2006. Abundance and co-occurrence patterns of core and

satellite species of ground beetles on small lake islands. Oikos. 114, 338–348.

Western, D., 2007. A half a century of habitat change in Amboseli National Park, Kenya.

African Journal of Ecology. 45, 302–310.

Western, D., Behrensmeyer, A.K., 2009. Bone Assemblages Track Animal Community

Structure over 40 Years in an African Savanna Ecosystem. Science. 324, 1061–

1064.

White, E.P., 2004. Two-phase species-time relationships in North American land birds:

Two-phase species-time relationships. Ecology Letters. 7, 329–336.

White, E.P., 2007. Spatiotemporal scaling of species richness: patterns, processes, and

implications. In: Storch, D., Marquet, P.A., Brown, J.H. (Eds.), Scaling

Biodiversity. Cambridge University Press, Cambridge, pp. 325–346.

White, E.P., Adler, P.B., Lauenroth, W.K., Gill, R.A., Greenberg, D., Kaufman, D.M.,

Rassweiler, A., Rusak, J.A., Smith, M.D., Steinbeck, J.R., Waide, R.B., Yao, J.,

141

2006. A comparison of the species-time relationship across ecosystems and

taxonomic groups. Oikos. 112, 185–195.

White, E.P., Ernest, S.K.M., Adler, P.B., Hurlbert, A.H., Lyons, S.K., 2010. Integrating

spatial and temporal approaches to understanding species richness. Philosophical

Transactions of the Royal Society B: Biological Sciences. 365, 3633–3643.

White, E.P., Gilchrist, M.A., 2007. Effects of population-level aggregation,

autocorrelation, and interspecific association on the species–time relationship in

two desert communities. Evolutionary Ecology Research. 9, 1329–1347.

White, E.P., Hurlbert, A.H., 2010. The Combined Influence of the Local Environment

and Regional Enrichment on Bird Species Richness. The American Naturalist.

175, E35–E43.

Wiens, J.A., 1989. Spatial Scaling in Ecology. Functional Ecology. 3, 385–397.

Williams, C.B., 1943. Area and Number of Species. Nature. 152, 264–267.

Williams, C.B., 1964. Patterns in the balance of nature. Academic Press, London.

Williamson, M., 1988. Relationship of species number to area, distance and other

variables. In: Myers, A.A., Giller, P.S. (Eds.), Analytical Biogeography. Springer

Netherlands, Dordrecht, pp. 91–115.

Yu, J., Dobson, F.S., 2000. Seven forms of rarity in mammals. Journal of Biogeography.

27, 131–139.

Zeder, M.A., Pilaar, S.E., 2010. Assessing the reliability of criteria used to identify

mandibles and mandibular teeth in sheep, Ovis, and goats, Capra. Journal of

Archaeological Science. 37, 225–242.

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Chapter 4: Extrapolating richness in a modern large mammal community to predict fossil community richness: how ecologically different is the modern from the past?

Abstract

Comparing ecological pattern and process between modern and fossil communities is challenging because both exist on spatial, temporal, and taxonomic scales that vary by orders of magnitude. This presents an obstacle for the exchange of theory and methods between the two fields and the ability for researchers to successfully integrate both types of ecological data in order to study ecology across the full spectrum of scales that are available to us. I use a species-time-area relationship model (STAR) to scale large mammal richness in the modern Amboseli skeletal assemblage to the scales observed in the fossil Koobi Fora community, both of which are located in Kenya. I then explore how richness predictions using the STAR compare to observed fossil richness, and whether any systematic differences can shed light on how ecologically different the modern is from the past. I find in one Koobi Fora dataset that mean family-level richness is well predicted by the Amboseli model, but richness turnover across space is higher than predicted. In another Koobi Fora dataset, I find that the agreement between predicted and observed fossil species richness decreases as a function of increasing spatiotemporal scale. I conclude that the STAR model has serious shortcomings for extrapolating modern richness to fossil spatiotemporal scales because 1) the scaling relationship of richness with space and time substantially deviates from that of a power function and 2) the frequency of speciation events (even on short geological time scales of 104-105 years) changes the composition of the species pool, which fundamentally alters the way species accumulate with increasing spatiotemporal scale. These results

143 highlight the limitations of extrapolating modern ecological patterns to larger scales and the need to study the fossil record to understand large-scale ecological processes. Lastly, the difficulties of scaling up (and down) also mean that paleoecologists must be cautious when applying modern theory and methods when studying fossil communities.

1. Introduction

The field of ecology benefits from the fact that neo- and paleo-communities exist at very different spatiotemporal scales. Neoecologists draw upon the long time depth of the fossil record to learn about origination, extinction, responses to climate change, etc. as a way of contextualizing their modern-day studies (e.g., Ricklefs and Schluter 1993;

Brown 1995; Rosenzweig 1995; Brown et al. 2001; McGill et al. 2005; Mittelbach et al.

2007; Svenning and Skov 2007). Paleoecologists, on the other hand, apply modern ecological theory and method based on experiments or observations of dynamics that are impossible to see in the fossil record (e.g., Sepkoski 1978; Patzkowsky and Holland

2003; Harnik et al. 2012; Liow et al. 2015; Saupe et al. 2015; Lyons et al. 2016).

However, the validity of idea exchange between these two fields is based on the premise that the two sources of ecological data are actually comparable. Modern and fossil community data exist on spatiotemporal, and usually taxonomic, scales that vary by orders of magnitude. It is now well established, mainly based on research in modern ecology, that ecological pattern and process change as the spatial, temporal, and taxonomic scales of analysis change (Bell 1989; Wiens 1989; Levin 1992; Jablonski and

Sepkoski 1996; McGill et al. 2015). This presents an obstacle for the exchange of ideas and methods between neo- and paleoecology, which impedes the overall advancement of

144 ecology as a field.

One way to circumvent this issue is to look at how ecological patterns scale across multiple orders of magnitude (Brown et al. 2002; White 2007). The best studied example of this is the species-area relationship (SAR), which analyzes how species richness accumulates as a function of increasing spatial scale (Arrhenius 1921;

Rosenzweig 1995). Its temporal analogue, the species-time relationship (STR), is less well-studied, but renewed research has confirmed its existence and functional form

(White et al. 2006). More recently, these two scaling relationships have been unified as the species-time-area relationship (STAR) (Adler and Lauenroth 2003; Adler et al. 2005).

These studies have shown that the effects of area and time span are not independent but instead interact to influence the accumulation of richness as a function of increasing spatiotemporal scale. Specifically, the rate of species accumulation with area decreases as the study’s time span is increased and likewise, the rate of species accumulation with time decreases as area increases.

In my previous dissertation chapter, I used model selection methods to quantify the STAR in the large mammal skeletal assemblage of Amboseli National Park located in southern Kenya. The ultimate goal of this study is to use the STAR as a “scale bridge” to extrapolate richness on modern time scales to the larger temporal scales seen in the fossil record. The fossil data come from the Plio-Pleistocene Koobi Fora Formation, located on the east side of Lake Turkana in northern Kenya. The high degree of comparability between the modern Amboseli and fossil Koobi Fora data has the advantage of factoring out a lot of potential confounding factors which may otherwise introduce extra noise and possible bias into this study. For example, the skeletal nature of the Amboseli data means

145 many of the taphonomic processes that affect bone remains post-mortem in fossil assemblages are already incorporated into the analysis (Behrensmeyer et al. 1979;

Behrensmeyer and Dechant Boaz 1980; Western and Behrensmeyer 2009). Furthermore, many of the species found at Amboseli (Behrensmeyer and Dechant Boaz 1980; Miller et al. 2014) have either direct ancestors or closely related, extinct sister taxa in the Koobi

Fora fossil community (Bobe 2011). This means phylogenetically conserved traits among taxa (e.g., habitat preference, geographic range size, population structure, etc.) will be similar in both datasets, resulting in overall similar ecological community structure. Thus, comparison of the Amboseli and Koobi Fora datasets meets the necessary criteria for studying the scaling of richness between comparable modern and fossil communities.

Using the Amboseli STAR model to bridge the scale gap between the modern

Amboseli and fossil Koobi Fora data, I ask how does richness predicted using the STAR compare to observed fossil richness? If there are systematic differences, how do they inform how ecological processes in the past might have been fundamentally different than those in the present? And lastly, what does that mean for the exchange of theory and methods between neo- and paleoecology and the field of ecology as a whole?

2. Materials and Methods

2.1. Modern Amboseli data

To describe how large mammal richness scales with space and time in modern communities, I analyzed the same Amboseli skeletal dataset as in Chapter 3. As a brief review for how the data were collected, field observers walked transects across the

Amboseli landscape (n=103; median length=0.8 km; median width=0.1 km) and recorded

146 all encountered bone specimens along with their species identity and whether the bones belonged to one individual or not (Behrensmeyer et al. 1979; Behrensmeyer and Dechant

Boaz 1980). The data were collected intermittently in the late dry season months (August

– October) (Behrensmeyer 2007) from 1975 to 2010. Bones recorded in a given transect were aggregated into time bins (Figure 25) based on year documented as well as bone weathering stage (Behrensmeyer 1978). Small mammal data (<1kg) were excluded because of the empirical size-related bias against their recovery in the Amboseli bone assemblage (Behrensmeyer et al. 1979; Behrensmeyer and Dechant Boaz 1980; Miller et al. 2014). This resulted in the documentation of a total of 35 species and bones from 3181 individuals. Chapter 3 should be consulted for more details on how data were collected at

Amboseli.

2.2. Data from Koobi Fora Formation fossils

Fossil mammal data are from the Koobi Fora Formation, which is located on the east side of Lake Turkana in northern Kenya. Data were collected from two main sources representing different spatiotemporal and taxonomic scales. The first set of data comes from A.K. Behrensmeyer’s dissertation work (Behrensmeyer 1975). In the late

1960s/early 1970s, Behrensmeyer implemented a “squares” data collection protocol, where 10x10m squares were laid down at least 20m apart within a single, well-resolved stratigraphic horizon (Behrensmeyer 1975). All surface fossil specimens within each square were identified to the lowest taxonomic level possible. Given the small spatiotemporal scale of these sampling units and the fragmentary nature of fossil specimens, however, sample sizes were only large enough for analysis at the family- level. Tentative family-level identifications were retained to boost sample sizes.

147

Analyzed squares data come from five collecting areas (Areas 8, 10, 102, 105, 130) and sample three different geological members (Upper Burgi, KBS, and Okote). Thus, the squares represent a total temporal extent of about 400,000 years (Brown and McDougall

2011), but the amount of time represented by each collecting area’s set of squares is estimated to be between 1000-10,000 years. See Table 8 for a summary of the squares data.

The second set of data include surface fossils of mammals from the Ileret subregion in the northern portion of the exposed Koobi Fora Formation. Whereas the

Behrensmeyer squares data sample a restricted spatiotemporal but coarse taxonomic scale

(i.e., family-level), the Ileret data are resolved to the species-level but sample spatial and temporal scales that are orders of magnitude larger (compare Table 8 and Table 9).

