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Patterns in Nature

The Analysis of Species Co-Occurrences

What species occur where, and why, and why some places harbor more species than others are basic questions for ecologists. Some species simply live in different places: fish live underwater; birds do not. Adaptations follow: most fish have gills; birds have lungs. But as Patterns in Nature reveals, not all patterns are so trivial.

Travel from island to island and the species change. Travel along any gradient—up a mountain, from forest into desert, from low tide to high tide on a shoreline —and again the species change, sometimes abruptly. What explains the patterns of these distributions? Some patterns might be as random as a coin toss. But as with a coin toss, can ecologists differentiate associations caused by a multiplicity of complex, idiosyncratic factors from those structured by some unidentified but simple mechanisms? Can simple mechanisms that structure communities be inferred from observations of which species associations naturally occur? For decades, community ecologists have debated about whether the patterns are random or show the geographically pervasive effect of competition between species. Bringing this vigorous debate up to date, this book undertakes the identification and interpretation of nature’s large-scale patterns of species co-occurrence to offer insight into how nature truly works.

Patterns in Nature explains the computing and conceptual advances that allow us to explore these issues. It forces us to reexamine assumptions about species distribution patterns and will be of vital importance to ecologists and conservationists alike.

184 pages | 34 halftones, 15 tables | 6 x 9 | © 2015

Biological Sciences: Conservation, Ecology, Evolutionary Biology, Natural History


“Unpicking why and how certain adaptations within species appear to be linked with particular habitats, the authors hope to reveal intriguing insights into community ecology.”

Observer (UK)

“Sanderson and Pimm provide a thorough historical overview of this contentious debate between Diamond and Connor and Simberloff. This is particularly helpful for younger scientists. . . . This book serves as an excellent reminder of the importance of the clear and explicit articulation of one's research questions and hypotheses—that null models are the building blocks to hypothesis testing using a statistical-model approach. . . . Furthermore, Sanderson and Pimm provide a wise reminder that as scientists, if we are to move our science forward, sometimes it is important to revisit concepts using a fresh perspective or new technologies, regardless of the perceived scientific ‘sexiness’ of doing such a thing.”


“A valuable and stimulating review of decades of work. The focus on intellectual content is refreshing, because there seems little to be gained from rekindling what the authors term an ‘academic war,’ and, overall, I feel that the major contributions arising from both entrenched positions are well recognized here (the occasional pointed aside notwithstanding). There is a clear moral too, that increased openness can help us to avoid future ‘wars.’ . . . Was it worth these decades of hostility? Are we now in a much stronger position to robustly predict how ecological communities will respond to an uncertain future? I am not sure. But, I am convinced by the authors’ statement that doing so will require increased cooperation between those able to identify, analyze, and explain repeated patterns in nature.”

Thomas J. Webb, University of Sheffield | Trends in Ecology & Evolution

“Sanderson and Pimm . . . are not about to let the dust settle. Their text is an accessible summary of the crux of the debate, and an attempt to persuade a general readership that the proper design of null models provides the key to resolving all such disagreements. . . . What they achieve in their book, rather than a resolution, is to resurrect the debate in the light of recent theoretical developments, particularly the means to more fully explore the null model space. Regardless of whether you ultimately agree with their conclusions, this makes it an important and worthwhile read.”

Markus Eichhorn, University of Nottingham | Frontiers of Biogeography

“The strength of the book is that it goes beyond simply revisiting a historical debate, in which the authors themselves participated, to present a robust way forward that draws on insights gained from a range of re-analyses, including those central to perhaps the most heated debate in ecology. An exciting next step would be to take advantage of modern computing power and apply this approach to a wider array of taxa and localities to more fully understand how species interactions structure ecological communities across scales.”

