The Genetics of Altruism

459 Pages·1980·7.13 MB·English

by  Scott Boorman (Auth.)

The Genetics of Altruism
SCOTT A. BOORMAN PAUL R. LEVITT
Department of Sociology Department of Sociology
Yale University Harvard University
New Haven, Connecticut Cambridge, Massachusetts
ACADEMIC PRESS
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Library of Congress Cataloging in Publication Data
Boorman, Scott A
The genetics of altruism.
Bibliography: p.
Includes index.
1. Social behavior in animals—Mathematical
models. 2. Altruistic behavior in animals—
Mathematical models. 3. Sociobiology —
Mathematical models. 4. Animal genetics—
Mathematical models. 5. Human genetics—
Mathematical models. I. Levitt, Paul R. , joint
author. II. Title.
QL775.B59 591.5Γ028 79-52792
ISBN 0-12-115650-8
PRINTED IN THE UNITED STATES OF AMERICA
80 81 82 83 9 8 7 6 5 4 3 2 1
To
S. A. R.
From both of us
Preface
In 1974, in a New York Times essay bearing the same title as this book, we
suggested that "the [population] genetic approach to social evolution is... one
of the few fundamentally fresh ways of looking at problems on the boundaries
between behavioral biology and sotial science." In the years since, the entire
subject of social evolution has undergone dramatic growth as a scientific
research field, with facets now touching numerous areas of biological and
physical as well as social science. The volume of data being gathered speaks for
itself. To cite one example, a recent bibliography on invertebrate chemical
communication and signaling systems lists over 700 articles on this one topic,
most of them published since the early 1970s. Social vertebrate behavior studies
have seen comparable growth.
New research on this scale, backed by increasing research funding, has
brought into prominence a central gap in the literature on social evolution.
Although innumerable genetic ideas and evolutionary models are presently "in
circulation," and excellent survey treatments exist for many areas, only quite
limited efforts have yet been made to draw this work together into a unified
technical foundation for the discipline. As the chemical communication
example documents, there is risk of losing perspective in the mass of information
being accumulated, with detriment to theoretical and empirical research alike.
In addition, a review of contemporary literature on social evolution suggests
that many basic connections have not been made or principles clearly stated in
their natural generality. Working out certain of these connections on the level of
population genetics is the goal of this book.
To draw a parallel with developmental cycles commonly recognized in
literature and the arts, this goal is in many ways a "classical" objective in a
distinctively "romantic" era of biology, at a time when the whole field of
evolution is in ferment and old dividing lines are being challenged and
overturned. For this reason, a further objective of this book is to establish a
xi
xü Preface
system of genetic boxes in which new knowledge about social evolution may be
gradually sorted and systematized as it accumulates and by which new ideas may
be evaluated in anticipation of the next classical era of the subject.
In keeping with a basic decision to address our topic from a population
genetics standpoint, we made an early choice not to expand coverage to
some evolutionary topics in which the genetic bases of evolution remain implicit
and model-building is phenotypic only. Thus, one exclusion is of research
developing the concept of "evolutionarily stable strategies" (ESS), even though
this study opens an important set of direct linkages between social evolution and
modeling in a strategic or game-theoretic tradition. A further exclusion is of
group selection above the species level, via competition among higher taxo-
nomic units representing different kinds of biological organization.
One consequence of writing on population genetics is that the analyses require
substantial mathematics. Citing an analogy to the early mathematical work of
economists, we feel that a mathematical frame of reference is inherent in the
logical structure of the present field. On the other hand, biologists as well as
social scientists are often not applied mathematicians. Therefore, in writing this
book we have sought as far as possible to extract the primary evolutionary
findings from mathematical language and details, and have written independent
substantive essays around these results in Chapters 1 and 12. Most of the rest of
this book requires fluency in undergraduate mathematics at the level of calculus
and elementary probability theory; several chapters (especially Chapters 2, 3,5,
6-8) have been used successfully as text material in seminars and undergraduate
model-building courses at Harvard and Yale. Interpolated "Comments and
Extensions" sections as well as Notes at the end of each chapter locate many of
the references to more advanced mathematical topics outside the flow of the
main text. Finally, an appendix at the end of this book also makes it self-
contained with respect to basic population genetics principles, and a glossary
defines major technical terms as used in the present subject.