Therefore, these two datasets are complementary in the patterns they reveal at different scales (Figure 26). The faunal data come from the Turkana Basin Institute Database, which was kindly provided by Mikael Fortelius and Meave Leakey. This database includes the public Turkana Database (Bobe 2011; http://www.mnh.si.edu/ete/ETE_Datasets_Turkana.html), recently published specimens, and collected but unpublished fossils. Because each fossil individual in the database is given a unique specimen number, number of individuals can be calculated. Individuals only identified to the genus level were retained only if there were no other congeners that could be identified to the species level. Individuals with cf. and aff. genus and species modifiers were lumped with species lacking those modifiers to increase sample size.

Species from the orders Rodentia and Lagomorpha were excluded due to the preservation and sampling bias against small-bodied individuals (Behrensmeyer et al. 1979;

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Behrensmeyer and Dechant Boaz 1980; Miller et al. 2014).

Because Gathogo (2003) mapped the Ileret outcrops at the member level (his

Figure 4), the area of target fossil-bearing outcrops could be calculated via digitization of his map using ImageJ. Similarly, the amount of time represented by these fossil-bearing deposits was estimated by using ImageJ to calculate the proportion of fossiliferous strata in his geological sections (Gathogo and Brown 2006). These proportions were then multiplied by the total temporal duration of the geological member to get the total amount of time represented by each fossil assemblage. This implicitly assumes a uniform rate of sedimentation, which is likely not true but serves as a useful first-order approximation.

See Table 9 for a summary of the Ileret data.

2.3. Constructing the Amboseli STAR model

Whereas the goal of Chapter 3 was parameter estimation, this chapter’s goal is to use the STAR model to predict richness in fossil communities. In order to rigorously evaluate the generality and transferability of the STAR model to novel data, 25% of the

Amboseli transects (which contain 29% of all individuals) were set aside as test data

(Figure 25), while the remaining 75% were used to train the model. The test transects sampled all time bins and a spatially segregated corner of the landscape. This was done to minimize the influence of spatial and temporal autocorrelation so that independence is maximized between the two datasets. Doing so provides an honest assessment of one’s model and its ability to predict richness in novel, out-of-sample situations (Bahn and

McGill 2013).

As in Chapter 2, nested SARs and STRs were constructed by iteratively aggregating transects that were adjacent across space and through time. This allowed the

149 creation of sequentially larger nested spatial and temporal combinations, along with their respective richness estimates. For all duplicated area and time span combinations, the geometric mean of richness was calculated, so each unique combination of space and time only had one accompanying richness estimate. These three variables were then log10-transformed and used to construct a power function STAR model with a space by time interaction term: 푙표푔10푆 = 푙표푔10푐 + 푧1 푙표푔10퐴 + 푤1 푙표푔10푇 +

푢 (푙표푔10퐴)(푙표푔10푇), where S is richness, A is area, T is time, z1 is the time-independent rate of richness increase with area at unit time (i.e., one year), w1 is the area-independent rate of increase with time at unit area (i.e., one km2), and u is the interaction parameter

(Adler and Lauenroth 2003; Adler et al. 2005). STAR models were generated at the species and family level to match the taxonomic scales of the fossil datasets.

Fossils undergo a number of taphonomic processes, however, which cause them to be destroyed or fragmented (which hinders taxonomic identification, effectively removing the specimens from study) (Behrensmeyer et al. 2000). These processes decrease the number of specimens/individuals in an assemblage, which in turn decreases richness. This creates a problem when comparing modern and fossil richness if the goal is to predict absolute number of species. In large mammals, taphonomic deletion can be assumed as more or less random (though there is a secondary body size related preservation bias) (Western and Behrensmeyer 2009), so its effect can be accounted for statistically. To separate out the effects of area, time, and abundance on richness, I included number of individuals as a covariate in the Amboseli STAR model. Area and number of individuals together exhibit a strong linear relationship (r=0.724), however, which introduces collinearity into the model. To get around this, I ran a principal

150 components analysis (PCA) using a correlation matrix of area and number of individuals

(both log10-transformed). PCA axis 1 (PC 1) explained 89% of the variance in these two variables, so PC1 scores were used as a surrogate for both area and number of individuals in the Amboseli STAR model. This was only done for the species-level model since abundance data were not available for the Behrensmeyer squares dataset. I will discuss how I dealt with the taphonomy issue in the squares data in the next section (“Estimating fossil richness using the STAR model”).

Prediction accuracy of the Amboseli STAR model was assessed by first inputting the test dataset’s log10(area) (or PC1 scores in the species-level model) and log10(time) measurements into the trained model to get predicted test richness. For the species-level model, I first projected the test dataset’s log10(abundance) and log10(area) onto the training model’s PCA to get PC1 scores, which were used instead of log(area). Then, I calculated R2 and root-mean-square error by comparing the test data’s predicted richness with its actual observed richness values at the species and family level.

2.4. Estimating fossil richness using the STAR model

The family-level, fossil squares data lack abundance information. As a result, any analysis comparing absolute richness differences between modern and fossil communities in these data will be confounded by “real” ecological differences and taphonomic processes decreasing the number of individuals in fossil assemblages. Thus, instead of comparing absolute family richness, the goal of the squares analysis was to see if the relative rate of spatial turnover was the same between the Amboseli and fossil data. To this end, nested SARs were created for each fossil collecting area by iteratively aggregating squares in the same manner as was done in the Amboseli analysis. Then, a

151 power function SAR model was fit to the data: 푙표푔10푆 = 푙표푔10푐 + 푧 푙표푔10퐴. The squares

SAR coefficients were then compared to Amboseli SAR coefficients extrapolated to time spans of 500, 1000, 5000, and 10,000 years, thereby making the two temporal scales commensurate. Four time span estimates were used to assess the effect of time span uncertainty on the results. The Amboseli SAR coefficients for each time span were obtained by inputting each year number as the time span estimate into the STAR model.

z coefficients in SARs measure the relative rate of richness accumulation (i.e., the proportional increase in richness with a proportional increase in area) (Rosenzweig

1995). Therefore, assuming taphonomic processes modify fossil assemblages in a random, proportional manner (e.g., 90% of bones are randomly destroyed across assemblages [100→10; 1000→100]), the relative rate of richness accumulation with area should be largely unaffected, enabling a straightforward comparison between the

Amboseli and fossil squares z coefficients. The c coefficient, on the other hand, is affected by number of individuals (Rosenzweig 1995). Because of this, I predict c should be smaller in the fossil squares data if only taphonomic processes affecting number of individuals (and thus family richness) were operating, with all else held equal.

The Ileret species-level data do have abundance information, so the goal of this analysis was to compare observed absolute richness with that predicted by the Amboseli

STAR model. This was done for four different data subsets partitioned by geological member, some of which were nested within each other: the Upper Burgi Member, the upper part of the KBS Member, the entire KBS Member, and the Upper Burgi and KBS

Members combined (Table 9). For each data subset, log10(number of individuals) and log10(area) were projected onto the Amboseli training model’s PCA to get PC1 scores.

152

The PC1 scores and log10(time span) values were input into the Amboseli STAR model to predict species richness for each data subset. In addition to using the time span represented by each data subset’s fossil assemblage, I also calculated predicted richness using the total temporal extent of each data subset to see if underpredicted richness could be attributed to the large temporal spacing between fossiliferous beds (McKinney and

Frederick 1999). This phenomenon is akin to aggregating noncontiguous plots in space, which has the effect of compressing environmental gradients and overestimating the rate of spatial turnover (McKinney and Frederick 1999; Adler and Lauenroth 2003; Adler et al. 2005). If this is what is causing richness to be under-predicted, then using total temporal extent should erase the discrepancy between observed and predicted richness, or richness may even be over-predicted.

2.5. Modeling the number of speciation events in the time span covered by the Ileret data

One might expect that the observed number of fossil species in the Ileret dataset would be under-predicted by the Amboseli STAR model. This is because the modern

Amboseli data do not incorporate large-scale events (i.e., speciations) that likely occurred in the fossil assemblages. Therefore, I used a simple Poisson probability model to get an approximation of how many speciation events might be expected in the Ileret datasets.

The average duration of a fossil mammal species in the Turkana Basin is estimated to be about 1.3 million years (obtained by averaging the mean [1.4 Ma] and median [1.2 Ma] species durations from Bibi & Kiessling, 2015). I assume this equates to an average of one speciation event per 1.3 million years per species. Using the number of species observed in and the time span covered by each Ileret dataset (Table 9), I calculated the expected number of speciation events (observed number of species * temporal extent /

153

1.7 million). This was used as the lambda parameter in the Poisson model, and 95% confidence intervals for the expected number of speciation events were calculated using the qpois() function in the R “stats” package.

All analyses were done in R version 3.3.1. (R Core Team 2015).

3. Results

The trained Amboseli STAR model does moderately well when validated on an independent test dataset. R2 is 0.511 for the species-level model and 0.381 for the family- level model (Table 8). This is a large drop-off from their respective R2 of 0.774 and 0.637 when the models are trained and tested on the same dataset (Table 8). This illustrates how the use of a non-independent test dataset can lead to overly optimistic models when attempting to generate predictions in novel conditions (Bahn and McGill 2013). Root- mean-square error is 0.134 log10(richness) units for the species-level model, which is

12% of mean species log10(richness) (Table 8). Family-level root-mean-square error is

0.141 log10(richness) units which is 17% of mean family-level log10(richness) (Table 8).

Predicted richness for both models generally corresponds with the observed richness of their respective test datasets (Figure 27). This is fine if one wants to predict relative richness, for example, when comparing across multiple fossil communities. However, there are systematic biases, which complicate the prediction of absolute richness values.

Specifically, richness is over-predicted at low values and under-predicted at high ones

(Figure 27).

Comparing observed fossil squares SAR coefficients to those predicted by the

Amboseli STAR model at comparable time spans show z coefficients are always higher

154 in fossil square SARs (Figure 28B). The intercepts (i.e., log10(c)) of fossil square SARs are well predicted by the Amboseli SAR when extrapolated to time spans of 5000 and

10,000 years (Figure 28A). The only exception is the intercept of the fossil square SAR from collecting area 130, which is much higher than that predicted by the Amboseli SAR.

Observed species richness in the fossil Ileret assemblages is well predicted at relatively smaller spatiotemporal scales (i.e., in the Upper Burgi and upper KBS data subsets) (Figure 29). However, species richness is under-predicted at larger spatiotemporal scales in the all KBS and Upper Burgi & KBS datasets (Figure 29). More precisely, the differences between observed and predicted richness increases monotonically (i.e., -0.03, 0.08, 0.47, 0.55) as a function of total temporal extent (Table

9) (r=0.97). I previously mentioned that such a pattern may be attributed to the lumping of noncontiguous, fossil-bearing strata into one coherent time span (McKinney and

Frederick 1999). This effectively compresses species temporal gradients and inflates rates of species accumulation over time. To test this idea, I also used the total temporal extent represented by each of these datasets as the time span estimate in the Amboseli STAR to predict fossil richness. Results show that even this extreme overestimation of time span produces an underpredicted richness estimate (Figure 29), so the large number of observed species cannot be wholly attributed to the temporal separation of fossil-bearing strata.

