Food Webs and Niche Space

by Joel E. Cohen, David W. Stephens

Overview

What is the minimum dimension of a niche space necessary to represent the overlaps among observed niches? This book presents a new technique for obtaining a partial answer to this elementary question about niche space. The author bases his technique on a relation between the combinatorial structure of food webs and the mathematical theory of interval graphs.


Professor Cohen collects more than thirty food webs from the ecological literature and analyzes their statistical and combinatorial properties in detail. As a result, he is able to generalize: within habitats of a certain limited physical and temporal heterogeneity, the overlaps among niches, along their trophic (feeding) dimensions, can be represented in a one-dimensional niche space far more often than would be expected by chance alone and perhaps always. This compatibility has not previously been noticed. It indicates that real food webs fall in a small subset of the mathematically possible food webs.


Professor Cohen discusses other apparently new features of real food webs, including the constant ratio of the number of kinds of prey to the number of kinds of predators in food webs that describe a community. In conclusion he discusses possible extensions and limitations of his results and suggests directions for future research.

Product Details

ISBN-13:	9780691082028
Publisher:	Princeton University Press
Publication date:	08/21/1978
Series:	Monographs in Population Biology , #11
Pages:	208
Product dimensions:	5.50(w) x 8.50(h) x (d)

Table of Contents

	Preface	ix
	List of Tables	xi
	List of Figures	xiii
1.	Introduction	3
2.	A Relation between Food Webs and Niche Space	6
2.1	Interval Graphs and the Dimensionality of Niche Space	6
2.2	Food Webs Defined by Community, by Sources, and by Sinks	20
2.3	Food Webs of Single Habitats and of Composite Communities	23
2.4	Competition and Niche Overlap	24
2.5	Summary	26
3.	Which Food Webs Are Interval?	28
3.1	Sources of Data	28
3.2	Review of Food Webs	31
3.3	Summary	40
4.	Statistics of Food Webs	41
4.1	Why Statistics of Food Webs?	41
4.2	The Food Web Matrix	44
4.2.1	Are Predators and Prey Fussy?	44
4.2.2	The Ratio of Prey to Predators	51
4.2.3	The Length of Food Chains	56
4.3	The Niche Overlap Matrix	58
4.3.1	Six Models Based on the Food Web	58
4.3.2	The Distribution of Niche Overlaps	71
4.4	Summary	73
5.	Frequencies of Interval Food Webs in Observed and Monte Carlo Samples	75
5.1	Matching Food Web Characteristics	75
5.2	Matching Niche Overlap	81
5.3	Calibrating the Lottery	86
5.4	Summary	92
6.	If Niche Space Is One-Dimensional	93
6.1	What Is the One Dimension?	93
6.1.1	Non-Uniqueness	93
6.1.2	Suggestions from the Food Web Studies	95
6.1.3	Suggestions from Other Studies	97
6.2	What Follows from One Dimension?	100
6.3	Why One Dimension?	104
6.4	Summary	109
7.	Extensions and Critique	111
7.1	Extensions of This Approach	111
7.1.1	Higher Dimensions	111
7.1.2	Nearly Interval Food Webs	115
7.2	Critique	118
7.2.1	Ambiguous Primitives	118
7.2.2	Statistical Shortcomings of the Data	120
7.2.3	Lack of Quantitative Content	122
7.2.4	Lack of Dynamic Theory	124
7.3	Summary	125
8.	Review of Open Problems	126
8.1	Introduction	126
8.2	Theoretical	126
8.3	Empirical	129
Appendix 1	Sample of Food Webs	133
Appendix 2	The Mean and Variance of Niche Overlap according to Six Food Web Models	166
Appendix 3	Expected Niche Overlaps Assuming Randomly Overlapping One-Dimensional Niches	173
	References and Author Index	174
	Index	185