Acknowledgments
We thank many colleagues for their valuable comments on various specific
models and writeups and for other support on the project. Thanks are
particularly owing to Kenneth Arrow, Elliot Bailis, James Crow, Burton
Dreben, Jerry Green, George Homans, Frank Hoppensteadt, Tsuneo Ishikawa,
Joseph Keller, Nathan Keyfitz, Peter Lax, Richard Levins, Richard Lewontin,
George Papanicolaou, Donald Ploch, Harry Quigley, Walter Rothenbuhler,
Amy Schoener, Thomas Schoener, David Shapiro, James Truman, Harrison
White, and Edward Wilson. Conversation s with the late Robert MacArthur
greatly influenced our subsequent development of the Chapter 2 models and
their evolutionary interpretations . We are also indebted to Phipps Arabie, whose
assistance in carrying out preliminar y numerical studies of the asymptotic
behavior of Eqs. (3.5)-(3.8) gave important initial insight into the phase plane
structure of the Chapter 4 models.
The production of this book was a major logistical task. It is an additional
pleasure to acknowledge our research assistants over six years for their efficient
and resourceful aid in the project logistics. In this regard, special thanks go to
David Kelley and to Mrs. Kitty Munson Bethe. Mrs. Mary Bosco superbly typed
all intermediate and final manuscripts. We wish to express our indebtedness to
her for this work, and to William Minty, Lola Chaisson, and James Brosious for
their excellent drafting of the figure originals.
This research was funded primarily through the generous support of the
National Science Foundation. We particularly acknowledge support from NSF
Grants SOC76-24512 and SOC76-24394 and predecessor grants, as well as from
GB-7734. Early funding support was also received from the Society of Fellows of
Harvard University. Supplementary research space was furnished at various
times through the courtesy of Arthur Dempster, Nathan Keyfitz, Richard
Lewontin, and the Cowles Foundation for Research in Economics at Yale
xiii
xiv Acknowledgments
University. The second author also wishes to thank Warren E. C. Wacker, M.D.,
and Ann M. Wacker, co-masters of South House at Harvard University, whose
generous sponsorship of living arrangements enabled him to carry on several
research projects, including the final prepublication stages of the present
research. Finally, we thank our colleagues at Academic Press for their
professionalism and craftsmanship in the production of this book.
List of Figures
Chapter 1 Page
Fig. 1.1. Levins (1970a) metapopulation, showing network of islands. 7
Chapter 2
Fig. 2.1. Minimal model: Graph illustrating pattern of cooperativ e ties
(partnerships). 39
Fig. 2.2. Cobweb diagram for selection of a recessive social trait. 41
Fig. 2.3. ßcrit as a function of ζ = σ/τ. 45
Fig. 2.4. ßcnt as a function of L. 47
Fig. 2.5. Per capita return as a function of the number of hunters. 51
Fig. 2.6. Model 2: Graph illustrating fitness transfers. 58
Fig. 2.7. Contact and fitness transfer graphs for Model 3. 61
Fig. 2.8. Viscous matrix for nearest neighbors. 63
Fig. 2.9. jScrit as a function of the dominance of a over A, parameterized by
h Ε [0, 1]. 69
Fig. 2.10. Contrast between minimal model selectio n of a recessive and of a
dominant social trait. 70
Chapter 3
Fig. 3.1. A stepping-stone model with an irregular network topology . 80
Fig. 3.2. A successful cascade late in its history with all sites well above
threshold. 84
Fig. 3.3. Failure of the social gene, reporting gene frequencies after 100
generations. 84
Fig. 3.4. Two-island approximation to outward spread from a site initially
fixated at the social trait. 88
Fig. 3.5. "Wheel" geometry of islands. 90
Fig. 3.6. Quantitative test of two-island approximation. 91
Chapter 4
Fig. 4.1. Two-island system. 99
Fig. 4.2. Initial displacement of fixed points as m is increased from zero. 99
XV
xvi List of Figures
Page
Fig. 4.3. Phase plane for a two-island system of arbitrary type θ or θ , with
m < moiy. 101
P
Fig. 4.4. Behavior of θ and θ two-island systems, classified by increasing