For each Ileret dataset, I used a Poisson probability model to calculate 95% confidence intervals surrounding the expected number of speciation events in each dataset. Results are shown in Table 9. In the smaller-scale Upper Burgi and upper KBS datasets, the expected numbers of speciation events (i.e., lambda) are small (2.20 and

155

4.77, respectively), and the 95% confidence intervals either encompass or barely exclude zero (0-5 and 1-9, respectively). For the larger scale KBS and combined Upper

Burgi/KBS datasets, lambda is 12.40 and 18.74, and the 95% confidence intervals are 6-

20 and 11-28, respectively.

4. Discussion

It is well known that ecological patterns change as one alters the spatial, temporal, and taxonomic scale of analysis (Bell 1989; Wiens 1989; Levin 1992; Jablonski and

Sepkoski 1996; McGill et al. 2015). This is especially true of species richness whose scaling relationship with area (Williams 1943; Preston 1960; Sepkoski 1976; Rosenzweig

1995, 1998; Hadly and Maurer 2001; Barnosky et al. 2005), time (Preston 1960;

Rosenzweig 1995, 1998; McKinney and Frederick 1999; Hadly and Maurer 2001; White

2004; White et al. 2006), and their interaction (Jacquemyn et al. 2001; Adler and

Lauenroth 2003; Adler et al. 2005; McGlinn and Palmer 2009; Raia et al. 2011) has been extensively studied. The aim of this study was to quantify these scaling relationships across different spatial, temporal, and taxonomic scales and to extrapolate these relationships to scales observed in the fossil record. This enables commensurate comparisons between modern and fossil communities and to see whether modern ecological process and pattern is truly different from the past (Williams and Jackson

2007; Lyons et al. 2016).

4.1. Interpreting the fossil squares results

SAR z coefficients measure the rate of taxa (family, in this case) accumulation with area, which has been shown to be related to the rate of spatial turnover (Harte and

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Kinzig 1997; Harte et al. 1999; Lennon et al. 2001; Koleff et al. 2003). Therefore, the larger z coefficients in the fossil squares data relative to those of the Amboseli SAR

(Figure 28B) may suggest that spatial turnover was more marked in the past when differences in scale are accounted for. This would agree with many studies which demonstrate communities are becoming more homogenized across space, thereby decreasing the rate of spatial turnover (McKinney and Lockwood 1999; Rahel 2000; La

Sorte and Boecklen 2005; Tóth et al. 2014). These studies were conducted at the species level, however, and more research is needed to see how homogenization affects higher taxonomic categories. The alternative is that the time span represented by these squares assemblages is less than 500 years, but that is highly unlikely.

A more parsimonious explanation for the large fossil z coefficients might be the small spatial scale at which the squares data were collected (Figure 26). It has been demonstrated theoretically (Preston 1962a, b; May 1975; Harte et al. 2009) and empirically (Williams 1943; Preston 1960; Rosenzweig 1995, 1998; White 2004; Fridley et al. 2006) that SARs are convex-up at small spatial scales even in log-log space. This equates to a steeper rate of taxon accumulation. Indeed, a family-level SAR fit to

Amboseli transects less than 0.01 km2 (n=17) has a z coefficient of 0.59, which is slightly higher than those seen in the fossil squares (Figure 28B). The z coefficient is expected to go down, however, as the study’s time span increases due to the negative area by time interaction term (Chapter 3; Adler et al. 2005). I do not have enough data from these small transects at this time to differentiate between these two possibilities, since a four parameter STAR model fit to 17 data points will be overly parameterized (indeed the estimated coefficients are extremely noisy).

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The intercepts of the family-level squares SARs match those estimated using the modern Amboseli data when time spans of 5000 and 10,000 years are used (except for collecting area 130, whose SAR intercept is larger) (Figure 28A). The intercept effectively measures the number of taxa (in this case, families) at unit area (i.e., 1 km2). It is interesting that the estimated SAR intercept for collecting area 130 is higher than predicted (Figure 28A), since the source level of these surface fossils was not well- defined and likely sampled multiple time periods. In general, with all else held equal, family richness should be lower in fossil assemblages due to taphonomic processes decreasing number of individuals, but this is not seen here. Therefore, this may be a real ecological signal, and ecosystems in the past may have supported a larger number of families. Conversely, ecosystems today (or Amboseli in particular) may be depauperate in family richness. Alternatively, the amount of time represented by these squares assemblages may be much larger than currently estimated, or the representation of families is relatively unaffected by sample size reduction represented in the squares assemblages.

Because these analyses were done at the family level, this result reflects the interaction of phylogenetically conserved traits with the environment and other taxa.

There is a dearth of ecological literature studying the drivers and correlates of richness above the species level (but see Russell et al. 2006; Hawkins et al. 2007; Punyasena et al.

2008), however, and the paleobiological literature may be more fruitful in this regard

(e.g., Sepkoski 1979; Labandeira and Sepkoski 1993; Clapham et al. 2016).

4.2. Interpreting the Ileret fossil results

The species-level Amboseli STAR model shows mixed results with richness at

158 small scales being well-predicted and richness at larger scales being poorly predicted

(Figure 29). In fact, the divergence between observed and predicted richness values increases as total temporal extent increases. I have already demonstrated earlier that this is not due to the temporal spacing between successive fossil-bearing strata. The inadequacy of the STAR model at increasing spatiotemporal scales could indicate a scale- break in pattern and process within the Ileret datasets, though scales only change across one or two orders of magnitude (Table 9).

This may suggest the presence of real ecological and evolutionary phenomenon, the latter of which had a substantial effect. Results of the Poisson model show that the

95% confidence intervals for number of speciation events definitively exclude zero only in the larger-scale datasets (i.e., the KBS and combined Upper Burgi and KBS) (Table 9), precisely where the scale-break is. In the KBS dataset, the difference between observed and predicted richness is 23 species, and the 95% confidence interval for speciation events in this dataset is 6-20 (Table 9). The difference between observed and predicted richness in the Upper Burgi and KBS dataset is 29, and the 95% speciation confidence interval is 11-28 (Table 9). Therefore, a substantial amount of the difference between observed fossil Ileret richness and richness extrapolated using the modern Amboseli data can be accounted for by speciation events.

However, number of speciation events likely does not account for the entire difference between predicted and observed fossil richness. This deficit might be attributable to large-scale climatic and environmental changes (or shifts in depositional environments) that would have shifted species composition over time in ways that could not be accounted for by the decadal Amboseli STAR model. Moreover, over longer time

159 scales, one would expect an increased occurrence of larger magnitude events

(endogenous or exogenous to the community) (Halley 1996). Examples include rare migration events connecting what were once two evolutionarily isolated regions (e.g., changing migration corridors between Africa and Asia via an Arabian land bridge). All of these would cause increased species turnover and can explain some of the increased divergences between observed and predicted richness as time scale increases.

Perhaps the most parsimonious explanation is that the power function STAR model is misspecified and does not describe the true underlying relationship between richness, time, and area. This can be seen in Figure 27, where systematic biases cause richness to be overpredicted at smaller scales and underpredicted at larger scales. As alluded to previously, this is most likely due to the convex-up nature of the STAR model at small scales. This pattern agrees with Figure 29, which shows overprediction of richness gradually giving way to underprediction as the temporal scale of analysis increases and exceeds that seen in the Amboseli data by four orders of magnitude (Figure

26).

The inadequacy of the STAR power function is not mutually exclusive with the idea that a different set of processes influence the accumulation of species on large time scales. In fact, Preston (1960) predicted the STR should not follow a strict power function over many orders of temporal magnitude but instead should be made up of three phases in log-log space: a convex-up sampling phase, a linear phase driven by habitat change and immigration, and a final concave-up phase driven by evolutionary processes. This can be seen in this study’s empirical STR (combining modern Amboseli and fossil Ileret data), which is clearly triphasic (Figure 30). The nonlinearity of species richness as a

160 function of time in log-log space emphasizes the shortcomings of the power function in scaling richness, and the idea that a different set of processes influences species turnover over large time scales.

At very large spatiotemporal scales, predicted species richness using the STAR model begins to decrease with increasing area and or time, which is empirically impossible (Figure 31). This is observed as one goes from predicted richness in the KBS to that in the combined Upper Burgi and KBS, as well as the upper KBS towards larger scales when using total temporal extent (Figure 29). This undesirable property of the

STAR model is caused by the negative interaction term and demonstrates the inability of the Amboseli STAR model to be extrapolated across many orders of magnitude of scale.

In fact, visual examination of Figure 5 in Chapter 3 shows that predicted richness extrapolated over increasing combinations of spatial and temporal scale must all converge on some larger richness estimate, which I implicitly identified as the species pool in that chapter (also see Figure 31). Using Chapter 3’s STAR model, this estimate is

72 species, which may serve as an indirect estimate of how large a species pool the

Amboseli community is sampling. From a statistical standpoint, this richness estimate suggests an upper limit beyond which richness should not be extrapolated. The upper limit for this chapter’s STAR model is 29 species (the difference is attributable to adding in number of individuals as a covariate via PCA). Once this upper limit is breached, predicted richness at progressively larger spatiotemporal scales will begin to decrease (as is seen in the KBS and combined Upper Burgi and KBS datasets which have richness values that far exceed the limit of 29 species). Because the species pool exerts such a strong constraint on how species accumulate with increasing space and time, the species

161 pool must be changing at larger scales in order to prevent a decrease in richness with increasing scale (Figure 31).

4.3. Larger implications for understanding the scaling of richness over large spatiotemporal scales

The scaling of richness with time and space (at least in the Amboseli ecosystem) does not strictly follow a power law, and this function should not be used to extrapolate richness over many orders of magnitude. One can try fitting other models, such as Harte’s

MaxEnt model (Harte et al. 2008, 2009) with an added time component, as has been previously suggested (White et al. 2010). However, given the likely importance of speciation in species temporal accumulation in this study, it may be better to adapt a larger-scale model of biodiversity, such as McGill’s continuum model (McGill and

Collins 2003).

Nevertheless, the “wrongness” of my STAR power function has raised some interesting questions, which deserve further study. The general explanation is that modern communities are structured differently than those in the past. Specifically, the nature of the species pool that a community samples changes as temporal scale is increased (Figure 9 in Chapter 3). I have shown that speciation likely played a large role in changing both the composition and size of the species pool, even over a geologically short time period (i.e., 104-105 years). Furthermore, large-scale ecological changes (e.g., climatic change), whose probability of occurrence increases as time scale increases

(Halley 1996), and changes in the sampled paleoenvironments will also cause the species pool to change in composition over time. Again, this finding supports Preston’s hypothesis that a third phase of species temporal accumulation exists and changes the

162 nature of richness scaling with time, which cannot be extrapolated from STRs on the time scales modern ecologists study (Figure 30). This serves as a source of caution for both neo- and paleo-ecologists alike: for paleoecologists, given how radically different fossil species turnover is from that of the modern over geologically short time spans (i.e., the duration of a single geological member), it is unwise to uncritically apply modern ecological theory and models to fossil communities. For neoecologists, these results highlight the importance of using the fossil record to explain ecological pattern and process over large spatiotemporal scales, which cannot be extrapolated from modern studies alone.