Phoebe L. Zarnetske, Michigan State University | Ecology

“Two fundamental questions of community ecology concern large-scale patterns of species communities. Do such patterns really exist? If they do exist, how can they be explained? Difficulties in answering these questions have given rise to much debate over the course of the last forty years. By assembling massive new databases and powerful new analytical techniques, Sanderson and Pimm have now produced this wonderfully clear account of this wonderfully complex subject. This book will be the standard reference work for everyone interested in the patterns of species communities.”

Jared Diamond, University of California, Los Angeles | author of the Pulitzer Prize-winning “Guns, Germs, and Steel”

“This stimulating book is centered upon an attempt, inspired by Robert MacArthur, to explain patterns of co-occurrences of bird species that might be caused by competition. Are the patterns real or no different from what is expected by chance? The authors adopt an engaging conversational style in confronting the contentious issues and surprising complexity of distinguishing between these stark alternatives. The book will be valuable in showing how ecologists grapple with fundamentally different opinions on how to analyze data.”

Peter R. Grant, Princeton University | coauthor of "40 Years of Evolution: Darwin's Finches on Daphne Major Island"

“A very interesting book on large-scale species distribution patterns, this is not a repeat of what has been published voluminously on the debate between Diamond and Connor/Simberloff, but a well-written, fairly balanced, and updated account of the positive contributions to science from both camps and the lessons that we all can learn from such heated debates. For those who are interested in island biogeography, for those who are enthused by ‘laws’ in ecology, and for those who are intrigued by historical developments in community ecology and beyond, this is a fascinating read. And for those who want to learn useful techniques and algorithms in null model analysis, Patterns in Nature is an entertaining and valuable book.”

Jianguo (Jingle) Wu, Arizona State University | coeditor of "Key Topics in Landscape Ecology"

Table of Contents


Part I. The Distribution of Species on Islands

Chapter 1. Patterns or Fantasies?
Species Co-occurrences
The Night Sky Effect
Patterns in Nature
Finding the Null
What This Book Is About
How This Book Is Organized

Chapter 2. Diamond’s Assembly Rules
Robert MacArthur, 1930–1972
Special Islands and Their Birds
What Is a Checkerboard Distribution?
The Theoretical Context
The Cuckoo Doves
Patchy Distributions

Chapter 3. The Response of Connor and Simberloff
The Backlash
How Likely Are Checkerboards?
Prior Expectations
The Analysis of Vanuatu

Part II. A Technical Interlude

Chapter 4. How to Incorporate Constraints into Incidence Matrices
Definitions and Notation
The Numbers of Null Matrices and the Effect of Constraints
The Hypergeometric Distribution
The Three Ecological Constraints Proposed by Connor and Simberloff in Their Studies of Birds and Bats on Islands
Why Constraints? And What Does “Representative” Mean?

Chapter 5. How to Fill the Sample Null Space
Null Space Creation Algorithms
Creating a Uniform Random Sample Null Space
The Trial-Swap Algorithm

Chapter 6. How to Characterize Incidence Matrices
Then You Need a Metric . . .
The Metric of Connor and Simberloff (1979)
Wright and Biehl (1982)
Harvey et al.’s (1983) Review of Null Models in Ecology
Stone and Roberts (1990, 1992) and Roberts and Stone (1990)
Why Ensemble Metrics Fail—An Example

Part III. Reanalysis and Extensions

Chapter 7. Vanuatu and the Galápagos
The Birds of Vanuatu
The Birds of the Galápagos

Chapter 8. The Birds of the Bismarck and Solomon Islands
The Issue of Superspecies
The Patterns
Taxonomic Sieving and Incidence Effects
Which Genera Develop Checkerboards?
When the Incidences Do Not Overlap

Chapter 9. Species along a Gradient
The Herptofauna of Mount Kupe, Cameroon
Why Do the Results Differ from Previous Results?
The Second Question: Do Species Form Distinct Communities?

Chapter 10. Applications to Food Webs: Nestedness and Reciprocal Specialization
Groupings of Species Interactions

Chapter 11. Coda
MacArthur’s Original Vision
The Patterns Themselves
The Need for Null Hypotheses


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