m. 102
Fig. 4.5. Phase plane for system of the θ type with m i < m < m. 103
poy E
Fig. 4.6. Phase plane for system of the θ type with m < m. 104
E
Fig. 4.7. Phase plane for system of the θ type with m i < m < m. 106
poy E
Fig. 4.8. Phase plane for system of the θ type with m < m, illustrating
E
corner-turning phenomenon (occurring when m - m it). 106
cr
Fig. 4.9. Phase plane for approximation (3.5)-(3.8), showing initial move-
ment of fixed points as m is increased from zero. 111
Fig. 4.10. Phase plane for very small m in system (3.5)-(3.8) when 1. 112
Fig. 4.11. Phase plane of (3.5)-(3.8) before and after corner turning. 115
Fig. 4.12. Island site coupled to a single large population fixated at the asocial
trait. 121
Fig. 4.13. Competition for an island site by two oppositely fixated source
populations. 122
Chapter 5
Fig. 5.1. M(y) versus y for a recessive or dominant. 131
Fig. 5.2. Fixation probability of α as a function of its initial frequency. 132
Fig. 5.3. Graphs of fixation probabilities versus Ν = 10 2 to 104. 138
Fig. 5.4. The local network around a mother site. 140
Fig. 5.5. An unsuccessful choice of initial fixation. 144
Fig. 5.6. An island topology exhibiting cluster of central sites (Sites 1 -6) and
a further set of peripheral sites (Sites 7-15). 145
Fig. 5.7. Illustration of one pattern of takeover by the social trait in the
topology of Fig. 5.6. 146-147
Fig. 5.8. As in Fig. 5.7, but now the social trait starts at Site 2. 148
Fig. 5.9. Unsuccessful attempt to reverse the successful transition to sociality
in Fig. 3.2. 152
Fig. 5A.1. Coding of starting configurations used for stepping-stone runs. 157
Chapter 6
Fig. 6.1. Population of donor-recipient pairs. 169
Fig. 6A.1. Number of genes i.b.d. shared by diploid full sibs. 191
Fig. 6A.2. Expected values of r for selected kin relationships under haplo-
diploidy. 192
Fig. 6A.3. Diploid r values. 192
Chapter 7
Fig. 7.1. Implication ordering (=>) of altruist stability conditions in general
[S(0), Α(θ)] models. 201
Fig. 7.2. Ordering of nonaltruist stability conditions. 202
Fig. 7.3. Individual fertility effects of social evolution in polygynous
Hymenoptera. 206-207
Fig. 7.4. Comparison of stability conditions under S(6) = 1. 208-209
Chapter 8
Fig. 8.1. Graph illustrating fitness transfer in a sibship. 228
Fig. 8.2. Tree of survival probabilities for altruist and nonaltruist sibs. 230
List of Figures xvii
Page
Fig. 8.3. Graphs of [σ±(ε), ο (ε)] for ρ - .05. 233
0
Fig. 8.4. As Fig. 8.3, similar information presented in (y, δ) coordinates,
p = .\. 234
Fig. 8.5. a(y) and v{y) for one-many transfer model (with Ζ = 20) compared
with the original "one-one" transfer model having coefficients (8.1)
and (8.2); q - .1. 240
Fig. 8.6. Support graph for restricted fitness transfer. 241
Fig. 8.7. Support graph for elective fitness model. 243
Fig. 8.8. Comparison among three fitness transfer rules, comparing condi-
tions for stability at altruist fixation. 244
Fig. 8.9. A simplifed presentation of the divergence between k > (1/r) and
the Case 1 diploid altruist stability condition. 251
Chapter 9
Fig. 9.1. Sib altruism compared with child-parent altruism. 275
Fig. 9.2. Sib altruism compared with parental investment. 282-283
Chapter 10
Fig. 10.1. Alternative possibilities for φ^χ), showing variation with h. 299
Fig. 10.2. Impact of group selection, illustrated through comparison of input
distribution/^) = CJC^'O-*)*"', A = .01, Β = 2, mean = .5%, with
output distribution φ^χ), mean = 90%. 300
Chapter 11
Fig. 11.1. Parameter hierarchy for group selection in the model (11.1). 326
Fig. 11.2. Concave Eu Behavior of (11.1) with E < {Ex + £ )/2. 330
2 3
Fig. 11.3. Convex Eu Behavior of (11.1) with E > (Ει + £ )/2. 331
2 3
Technical Appendix
Fig. TA.l. The action of natural selection in a one-locus biallelic model. 369
Fig. TA.2. Graph describing frequency-dependent selection leading to stable
polymorphism at β. 371
Fig. TA.3. Offspring genotype determination under haplodiploidy. 374