5. Conclusions

Comparing biodiversity patterns between modern and fossil communities is complicated by the fact that ecological pattern and process are known to change across spatial, temporal, and taxonomic scales. In Chapter 3, I developed a model for how richness changes as a function of these three different types of scale. In this chapter, I aimed to use the STAR model to see if spatiotemporal scale can be extrapolated to predict richness in fossil communities (or at the very least, compare modern and fossil richness at commensurate scales). I found the STAR power function model is problematic for a number of reasons. Firstly, richness does not strictly scale as a power function, so it cannot be used to extrapolate and predict absolute richness across many orders of magnitude. However, it may still be used as a general tool to investigate broader patterns of richness scaling. Secondly, the pitfalls of the STAR power model revealed that the nature of the species pool exerts a strong control on how species accumulate with

163 increasing spatiotemporal scale. Thus, the species pool that communities sample must change and grow as a function of increasing time scale. This may be attributed to larger- scale ecological changes that happen over longer time periods that are not encountered on modern time scales. Additionally, the appearance of new species via speciation likely played an important role in altering the species pool. This was independently corroborated with a Poisson model demonstrating that speciation could add a surprisingly large number of species to the pool given the relatively short geological time span of this study (i.e., a single geological member). Therefore, the past is indeed ecologically different from the modern, mainly because the former involves a different set of processes given its larger temporal scale (i.e., speciation, large-scale climatic change, rare inter-regional migration events, etc.). In conclusion, scaling up from neoecology is theoretically challenging, though informative, highlighting the importance of using the fossil record to study ecological processes at very large spatiotemporal scales. Likewise, scaling down is difficult, demanding caution when applying modern ecological theory and method to time-averaged fossil communities.

164

Figures

Figure 25. 3D plot showing the location of each Amboseli transect across space and through time. Each transect is a point color-coded by which time bin it occupies. Easting spans 30.2 km while northing spans 14.2 km. The transparent blue box circumscribes which transects were withheld as the test dataset (25% of all transects, which contain

29% of all individuals).

165

Figure 26. Scale diagram showing the spatial and temporal scales at which the data were collected. Gray shading is directly proportional to the taxonomic scale of these datasets with darker grays representing coarser taxonomic scales. The fossil squares data are at the family level, while the fossil Ileret data are resolved to the species level. Modern

Amboseli’s gray shading is an average of the two, reflecting the fact that these data were used to train and test models at both the species and family level in order to match the taxonomic scales of the two fossil datasets.

166

Figure 27. Comparing the test dataset’s observed richness with that predicted from the training dataset at the species and family level. Specifically, predicted richness was calculated by first fitting the STAR model to the training dataset, and then plugging in log10(area) (or PC1 for the species-level model) and log10(time span) estimates from the test dataset. A model with accurate and precise predictions should have all points fall along the 1:1 line. The red lowess line highlights how both STAR models over-predict richness at small scales and under-predict at larger scales.

167

Figure 28. Comparison between predicted (horizontal dashed lines) and observed intercepts (A) and z coefficients (B) from family-level species-area models. The four predicted values for each coefficient represent predictions using four differ time span estimates (500, 1000, 5000, and 10,000 years).

168

Figure 29. Comparison between observed fossil species richness and that predicted from the Amboseli STAR model. “Predicted” and “Predicted using extent” richness estimates differ based on the time span estimate that is plugged into the STAR model. For

“Predicted” richness, time span is calculated as the sum of time represented by each individual fossil-bearing stratum while ignoring the temporal gaps in between. “Predicted using extent” richness uses the entire temporal extent of the strata in question, summing time span represented by each fossil-bearing stratum and including the temporal gaps in between. Bars represent ±1 root-mean-square error.

169

Figure 30. Empirical species-time relationship combining modern Amboseli data with fossil Ileret data. Because the rate of species accumulation with time varies as a function of area (Adler and Lauenroth 2003; Adler et al. 2005), I only included Amboseli richness and time span estimates that had corresponding area estimates on the order of 100 km2

(similar to the spatial scale of the fossil Ileret data; Table 9). The geometric mean of

Amboseli species richness was calculated for each unique time span to reduce the number of points for clarity’s sake. I used the amount of time represented by fossiliferous beds instead of the total temporal extent for the fossil Ileret data (“Total amount of time” in

Table 9). Line was fit using a third order polynomial regression. Note the triphasic form of the STR, as originally predicted by Preston (1960). To the best of my knowledge, this is the first published empirical triphasic STR.

170

Figure 31. Conceptual figure illustrating how the species pool exerts a strong influence on how species richness accumulates with area and time. Progressively darker lines represent SARs estimated using data collected over increasingly longer time spans. The

SARS are non-parallel (due to the negative STAR interaction term) and converge to a point (the inferred species pool) as scale increases. Once the SARs are extrapolated past the species pool (represented by dotted lines), species richness actually decreases with increased time span, which is empirically impossible. Therefore, the position of the species pool must shift as scale is increased. I propose large-scale processes (e.g., speciation, large-scale climatic and environmental changes) not encountered at smaller scales – and which cannot be inferred from simple extrapolation from smaller scales – fundamentally alter the composition of the species pool at large spatiotemporal scales.

This is supported by the existence of a third phase in triphasic SARs and STRs (Figure

30), which exhibits different behavior from the other two, smaller-scale phases and is hypothesized to be driven by a completely different set of processes.

171

Table 8. Summary of Koobi Fora data collected from 10x10m sampling squares. Area and faunal data are from Behrensmeyer (1975).

Collecting Geological Total area Estimated time Total number of area member sampled (km2) (yrs) families 8 Okote 0.0047 1000 9 10 KBS 0.0014 5000 4 102 KBS 0.0027 1000 9 105 KBS 0.0025 10,000 11 130 Upper Burgi 0.0008 10,000 5

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Table 9. Summary of Koobi Fora data from the Ileret subregion along with expected number of speciation events calculated using a simple Poisson model. Total area sampled was calculated from digitizing Figure 4 from Gathogo (2003). Total amount of time represented by each fossil assemblage was calculated as the proportion of fossil-bearing strata multiplied by the temporal duration of the geological member (this implicitly assumes a uniform sedimentation rate). Proportion of fossil-bearing strata was calculated from digitized stratigraphic sections in Gathogo and Brown (2006). Number of species and individuals were obtained from the Turkana Basin Institute Database.

Geological Collecting Total Total Total Total Total Expected member areas area amount temporal number number of number of sampled of time extent of individuals speciation (km2) (years) (years) species events (95% confidence intervals) Upper 8, 10, 12 2.846 7,700 110,000 26 84 2.20 (0-5) Burgi Upper 1, 3, 6, 2.123 3,000 ~200,000 31 93 4.77 (1-9) KBS 6A, 9 KBS 1, 3, 6, 9.675 52,900 310,000 53 440 12.40 (6- 6A, 7, 8, 20) 8A, 8B, 9, 10, 11, 12 Upper 1, 3, 6, 12.521 60,600 420,000 58 515 18.74 (11- Burgi & 6A, 7, 8, 28) KBS 8A, 8B, 9, 10, 11, 12

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Table 10. STAR model parameter estimates and calculated goodness-of-fit and prediction accuracy statistics at the species and family level. Parameter estimates with

“PC1” refer to the species-level STAR model, whereas “Area” refers to the family-level

STAR (see main text). “Resubstitution” statistics were calculated using the same dataset that was used to fit the model (i.e., how R2 is traditionally calculated in linear models).

“Using test data” refers to statistics calculated on test data using a model that has been trained on another dataset.

Parameter Species Family Intercept 0.996 0.491 Time 0.116 0.361 PC1 or Area 0.186 0.346 Time:PC1 or -0.046 -0.031 Time:Area

Statistic Resubstitution Using Resubstitution Using test test data data 2 R 0.774 0.511 0.637 0.381 Root-mean-square 0.095 0.134 0.117 0.141 error

174

References

Adler, P. B., and W. K. Lauenroth. 2003: The power of time: spatiotemporal scaling of

species diversity. Ecology Letters 6:749–756.

Adler, P. B., E. P. White, W. K. Lauenroth, D. M. Kaufman, A. Rassweiler, and J. A.

Rusak. 2005: Evidence for a general species-time-area relationship. Ecology

86:2032–2039.

Arrhenius, O. 1921: Species and Area. Journal of Ecology 9:95–99.

Bahn, V., and B. J. McGill. 2013: Testing the predictive performance of distribution

models. Oikos 122:321–331.

Barnosky, A. D., M. A. Carrasco, and E. B. Davis. 2005: The Impact of the Species–Area

Relationship on Estimates of Paleodiversity. PLoS Biology 3:e266.

Behrensmeyer, A. K. 1975: The taphonomy and paleoecology of Plio-Pleistocene

vertebrate assemblages east of Lake Rudolf, Kenya. Bulletin of the Museum of

Comparative Zoology 146:473–578.

——— 1978: Taphonomic and ecologic information from bone weathering.

Paleobiology:150–162.

——— 2007: Changes through time in carcass survival in the Amboseli ecosystem,

southern Kenya. Pp.135–160 in T. R. Pickering, K. Schick, and N. Toth, eds.

Breathing Life into Fossils: Taphonomic Studies in Honor of CK (Bob) Brain.

Vol. 2. Stone Age Institute Press, Gosport, Indiana.

Behrensmeyer, A. K., and D. Dechant Boaz. 1980: The recent bones of Amboseli Park

Kenya in relation to East African paleoecology. Pp.72–92 in Fossils in the

Making: Vertebrate Taphonomy and Paleoecology. University of Chicago Press,

175

Chicago.

Behrensmeyer, A. K., D. Western, and D. E. D. Boaz. 1979: New Perspectives in

Vertebrate Paleoecology from a Recent Bone Assemblage. Paleobiology 5:12–21.

Behrensmeyer, A. K., S. M. Kidwell, and R. A. Gastaldo. 2000: Taphonomy and

Paleobiology. Paleobiology 26:103–147.

Bell, G. 1989: A Comparative Method. The American Naturalist 133:553–571.

Bibi, F., Kiessling, W., 2015. Continuous evolutionary change in Plio-Pleistocene

mammals of eastern Africa. Proceedings of the National Academy of Sciences.

112, 10623–10628.

Bobe, R. 2011: Fossil Mammals and Paleoenvironments in the Omo-Turkana Basin.

Evolutionary Anthropology: Issues, News, and Reviews 20:254–263.

Brown, F. H., and I. McDougall. 2011: Geochronology of the Turkana Depression of

Northern Kenya and Southern Ethiopia. Evolutionary Anthropology: Issues,

News, and Reviews 20:217–227.

