Table Of ContentTHE ADAPTIVE
GEOMETRY OF
Trees
MONOGRAPHS IN POPULATION BIOLOGY
EDITED BY ROBERT M. MAY
1. The Theory of Island Biogeography, by Robert H. Mac-
Arthur and Edward O. Wilson
2. Evolution in Changing Environments: Some Theoretical Ex-
plorations, by Richard Levins
3. Adaptive Geometry of Trees, by Henry S. Horn
4. Theoretical Aspects of Population Genetics, by Motoo Ki-
mura and Tomoko Ohta
5. Populations in a Seasonal Environment, by Stephen D. Fret-
well
6. Stability and Complexity in Model Ecosystems, by Robert M.
May
7. Competition and the Structure of Bird Communities, by Mar-
tin L. Cody
8. Sex and Evolution, by George C. Williams
9. Group Selection in Predator-Prey Communities, by Michael
E. Gilpin
10. Geographic Variation, Speciation, and Clines, by John A.
Endler
11. Food Webs and Niche Space, by Joel E. Cohen
12. Caste and Ecology in the Social Insects, by George F. Oster
and Edward O. Wilson
13. The Dynamics of Arthropod Predator-Prey Systems, by Mi-
chael P. Hassell
14. Some Adaptations of Marsh-Nesting Blackbirds, by Gordon
H. Orians
15. Evolutionary Biology of Parasites, by Peter W. Price
16. Cultural Transmission and Evolution: A Quantitative Ap-
proach, by L. L. Cavalli-Sforza and M. W. Feldman
17. Resource Competition and Community Structure, by David
Tilman
18. The Theory of Sex Allocation, by Eric L. Charnov
19. Mate Choice in Plants: Tactics, Mechanisms, and Conse-
quences, by Mary F. Willson and Nancy Burley
THE ADAPTIVE
GEOMETRY OF
Trees
BY HENRY S. HORN
PRINCETON, NEW JERSEY
PRINCETON UNIVERSITY PRESS
Copyright © 1971 by Princeton University Press
ALL RIGHTS RESERVED
L. C. Card: 70-140279
ISBN: 0-691-08089-5
ISBN: 0-691-02355-7 (pbk.)
This book has been composed in Linofilm Baskerville
Printed in the United States of America
Contents
Preface vii
Preface to the Second Printing ix
Symbols Used xii
1. Introduction 3
2. Measurement of Light Intensity 8
3. Analysis of a Forest Succession 19
4. Theoretical Strategies of Leaf Distribution 45
5. Photosynthetic Response of the Strategies 64
6. Measurement of Actual Strategies 89
7. Speculations on the Shapes of Tree Crowns 104
8. On the Relation between Theory and Reality 118
Nomenclature 131
Bibliography 135
Index 141
Preface
I started this project almost by accident three years ago.
Robert MacArthur and I had been trying to find mechani-
cal ways to measure foliage profiles, which he had found to
be accurate predictors of the variety of birds in a habitat.
One of our machines was an adjustable- light meter that I
shall describe in Chapter 2. While testing it in the woods
on a Sunday afternoon, I recorded the meter readings
above various saplings, and I was struck by a general pat-
tern. Trees that typically invade old fields were never
found under a canopy. The familiar species of young
forests were found beneath openings in the canopy, and
denizens of virgin forests were found in deep shade. An
accumulation of many more measurements eventually
gave strong support to the foresters' axiom that species
which tolerate a canopy become progressively more
dominant as succession proceeds —a result that was more
gratifying than surprising. However, the analysis raised
new questions and cast new light on some old ones. I sub-
sequently invented a theory to explore these questions.
The theory led to new kinds of measurements, which led
to changes in the theory, and so on. The result to date is
this book, in which I simultaneously commit the sins of
vitalism and mechanism. Indeed, thinking of trees as crafty
green strategists has given me many new insights, and
simplified assumptions have allowed me to test these in-
sights. I have organized my ideas around the traditional
problem of plant succession, but my basic interest is the
prediction and testing of patterns of adaptive strategies
among trees. I sincerely hope that my ideas will not be
viewed as a contribution to past and current controversies
about the appropriateness of successional terminologies.
v 11
PREFACE
Rather, I am much more interested in the way that nature
shapes theory than in the constraints that theory imposes
on nature. The greatest homage that can be paid to an em-
pirical theory is the constructive criticism that makes it
obsolete at an early age.
Throughout this study I have had continual discussions
with Robert MacArthur and Egbert Leigh. I am indebted
to them for elegant improvements in the theory and for
critical empirical observations. I have also had very helpful
comments and observations from John Bonner, Gordon
Orians, Daniel Janzen, Christopher Smith, Woodruff Ben-
son, and J. Merritt Emlen.
For permission to work on their land, or for tolerating
my presence without permission, I am grateful to those in
charge of the Institute Woods, Herrontown Woods County
Park, and the Stony Ford Field Station at Princeton, N.J.;
Mammoth Cave National Park, Ky.; Calaveras County
Big Tree Park, Calif.; and Finca las Cruces, San Vito de
Java, Puntarenas Prov., Costa Rica. For help in the field
and in the lab, I am indebted to my wife, Elizabeth, to
Thomas Gibson, to Robert Millaway, and to several
students in the August 1969 O.T.S. Advanced Population
Biology group.
The funds for this study were scrounged from many
sources. My wife allowed me to use part of the family
budget that she earned. The Eugene Higgens Trust Fund
of the Princeton Department of Biology provided pin
money. I had free use of electronic gadgets provided and
maintained by the Whitehall Foundation. The Organiza-
tion for Tropical Studies paid my way to and in Costa Rica
in return for a series of lectures on theoretical forestry.
Although they don't know it yet, the Princeton University
Computer Center provided free computer time, charged
to a grant from the National Science Foundation.
For reading the entire manuscript and tendering valu-
vl I i