Brown, J. H. 1995: Macroecology. University of Chicago Press, Chicago, p.

Brown, J. H., S. K. M. Ernest, J. M. Parody, and J. P. Haskell. 2001: Regulation of

diversity: maintenance of species richness in changing environments. Oecologia

126:321–332.

Brown, J. H., V. K. Gupta, B.-L. Li, B. T. Milne, C. Restrepo, and G. B. West. 2002: The

fractal nature of nature: power laws, ecological complexity and biodiversity.

Philosophical Transactions of the Royal Society B: Biological Sciences 357:619–

626.

Clapham, M. E., J. A. Karr, D. B. Nicholson, A. J. Ross, and P. J. Mayhew. 2016:

176

Ancient origin of high taxonomic richness among insects. Proceedings of the

Royal Society B: Biological Sciences 283:20152476.

Fridley, J. D., R. K. Peet, E. van der Maarel, J. H. Willems, A. E. C. H. Flather, and E. J.

B. Losos. 2006: Integration of Local and Regional Species‐Area Relationships

from Space‐Time Species Accumulation. The American Naturalist 168:133–143.

Gathogo, P. N. 2003: Stratigraphy and paleoenvironments of the Koobi Fora Formation

of the Ileret Area, northern Kenya. Master’s Thesis, University of Utah.

Gathogo, P. N., and F. H. Brown. 2006: Stratigraphy of the Koobi Fora Formation

(Pliocene and Pleistocene) in the Ileret region of northern Kenya. Journal of

African Earth Sciences 45:369–390.

Hadly, E. A., and B. A. Maurer. 2001: Spatial and temporal patterns of species diversity

in montane mammal communities of western North America. Evolutionary

Ecology Research 3:449–463.

Halley, J. M. 1996: Ecology, evolution and 1f-noise. Trends in Ecology & Evolution

11:33–37.

Harnik, P. G., C. Simpson, and J. L. Payne. 2012: Long-term differences in extinction

risk among the seven forms of rarity. Proceedings of the Royal Society B:

Biological Sciences 279:4969–4976.

Harte, J., and A. P. Kinzig. 1997: On the Implications of Species-Area Relationships for

Endemism, Spatial Turnover, and Food Web Patterns. Oikos 80:417.

Harte, J., A. B. Smith, and D. Storch. 2009: Biodiversity scales from plots to biomes with

a universal species-area curve. Ecology Letters 12:789–797.

Harte, J., T. Zillio, E. Conlisk, and A. B. Smith. 2008: Maximum entropy and the state-

177

variable approach to macroecology. Ecology 89:2700–2711.

Harte, J., S. McCarthy, K. Taylor, A. Kinzig, and M. L. Fischer. 1999: Estimating

Species-Area Relationships from Plot to Landscape Scale Using Species Spatial-

Turnover Data. Oikos 86:45.

Hawkins, B. A., J. A. F. Diniz‐Filho, C. A. Jaramillo, S. A. Soeller, and S. E. S. Harrison.

2007: Climate, Niche Conservatism, and the Global Bird Diversity Gradient. The

American Naturalist 170:S16–S27.

Jablonski, D., and J. J. Sepkoski. 1996: Paleobiology, Community Ecology, and Scales of

Ecological Pattern. Ecology 77:1367–1378.

Jacquemyn, H., J. Butaye, and M. Hermy. 2001: Forest plant species richness in small,

fragmented mixed deciduous forest patches: the role of area, time and dispersal

limitation: Plant species richness in small, fragmented forests. Journal of

Biogeography 28:801–812.

Koleff, P., K. J. Gaston, and J. J. Lennon. 2003: Measuring beta diversity for presence-

absence data. Journal of Animal Ecology 72:367–382.

La Sorte, F. A., and W. J. Boecklen. 2005: Temporal turnover of common species in

avian assemblages in North America. Journal of Biogeography 32:1151–1160.

Labandeira, C. C., and J. J. Sepkoski. 1993: Insect diversity in the fossil record. Science

261:310–315.

Lennon, J. J., P. Koleff, J. J. D. Greenwood, and K. J. Gaston. 2001: The geographical

structure of British bird distributions: diversity, spatial turnover and scale. Journal

of Animal Ecology 70:966–979.

Levin, S. A. 1992: The Problem of Pattern and Scale in Ecology: The Robert H.

178

MacArthur Award Lecture. Ecology 73:1943–1967.

Liow, L. H., T. Reitan, and P. G. Harnik. 2015: Ecological interactions on

macroevolutionary time scales: clams and brachiopods are more than ships that

pass in the night. Ecology Letters 18:1030–1039.

Lyons, S. K., K. L. Amatangelo, A. K. Behrensmeyer, A. Bercovici, J. L. Blois, M.

Davis, W. A. DiMichele, A. Du, J. T. Eronen, J. Tyler Faith, G. R. Graves, N.

Jud, C. Labandeira, C. V. Looy, B. McGill, J. H. Miller, D. Patterson, S. Pineda-

Munoz, R. Potts, B. Riddle, R. Terry, A. Tóth, W. Ulrich, A. Villaseñor, S. Wing,

H. Anderson, J. Anderson, D. Waller, and N. J. Gotelli. 2016: Holocene shifts in

the assembly of plant and animal communities implicate human impacts. Nature

529:80–83.

May, R. M. 1975: Patterns of species abundance and diversity. Pp.81–120 in M. L. Cody

and J. M. Diamond, eds. Ecology and Evolution of Communities. Harvard

University Press, Cambridge.

McGill, B., and C. Collins. 2003: A unified theory for macroecology based on spatial

patterns of abundance. Evolutionary Ecology Research 5:469–492.

McGill, B. J., E. A. Hadly, and B. A. Maurer. 2005: Community inertia of Quaternary

small mammal assemblages in North America. Proceedings of the National

Academy of Sciences 102:16701–16706.

McGill, B. J., M. Dornelas, N. J. Gotelli, and A. E. Magurran. 2015: Fifteen forms of

biodiversity trend in the Anthropocene. Trends in Ecology & Evolution 30:104–

113.

McGlinn, D. J., and M. W. Palmer. 2009: Modeling the sampling effect in the species–

179

time–area relationship. Ecology 90:836–846.

McKinney, M. L., and D. L. Frederick. 1999: Species–time curves and population

extremes: ecological patterns in the fossil record. Evolutionary Ecology Research

1:641–650.

McKinney, M. L., and J. L. Lockwood. 1999: Biotic homogenization: a few winners

replacing many losers in the next mass extinction. Trends in Ecology & Evolution

14:450–453.

Miller, J. H., A. K. Behrensmeyer, A. Du, S. K. Lyons, D. Patterson, A. Tóth, A.

Villaseñor, E. Kanga, and D. Reed. 2014: Ecological fidelity of functional traits

based on species presence-absence in a modern mammalian bone assemblage

(Amboseli, Kenya). Paleobiology 40:560–583.

Mittelbach, G. G., D. W. Schemske, H. V. Cornell, A. P. Allen, J. M. Brown, M. B.

Bush, S. P. Harrison, A. H. Hurlbert, N. Knowlton, H. A. Lessios, C. M. McCain,

A. R. McCune, L. A. McDade, M. A. McPeek, T. J. Near, T. D. Price, R. E.

Ricklefs, K. Roy, D. F. Sax, D. Schluter, J. M. Sobel, and M. Turelli. 2007:

Evolution and the latitudinal diversity gradient: speciation, extinction and

biogeography. Ecology Letters 10:315–331.

Patzkowsky, M. E., and S. M. Holland. 2003: Lack of community saturation at the

beginning of the Paleozoic plateau: the dominance of regional over local

processes. Paleobiology 29:545–560.

Preston, F. W. 1960: Time and Space and the Variation of Species. Ecology 41:611–627.

——— 1962a: The Canonical Distribution of Commonness and Rarity: Part I. Ecology

43:185.

180

——— 1962b: The Canonical Distribution of Commonness and Rarity: Part II. Ecology

43:410–432.

Punyasena, S. W., G. Eshel, and J. C. McElwain. 2008: The influence of climate on the

spatial patterning of Neotropical plant families. Journal of Biogeography 35:117–

130.

R Core Team. 2015: R: A Language and Environment for Statistical Computing. R

Foundation for Statistical Computing, Vienna, Austria, p.

Rahel, F. J. 2000: Homogenization of Fish Faunas Across the United States. Science

288:854–856.

Raia, P., F. Carotenuto, C. Meloro, P. Piras, and C. Barbera. 2011: Species accumulation

over space and time in European Plio-Holocene mammals. Evolutionary Ecology

25:171–188.

Ricklefs, R. E., and D. Schluter. 1993: Species diversity in ecological communities:

historical and geographical perspectives. University of Chicago Press, Chicago, p.

Rosenzweig, M. L. 1995: Species Diversity in Space and Time. Cambridge University

Press, Cambridge, United Kingdom, p.

——— 1998: Preston’s ergodic conjecture: the accumulation of species in space and

time. Pp.311–348 in Biodiversity Dynamics: Turnover of Populations, Taxa, and

Communities. Columbia University Press, New York.

Russell, R., S. A. Wood, G. Allison, B. A. Menge, A. E. W. G. Wilson, and E. D. L.

DeAngelis. 2006: Scale, Environment, and Trophic Status: The Context

Dependency of Community Saturation in Rocky Intertidal Communities. The

American Naturalist 167:E158–E170.

181

Saupe, E. E., H. Qiao, J. R. Hendricks, R. W. Portell, S. J. Hunter, J. Soberón, and B. S.

Lieberman. 2015: Niche breadth and geographic range size as determinants of

species survival on geological time scales. Global Ecology and Biogeography

24:1159–1169.

Sepkoski, J. J. 1976: Species diversity in the Phanerozoic: species-area effects.

Paleobiology 2:298–303.

——— 1978: A kinetic model of Phanerozoic taxonomic diversity I. Analysis of marine

orders. Paleobiology 4:223–251.

——— 1979: A Kinetic Model of Phanerozoic Taxonomic Diversity II. Early

Phanerozoic Families and Multiple Equilibria. Paleobiology 5:222–251.

Svenning, J.-C., and F. Skov. 2007: Could the tree diversity pattern in Europe be

generated by postglacial dispersal limitation? Ecology Letters 10:453–460.

Tóth, A. B., S. K. Lyons, and A. K. Behrensmeyer. 2014: A Century of Change in

Kenya’s Mammal Communities: Increased Richness and Decreased Uniqueness

in Six Protected Areas. PLoS ONE 9:e93092.

Western, D. 2007: A half a century of habitat change in Amboseli National Park, Kenya.

African Journal of Ecology 45:302–310.

Western, D., and A. K. Behrensmeyer. 2009: Bone Assemblages Track Animal

Community Structure over 40 Years in an African Savanna Ecosystem. Science

324:1061–1064.

White, E. P. 2004: Two-phase species-time relationships in North American land birds:

Two-phase species-time relationships. Ecology Letters 7:329–336.

——— 2007: Spatiotemporal scaling of species richness: patterns, processes, and

182

implications. Pp.325–346 in D. Storch, P. A. Marquet, and J. H. Brown, eds.

Scaling Biodiversity. Cambridge University Press, Cambridge.

White, E. P., S. K. M. Ernest, P. B. Adler, A. H. Hurlbert, and S. K. Lyons. 2010:

Integrating spatial and temporal approaches to understanding species richness.

Philosophical Transactions of the Royal Society B: Biological Sciences

365:3633–3643.

White, E. P., P. B. Adler, W. K. Lauenroth, R. A. Gill, D. Greenberg, D. M. Kaufman, A.

Rassweiler, J. A. Rusak, M. D. Smith, J. R. Steinbeck, R. B. Waide, and J. Yao.

2006: A comparison of the species-time relationship across ecosystems and

taxonomic groups. Oikos 112:185–195.

Wiens, J. A. 1989: Spatial Scaling in Ecology. Functional Ecology 3:385–397.

Williams, C. B. 1943: Area and Number of Species. Nature 152:264–267.

Williams, J. W., and S. T. Jackson. 2007: Novel climates, no-analog communities, and

ecological surprises. Frontiers in Ecology and the Environment 5:475–482.

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Chapter 5: Conclusions

In the Introduction chapter of this dissertation, I laid out my overarching research goals. The main unifying theme was an appreciation of scale2 and a desire to understand how scale differences among ecological datasets affect our interpretation of ecological pattern and process. Some questions included, “Which processes are important at which scales? Are small-scale ecological processes simply inscrutable from large-scale fossil data? Likewise, are larger-scale processes just as unknowable from smaller-scale modern data? In general, is scaling up (and down) possible, and can the scale divide between modern and fossil datasets be reconciled using analytical methods?”

The general conclusion from all three chapters is that the processes driving ecological patterns at small and large scales are fundamentally different, as has been hypothesized by previous researchers (Shmida and Wilson, 1985; Wiens, 1989; Levin,

1992; McGill, 2010). The use of simple power-law scaling relationships is not enough to bridge the disparate patterns seen across modern and fossil scales (Chapter 4). This might not be so surprising, as others have demonstrated that it is mathematically impossible to scale up (i.e., Jensen’s inequality; Ruel and Ayres, 1999). However, this question has rarely been addressed with empirical data spanning multiple orders of temporal scale.

The main reason for this (I assume) is the lack of appropriate datasets that are derived from the same region, comprise the same taxonomic group, and span the time scales of interest. To be clear, “datasets that span the time scales of interest,” in this case, refer to datasets that encompass both modern and fossil time scales (i.e., 100-106 years). There are

2 Scale here refers to three different dimensions which are theoretically independent but usually covary somewhat across modern and fossil scales. The three dimensions of scale are spatial, temporal, and taxonomic.

184 plenty of paleoecological studies that cover multiple orders of temporal magnitude (i.e.,

104-108 years), but they do not overlap with modern time scales, thus leaving the gap between neo- and paleoecological scales unbridged.

I have had the good fortune to have had access to a modern and a fossil dataset, both of which were collected on mammals in Kenya. The modern dataset is from the surface bone assemblage of Amboseli National Park and encompasses time scales of 100-

101 years (Behrensmeyer et al., 1979; Western and Behrensmeyer, 2009). Thus, the

Amboseli dataset is more time-averaged than the typical ecological dataset, which reduces the scale gap between this and fossil datasets. The fossil datasets I analyzed are from the Turkana Basin Institute Database (which is ultimately derived from the Public

Turkana Database3) and the American Shungura Database, both of which cover time scales of 104-106 years. Because these three datasets fulfill the criteria I outlined in the previous paragraph, I am in a unique position to address my original, overarching research questions of how does scale affect our interpretation of ecological pattern and process, and can the scale gap between modern and fossil datasets be bridged using analytical methods. With this in mind, I summarize the main findings from each of my three research chapters. I then conclude this chapter with the larger implications my findings have for ecology and paleoanthropology and finish with some potential avenues for future research.

Summary of research chapters

In Chapter 2, I applied a well-studied theoretical framework from modern ecology

(i.e., core-transient theory [Magurran and Henderson, 2003; Supp et al., 2015]) to the

3 http://naturalhistory.si.edu/ete/ETE_Datasets_Turkana.html

185 fossil record without any scaling adjustments. The main goal here was to see if the same processes that drive core-transient patterns in modern ecological systems may also be acting on larger time scales in fossil systems. Results showed moderate correspondence between the predictions from modern core-transient theory and the empirical patterns from the fossil record. There are a number of potential reasons for the mismatch (e.g., the collected ecological data from the fossil communities are not accurately reflecting the ecological processes of interest), but the most parsimonious explanation is that different ecological processes are operating in the fossil system compared to modern ones due to the large spatiotemporal scale discrepancy between the two.

In Chapter 3, I constructed a species-time-area relationship model (STAR) using the modern Amboseli data in order to extrapolate richness to the spatiotemporal scales observed in the fossil record. Results showed Amboseli richness scales with area and time much as in other systems (Adler et al., 2005), where the rate of richness increase with area (or time) decreases as one increases the time (or spatial) scale of sampling.

Furthermore, it is hypothesized that progressive sampling of a relatively static species pool causes this pattern. Rarer species become incorporated into one’s sample as the pool is more completely sampled with increasing scale. And because the richness of rare species is driven by more regional factors, an increase in the time scale of sampling (i.e., increased time-averaging) will result in communities that exhibit a coarse, regional-scale ecological signal. This relationship between temporal and spatial averaging can be quantified using the STAR model. These correlations between rarity, sampling order, and drivers of richness need to be tested more explicitly in the Amboseli data, and this is something I return to in the future research directions section.

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In Chapter 4, I generated predictions for fossil richness by extrapolating the spatiotemporal scale of the Amboseli STAR model, and compared these predictions to observed richness patterns in the fossil datasets. I found the STAR power function was inadequate for describing richness across multiple orders of spatiotemporal scale. The deviation of the power function at smaller and larger scales, however, reflects the fact that different processes are driving richness patterns at these scales. At the larger time scales of the fossil datasets, species richness is underpredicted using the STAR model, likely due to speciation and large-scale climatic shifts changing the composition of the species pool. A Poisson model corroborated this intuition and showed that a large portion of the deficit between predicted and observed richness could be accounted for speciation events, even on relatively short geological time scales (i.e., a single geological member).

Therefore, a completely different set of processes drives richness patterns at large temporal scales, making it difficult to commensurately compare modern and fossil communities. Also, because I had access to comparable datasets (i.e., collected on

Kenyan large mammals) that spanned modern and fossil time scales, I was able to construct the first empirical species-time relationship, demonstrating that the relationship is indeed triphasic as has been hypothesized previously (Preston, 1960).

Larger implications for the fields of neo- and paleoecology

Ecological pattern and process do not easily translate across scales. Currently, the scaling of species richness with area across six orders of magnitude can be explained by a minimum of two models (McGill, 2010). The smaller-scale model fails at larger spatial scales, and the larger-scale model fails at smaller scales. This may simply suggest that we

187 have yet to derive an adequate model for explaining richness at all possible scales.

However, if this feat proves to be analytically intractable as some researchers have suggested4, that means neoecologists and paleoecologists need to share data and collaborate in order to study ecology across the full spectrum of scales available to us

(i.e., from local habitats to continents, and from years to millions of years). That is, neo- and paleoecological theory and data are each incomplete: neoecologists need to analyze fossil data if they want to study ecology at large time scales, and paleoecologists need to examine modern data and theory in order to understand smaller-scale processes. On the other hand, instead of building a single model that would span all possible scales, researchers can do a better job of scaling their data. For example, neoecologists can use dynamic models (or more robust theory, e.g., Harte et al., 2009) to scale up their data (but not necessarily to large fossil scales). Paleoecologists can then meet neoecologists half way by either collecting data at finer scales, or analytically partitioning their data into subsets that correspond to finer scales. An example of the latter exercise can be found not in the paleoecology literature, but in the paleoanthropology literature. I, along with my co-authors, have studied hominin brain size evolution through time and partitioned brain size increase into change that occurs between and within lineages (Du et al., submitted).

We then found observed within-lineage brain size change was too slow compared to a scaled-up microevolutionary model. Though there is still a scale-break here, this research illustrates the promise of breaking down observed fossil patterns into smaller-scale components, which can then be compared to analytically scaled-up modern data.

Larger implications for paleoanthropology

4 https://dynamicecology.wordpress.com/2012/10/15/scaling-up-is-hard-to-do/

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First of all, it is clear from Chapter 3 that the effects of time-averaging roughly correspond to the effects of spatial averaging. That is, both are just different avenues for uncovering the rarer species in the larger species pool. As a result, time-averaged fossil assemblages likely represent a larger spatial scale than that seen in modern communities at the local scale. This is corroborated by studies which used neutral models to demonstrate that increased time-averaging in invertebrate death assemblages causes community patterns to converge on that of the larger metacommunity (Tomašových and

Kidwell, 2009, 2010a, 2010b). The relationship between time-averaging and spatial averaging can be quantified using the ratios of time-area equivalence from Chapter 3, assuming fossil communities turned over across space and time in ways analogous to

Amboseli. Results show that 10,000 years of time-averaging equates to about 895 km2 of spatial averaging which is 1.5 times the size of Amboseli and ~75% of the size of the

Koobi Fora region (Brown and Feibel, 1991). This is a conservative estimate, as I have demonstrated in Chapter 4 that the rate of species accumulation with time actually increases at larger temporal scales.

For paleoanthropologists, that means it is less than straightforward to infer smaller-scale ecological processes from fossil assemblages. For example, paleoenvironments reconstructed at fossil sites might reflect a more regional picture than the local ones that paleoanthropologists are interested in (e.g., for hominin “habitat preference” purposes). In fact, this may be a first-order explanation for why so many hominin habitats are reconstructed as mosaics (Reynolds et al., 2015): larger spatial scales will always encompass a greater variety of habitats relative to smaller spatial scales, with all else held equal. Likewise, inferring competition or predator-prey

189 relationships from assemblage co-occurrence data might be fraught for the same reasons.

Results from Chapter 2 reiterate the difficulty of applying modern ecological theory

(which was conceived at small temporal scales) to fossil assemblages.

Secondly, I was somewhat surprised in Chapter 4 by the predominance of large- scale evolutionary processes at the temporal scale of a single geological member in the

Koobi Fora dataset (i.e., 105 years). This emphasizes how fundamentally different the processes are in fossil systems compared to modern ones, where speciation is rarely observed. Despite this, paleoanthropologists often use member-level fossil assemblages to infer small-scale ecological processes (e.g., competition). Recently, multiple publications have used member-level assemblages to suggest that hominins outcompeted carnivoran species to the point of extinction (Werdelin and Lewis, 2013; Fortelius et al.,

2016). However, this assumes hominin and carnivorans were at carrying capacity for some given resource, but we currently know very little about the role speciation plays in affecting carrying capacity and the degree of interspecific competition. Most research related to this topic in the neo-ecological literature is directed towards competition driving speciation (Rosenzweig, 1978; Dieckmann and Doebeli, 1999; Doebeli and

Dieckmann, 2000). Therefore, more research should be directed towards understanding how speciation and large-scale climatic shifts affect smaller-scale ecological processes.

Until then, caution should be exercised when trying to infer these small-scale processes from time-averaged fossil assemblages.

Future directions

As comes naturally with all research projects, more questions arise than are

190 answered, and my dissertation research is no different. For the core-transient Chapter 2, the results (and interpretations that stemmed from them) were very noisy, but that should come as no surprise given the data are noisy (fossil data affected by taphonomic processes) and the research field/question is noisy (variation is the norm in ecology).

Future research should aim to reduce the noise, either through more data collection or more powerful analytical methods. The following are some issues I see with the core- transient chapter that could be addressed with future studies:

1) Is 50% member occupation an effective cut-off for dividing species into core and transient categories? The distinction between labelling a species as core vs. transient is a less than straightforward exercise, and previous researchers have done it in a myriad of ways. When lots of data are available, researchers have taken advantage of the bimodal distribution of temporal occupancy (Magurran, 2007) and used that to identify species as core or transient, though a decision must still be made on what the final threshold is (e.g.,

Coyle et al., 2013). Others have looked for any discontinuities in temporal occupancy patterns to separate core from transient species (e.g., Magurran and Henderson, 2003).

Another option is to a priori define the cut-off (e.g., Belmaker, 2009), and an alternative quantitative method is to statistically partition the data into two classes (e.g., based on abundance distributions; Gray et al., 2005). There are plenty of other methods, but it is important to understand that none of these methods are perfect, and they all come with trade-offs. Therefore, this issue of how to define core and transient species will remain until more research is done on species’ temporal occupancy distributions and the mechanisms determining whether a species is core or not.

2) Perhaps using geological member as a time unit is temporally too coarse, and attempts

191 should be made to collect fossil data on finer time scales. Doing so implicitly states that ecological patterns and processes change across temporal scale (which is true), so presumably any attempt to collect data approaching the time scales of modern studies will show more concordant results. However, trying to collect higher resolution data to make the results agree with those of modern studies seems a bit tautological. Instead, the usefulness of such a study might be in discovering where the scale break between neo- and paleoecology is, as well as demonstrating fossil biases are not as severe as neoecologists assume. Furthermore, it is not clear that collecting finer-scale fossil data will remedy the issue since fossil data (which at best will be on the order of 103 years

[Behrensmeyer et al., 2000]) will always be orders of magnitude larger temporally than modern data.

3) Critics may claim that the diet categories I used for this study are relatively coarse

(i.e., grazer, mixed browser/grazer, browser, omnivore, carnivore). While other studies – which claim diet should be studied using finer categories (e.g., Pineda-Munoz and Alroy,

2014) – subdivide omnivores, they actually lump grazers, mixed browser/grazers, and browsers into a single “green plants” category. This reflects the ambiguity that surrounds what exactly a “high resolution dietary category” means, as well as the difficulty in accurately categorizing diet across trophic levels and taxonomic groups.

Coarser dietary categories should have the effect of lumping more species into a given diet category. Creating finer-grained categories will only more accurately characterize core and transient species if these species are non-randomly allocated to those finer categories. This could feasibly occur if the finer dietary categories were actually capturing which dietary resource was facilitating persistence through geological time.

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This may be the case in the Omo-Turkana paleo-communities, but the only way to find out is to develop higher-resolution dietary categories, which is not possible at this time.

4) Body mass is not a good proxy for ecological specialization or competitive dominance

(i.e., the ability to appropriate a disproportionately large share of resources). Though body mass has been argued as such (e.g., Brown and Maurer, 1986; McKinney, 1997;

Van Valkenburgh et al., 2004), perhaps that is not the case in the Omo-Turkana paleocommunities given their spatial and temporal scale. Alternatively, perhaps intraspecific distribution of body masses will be more informative in this regard, and assigning a single body mass estimate to an entire species might be obscuring interesting ecological information.

5) The habitats occupied by these paleo-communities are only broadly defined and more research needs to be done to generate higher-resolution reconstructions (though this is now starting to be done [Bobe, 2011; Levin et al., 2011; Fortelius et al., 2016]).

Furthermore, it is unclear how a spatially large habitat should be characterized over geological time (e.g., should a single average measure be used? Standard deviation?

Calculated over time, space, or both?). This has important implications for understanding what kind of predictions should be made regarding a core species’ ecological attributes

(assuming strong habitat filtering). Therefore, the inability to accurately character the three paleocommunities’ habitats resulted in my making a very general prediction (i.e., specialists should be more likely to be core). However, if these three paleo-communities can be characterized on average (which again may be a problematic description for a large, changing habitat over geological time) as woodlands or mixed woodland/grassland, then perhaps the higher probability of browsers being core species should have been

193 expected. Again, more research on accurately characterizing the ancient habitats of these three paleocommunities will shed more light on this issue.

I probably should have expected that the fossil core-transient results would not have matched the predictions of modern theory, given Chapter 4’s results (i.e., a fundamentally different set of processes affect communities over different time scales). It is unfortunate then that this phenomenon is confounded with the issues I laid out above, i.e., all increase the discrepancy between modern and fossil core-transient correspondence. Future research should be able to tease out these confounding factors and figure out what is really driving the discrepancy between modern and fossil patterns.

Either way, applying theoretical frameworks from neoecology (with caution!) to the fossil record is a useful heuristic exercise. It has shed light on these aforementioned problems which may not have been of interest before, and it serves as a way to bridge modern and fossil theory and data.

Chapter 3’s Amboseli STAR results analyzing a surface bone assemblage demonstrate the analogous effects time and space have on species accumulation and how many of the macroecological patterns seen in one dimension match those of the other

(e.g., abundance-occupancy relationships, nestedness, ecological correlates of these patterns; though this needs to be more explicitly tested in the Amboseli data, which would be relatively straightforward to do) (see also Preston, 1960; Guo et al., 2000;

Magurran, 2007). This should serve to unify seemingly disparate studies that independently study the effects of time and space on biodiversity. I also offered a mechanism by which these species accumulation patterns are unified: progressive sampling of a relatively static species pool. This phenomenon leads to a decrease in the

194 rate of species accumulation (with either area or time) as the spatial and temporal span of sampling increases (the two are interchangeable and reflect the same process) (cf. Adler et al., 2005; Harte et al., 2009). These results can then be unified with our current understanding of how species are distributed across space and through time (e.g., abundance-occupancy relationships, nestedness, ecological correlates of these patterns).

Future research should try to unify all these patterns and mechanisms into one coherent stochastic sampling model which can make a number of ecological predictions ranging from macroecological patterns to species life-history traits (though this model will not be able to explain patterns and process across all possible scales; see Chapter 4). For example, a numerically common species will have high spatial and temporal occupancy

(Guo et al., 2000; Magurran and Henderson, 2003; Gaston and He, 2011) and will be sampled first in any local community. These common species should exhibit lognormal abundance distributions, which reflects local adaption to the site in question, competition for resources, and overall density-dependent regulation (Magurran and Henderson, 2003;

Ulrich and Zalewski, 2006; Henderson and Magurran, 2014). Rare species will have low spatial and temporal occupancy (Guo et al., 2000; Magurran and Henderson, 2003;

Gaston and He, 2011) and will be preferentially sampled later as sampling scale increases. Their diversity patterns are mostly driven by the presence of source communities elsewhere (which in turn is driven by regional habitat heterogeneity) and stochastic dispersal processes (Jetz and Rahbek, 2002; White et al., 2010; Coyle et al.,

2013). The rare species fraction typically exhibits log-series (Magurran and Henderson,

2003) or power-law abundance distributions (Ulrich and Ollik, 2004). Finally, the demonstrated importance of the species pool on species accumulation patterns deserves

195 more theoretical and empirical study, and reemphasizes the importance of regional processes influencing local community patterns (e.g., Harrison and Cornell, 2008).

Chapter 3 also quantified the relationship between temporal and spatial averaging using calculated ratios of time-area equivalence (Adler et al., 2005). It would be interesting to test these “space-for-time” predictions. That is, given a certain amount of time-averaging and its respective turnover rate, does that match the observed turnover rate across the predicted amount of space in other datasets? Rates of spatial and temporal turnover change, however, as the temporal and spatial span of sampling change, respectively. This can be accounted for using the Amboseli STAR model to see if other communities’ richness can be predicted given their spatiotemporal scale (assuming the other datasets do not have the appropriate spatiotemporal data with which to construct their own STAR). However, it is difficult to find large mammal datasets with appropriate spatial and/or temporal data. A published Kenyan mammal dataset (Tóth et al., 2014) is promising, but the national parks therein are spaced hundreds of kilometers apart which will overestimate spatial turnover, producing under-predicted richness if the Amboseli

STAR is used. Another option is to analyze other modern East African surface bone assemblage datasets that have been published from Serengeti and Ngorongoro, Tanzania

(Blumenschine, 1989), Parc National des Virguna, Zaire (Tappen, 1995), and Ol Pejeta,

Kenya (Pobiner and Kovarovic, 2011).

Chapter 4 compared richness predictions made by the STAR to observed fossil richness from the upper Koobi Fora Formation. Results showed that the STAR power function was inadequate for prediction richness across orders of magnitude, and it under- predicts richness at large temporal scales. The latter emphasizes the importance of

196 speciation and other rare, large-magnitude events (e.g., climatic change, large-scale migration events) in fossil communities that are not encountered on modern time scales. I used a simple Poisson probability model to predict the number of speciation events given the temporal extent of these fossil datasets, but a more detailed, realistic evolutionary model may produce more accurate estimates. Likewise, understanding the frequency of large-scale climate changes (i.e., via Milankovitch cycles) and their impact on species turnover will further our understanding of how regional species richness (i.e., the species pool) turns over on evolutionary time scales. Though perhaps too complicated, integrating the Amboseli STAR model with one that takes into account speciation rates and climate’s effect on large-scale species turnover should generate more accurate richness predictions across all orders of spatiotemporal scale. On the other hand (as I mentioned in Chapter 4), one can repurpose stochastic geometric models (McGill, 2010) and incorporate a time component in order to predict richness. This may be less satisfying to those who wish for ecological mechanisms in their model, but these stochastic models are simple and may prove to be more accurate for predicting fossil richness and future biodiversity shifts resulting from large-scale climate change. Not to mention, the STAR model itself lacks explicit ecological mechanisms and is a phenomenological sampling model.

In Chapter 4, I also constructed the first (to my knowledge) empirical triphasic species-time relationship using the Amboseli and Koobi Fora data. This exercise demonstrates the power of combining modern and fossil datasets within a single analysis.

However, there were only four fossil data points in the species-time relationship plot.

With the collection of more appropriate fossil data (i.e., fossil richness data with

197 respective time and area estimates that are not too many orders of magnitude larger than those in the modern dataset), one can construct an empirical 3D STAR figure, with richness plotted as a function of time in one dimension and space in the other.

Final thoughts

The scale gap between neo- and paleoecology may seem to some like a depressing conundrum. From the neoecological perspective, how will researchers be able to model and predict the impact of large-scale processes on biodiversity? How can they study and predict the outcomes of the current climate change crisis? From the paleoecological perspective, how can researchers study small-scale ecological processes given the temporally and spatially averaged nature of fossil assemblages? One might argue these are the processes of most interest to paleoanthropologists, given that they study evolution of hominin species and populations (i.e., small taxonomic units). For the neoecologist, the solution is to study large-scale paleoecological theory and data. The solution is less straightforward for the paleoecologist. She can either assume that certain smaller-scale processes are acting and producing the observed patterns in fossil assemblages, though different small-scale processes may independently produce the same large-scale pattern (what taphonomists call “equifinality”; Lyman, 1994). This is where inferential rigor and a working knowledge of logic and philosophy of science will come in handy. A robust theoretical model should make multiple independent predictions

(Rosenzweig and Abramsky, 1997) so that instead of matching one predicted pattern to the fossil record (which may match due to equifinality or random chance), one can test multiple predictions empirically (the more, the better). Therefore, perhaps

198 paleoanthropologists should work on making the theoretical frameworks of their hypotheses more robust. As I mentioned earlier, small-scale processes can be up-scaled and larger-scale patterns can be dissected into smaller-scale components, and the two can be compared at some halfway meeting point (e.g., Du et al., submitted). Nevertheless, this does not mean there will still not be a scale gap; its existence will simply be more precisely known. Thus, perhaps a scale-gap is just something we must accept in the study of ecology, but that is a dissertation for another day (and another student).

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References

Adler, P.B., White, E.P., Lauenroth, W.K., Kaufman, D.M., Rassweiler, A., Rusak, J.A.,

2005. Evidence for a general species-time-area relationship. Ecology. 86, 2032–

2039.

Behrensmeyer, A.K., Kidwell, S.M., Gastaldo, R.A., 2000. Taphonomy and

Paleobiology. Paleobiology. 26, 103–147.

Behrensmeyer, A.K., Western, D., Boaz, D.E.D., 1979. New Perspectives in Vertebrate

Paleoecology from a Recent Bone Assemblage. Paleobiology. 5, 12–21.

Belmaker, J., 2009. Species richness of resident and transient coral-dwelling fish

responds differentially to regional diversity. Global Ecology and Biogeography.

18, 426–436.

Blumenschine, R.J., 1989. A landscape taphonomic model of the scale of prehistoric

scavenging opportunities. Journal of Human Evolution. 18, 345–371.

Bobe, R., 2011. Fossil Mammals and Paleoenvironments in the Omo-Turkana Basin.

Evolutionary Anthropology: Issues, News, and Reviews. 20, 254–263.

Brown, F.H., Feibel, C.S., 1991. Stratigraphy, depositional environments and

palaeogeography of the Koobi Fora Formation. In: Harris, J.M. (Ed.), The Fossil

Ungulates: Geology, Fossil Artiodactylas, and Palaeoenvironments, Koobi Fora

Research Project. Clarendon Press, Oxford, pp. 1–30.

Brown, J.H., Maurer, B.A., 1986. Body size, ecological dominance and Cope’s rule.

Nature. 324, 248–250.

Coyle, J.R., Hurlbert, A.H., White, E.P., 2013. Opposing Mechanisms Drive Richness

Patterns of Core and Transient Bird Species. The American Naturalist. 181, E83–

200

E90.

Dieckmann, U., Doebeli, M., 1999. On the origin of species by sympatric speciation.

Nature. 400, 354–357.

Doebeli, M., Dieckmann, U., 2000. Evolutionary Branching and Sympatric Speciation

Caused by Different Types of Ecological Interactions. The American Naturalist.

156, S77–S101.

Du, A., Zipkin, A.M., Hatala, K.G., Renner, E., Baker, J.L., Bianchi, S., Bernal, K.H.,

Wood, B.A., submitted. Tempo and mode of human brain evolution is scale-

dependent. Science Advances.

Fortelius, M., Žliobaitė, I., Kaya, F., Bibi, F., Bobe, R., Leakey, L., Leakey, M.,

Patterson, D., Rannikko, J., Werdelin, L., 2016. An ecometric analysis of the

fossil mammal record of the Turkana Basin. Philosophical Transactions of the

Royal Society B: Biological Sciences. 371, 20150232.

Gaston, K.J., He, F., 2011. Species occurrence and occupancy. In: Maguran, A.E.,

McGill, B.J. (Eds.), Biological Diversity: Frontiers in Measurement and

Assessment. Oxford University Press, Oxford, UK, pp. 141–151.

Gray, J.S., Bjørgesæter, A., Ugland, K.I., 2005. The impact of rare species on natural

assemblages. Journal of Animal Ecology. 74, 1131–1139.

Guo, Q., Brown, J.H., Valone, & T.J., 2000. Abundance and distribution of desert

annuals: are spatial and temporal patterns related? Journal of Ecology. 88, 551–

560.

Harrison, S., Cornell, H., 2008. Toward a better understanding of the regional causes of

local community richness. Ecology Letters. 11, 969–979.

201

Harte, J., Smith, A.B., Storch, D., 2009. Biodiversity scales from plots to biomes with a

universal species-area curve. Ecology Letters. 12, 789–797.

Henderson, P.A., Magurran, A.E., 2014. Direct evidence that density-dependent

regulation underpins the temporal stability of abundant species in a diverse animal

community. Proceedings of the Royal Society B: Biological Sciences. 281,

20141336–20141336.

Jetz, W., Rahbek, C., 2002. Geographic Range Size and Determinants of Avian Species

Richness. Science. 297, 1548–1551.

Levin, N.E., Brown, F.H., Behrensmeyer, A.K., Bobe, R., Cerling, T.E., 2011. Paleosol

carbonates from the Omo Group: Isotopic records of local and regional

environmental change in East Africa. Palaeogeography, Palaeoclimatology,

Palaeoecology. 307, 75–89.

Levin, S.A., 1992. The Problem of Pattern and Scale in Ecology: The Robert H.

MacArthur Award Lecture. Ecology. 73, 1943–1967.

Lyman, R.L., 1994. Vertebrate Taphonomy. Cambridge University Press, Cambridge

England ; New York.

Magurran, A.E., 2007. Species abundance distributions over time. Ecology Letters. 10,

347–354.

Magurran, A.E., Henderson, P.A., 2003. Explaining the excess of rare species in natural

species abundance distributions. Nature. 422, 714–716.

McGill, B.J., 2010. Matters of Scale. Science. 328, 575–576.

McGill, B.J., 2010. Towards a unification of unified theories of biodiversity: Towards a

unified unified theory. Ecology Letters. 13, 627–642.

202

McKinney, M.L., 1997. Extinction Vulnerability and Selectivity: Combining Ecological

and Paleontological Views. Annual Review of Ecology and Systematics. 28, 495–

516.

Pobiner, B.L., Kovarovic, K., 2011. The Bones of Ol Pejeta: Clues to the Past [WWW

Document]. Popular Archeology. URL http://popular-

archaeology.com/issue/03012014/article/the-bones-of-ol-pejeta-clues-to-the-past

(accessed 12.22.16).

Pineda-Munoz, S., Alroy, J., 2014. Dietary characterization of terrestrial mammals.

Proceedings of the Royal Society B: Biological Sciences. 281, 20141173–

20141173.

Preston, F.W., 1960. Time and Space and the Variation of Species. Ecology. 41, 611–

627.

Reynolds, S.C., Wilkinson, D.M., Marston, C.G., O’Regan, H.J., 2015. The “mosaic

habitat” concept in human evolution: past and present. Transactions of the Royal

Society of South Africa. 70, 57–69.

Rosenzweig, M.L., 1978. Competitive speciation. Biological Journal of the Linnean

Society. 10, 275–289.

Rosenzweig, M.L., Abramsky, Z., 1997. Two gerbils of the Negev: A long-term

investigation of optimal habitat selection and its consequences. Evolutionary

Ecology. 11, 733–756.

Ruel, J.J., Ayres, M.P., 1999. Jensen’s inequality predicts effects of environmental

variation. Trends in Ecology & Evolution. 14, 361–366.

Shmida, A., Wilson, M.V., 1985. Biological determinants of species diversity. Journal of

203

Biogeography. 1–20.

Supp, S.R., Koons, D.N., Ernest, S.K.M., 2015. Using life history trade-offs to

understand core-transient structuring of a small mammal community. Ecosphere.

6, art187.

Tappen, M., 1995. Savanna Ecology and Natural Bone Deposition: Implications for Early

Hominid Site Formation, Hunting, and Scavenging. Current Anthropology. 36,

223–260.

Tomašových, A., Kidwell, S.M., 2009. Fidelity of variation in species composition and

diversity partitioning by death assemblages: time-averaging transfers diversity

from beta to alpha levels. Paleobiology. 35, 94–118.

Tomašových, A., Kidwell, S.M., 2010a. The Effects of Temporal Resolution on Species

Turnover and on Testing Metacommunity Models. The American Naturalist. 175,

587–606.

Tomašových, A., Kidwell, S.M., 2010b. Predicting the effects of increasing temporal

scale on species composition, diversity, and rank-abundance distributions.

Paleobiology. 36, 672–695.

Tóth, A.B., Lyons, S.K., Behrensmeyer, A.K., 2014. Mammals of Kenya’s protected

areas from 1888 to 2013: Ecological Archives E095-150. Ecology. 95, 1711–

1711.

Ulrich, W., Ollik, M., 2004. Frequent and occasional species and the shape of relative-

abundance distributions. Diversity and Distributions. 10, 263–269.

Ulrich, W., Zalewski, M., 2006. Abundance and co-occurrence patterns of core and

satellite species of ground beetles on small lake islands. Oikos. 114, 338–348.

204

Van Valkenburgh, B., Wang, X., Damuth, J., 2004. Cope’s Rule, hypercarnivory, and

extinction in North American canids. Science. 306, 101–104.

Werdelin, L., Lewis, M.E., 2013. Temporal Change in Functional Richness and Evenness

in the Eastern African Plio-Pleistocene Carnivoran Guild. PLoS ONE. 8, e57944.

Western, D., Behrensmeyer, A.K., 2009. Bone Assemblages Track Animal Community

Structure over 40 Years in an African Savanna Ecosystem. Science. 324, 1061–

1064.

White, E.P., Ernest, S.K.M., Adler, P.B., Hurlbert, A.H., Lyons, S.K., 2010. Integrating

spatial and temporal approaches to understanding species richness. Philosophical

Transactions of the Royal Society B: Biological Sciences. 365, 3633–3643.

Wiens, J.A., 1989. Spatial Scaling in Ecology. Functional Ecology. 3, 385–397.

205