Sigma Xi, The Scientific Research Society
Evolution and the Theory of Games: In situations characterized by conflict of interest, the
best strategy to adopt depends on what others are doing
Author(s): J. Maynard Smith
Source: American Scientist, Vol. 64, No. 1 (January-February 1976), pp. 41-45
Published by: Sigma Xi, The Scientific Research Society
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J.Maynard
Evolution
Smith
and the Theory
of Games
In situations characterized by conflict of interest, .
the best strategy to adopt depends on what others
are doing
in this article to trace the
troduced, the concept of an "evolu
an
It
is
to
idea.
of
tionarily stable strategy/' It is the
history
beginning
become clear that a range of prob
history of this concept I want to dis
cuss.
lems in evolution theory can most
a
be
attacked
by
appropriately
modification of the theory of games,
Evolution of the sex ratio
a branch of mathematics
first for
first the evolution of the
and
Consider
mulated
by Von Neumann
sex ratio. In most
animals
and
(1944) for the analysis
Morgenstern
with
of human conflicts. The problems
separate sexes, approxi
plants
are diverse and include not only the mately equal numbers of males and
in contest sit
females are produced. Why should
behavior of animals
in
this be so? Two main kinds of an
uations but also some problems
swer have been offered. One
is
the evolution of genetic mecha
in terms of advantage
to
couched
nisms and in the evolution of eco
the population.
It is argued that the
systems. It is not, however, suffi
cient to take over the theory as it sex ratio will evolve so as to maxi
in sociology and
be
mize
the number of meetings
has been developed
sex.
to
In
tween
of
it
evolution.
individuals
sociology,
opposite
apply
it is supposed
is essentially a "group selec
This
and in economics,
tion" argument. The other, and in
that each contestant works out by
to my view certainly correct, type of
the best
strategy
reasoning
answer was
first put forward by
adopt, assuming that his opponents
are equally guided by reason. This
Fisher (1930). It starts from the as
leads to the concept of a "minimax"
sumption that genes can influence
the relative numbers of male and
strategy, in which a contestant be
female offspring produced by an in
haves in such a way as to minimize
dividual
his losses on the assumption
that
carrying the genes. That
sex ratio will be favored which max
his opponent behaves so as to maxi
imizes the number of descendants
mize them. Clearly, this would not
to animal con
the individual will have and hence
be a valid approach
the number of gene copies transmit
flicts. A new concept has to be in
ted. Suppose
that the population
consisted mostly of females: then an
which
individual
Smith was born in 1920. He
John Maynard
only
produced
and worked during
trained as an engineer
sons would have more grandchil
World War II in aircraft design. After the
dren. In contrast, if the population
Col
war, he studied
zoology at University
it would
consisted mostly of males,
J.
later
worked
under
where
he
lege London,
to
have
new
In 1965 he went to the
B. S. Haldane.
pay
daughters. If, however,
as the first dean of the
consisted of equal
the population
University
of Sussex
Sciences.
His
School
experi
of Biological
numbers of males and females, sons
concerned
been mainly
work has
mental
be equally
would
and daughters
and behavior
with the genetics, physiology,
valuable. Thus a 1:1 sex ratio is the
has
theoretical
He
published
of Drosophila.
on animal
evolution
locomotion,
only stable ratio; it is an "evolution
papers
and has written
?r ily stable strategy."
four
theory, and ecology
I want
Theory of Evolution, Mathemati
On Evolution,
and
in Biology,
cal
Ideas
in Ecology.
Address:
Models
Biology Build
books: The
University
ing, The
Brighton, Sussex BN1
of Sussex,
9QG, England.
Falmer,
Fisher allowed for the fact that the
cost of sons and daughters may be
different, so that a parent might
have a choice, say, between having
one daughter or two sons. He con
cluded that a parent should allocate
equal resources to sons and daugh
ters. Although Fisher wrote before
the theory of games had been devel
oped, his theory does incorporate
the essential feature of a game?
that the best strategy to adopt de
pends on what others are doing.
Since that time, it has been realized
that genes can sometimes influence
the chromosome or gamete inwhich
they find themselves, so as to make
that gamete more likely to partici
pate in fertilization. If such a gene
occurs on a sex-determining
(X or
then
Y) chromosome,
highly aber
rant sex ratios can evolve.
immediately relevant are the
strange sex ratios in certain parasit
ic hymenoptera
(wasps and ichneu
In this group of insects,
monids).
into females
fertilized eggs develop
and unfertilized eggs into males. A
female stores sperm and can deter
mine the sex of each egg she lays by
fertilizing it or leaving it unfertil
it
ized. By
Fisher's
argument,
More
should stfjlp$tyQf%w$\etoproduce
equal numbers of sons and daugh
it can be
ters. More
precisely,
shown that if genes affect the strat
egy adopted by the female, then a
1:1 sex ratio will evolve. Some par
asitic wasps lay their eggs in the lar
vae of other insects, and the eggs
within
their host. When
develop
adult wasps emerge, they mate im
Such
before dispersal.
mediately
species often have a big excess of fe
males. This situation was analyzed
byHamilton (1967). Clearly, ifonly
one
female lays eggs in any given
larva, it would pay her to produce
one male only, since this one male
could
fertilize all his sisters on
emergence. Things get more com
1976 January-February
41
if a single host larva is
plicated
found by two parasitic females, but
the details of the analysis do not
concern us. The important point is
looked for an "un
that Hamilton
beatable
is, a sex
strategy"?that
ratio which would be evolutionarily
stable. In effect, he used Fisher's
approach but went a step farther in
recognizing that he was looking for
a "strategy"
in the sense in which
that word is used by game theorists.
Animal contests and
game theory
journal. I then thought no more of
the matter until, about a year later,
I spent three months visiting the
department of theoretical biology at
I decided
to spend the
Chicago.
visit learning something about the
theory of games, with a view to de
veloping Price's idea in a more gen
eral form and applying it to certain
I was at that time
other problems.
work on
familiar with Hamilton's
work
the
the sex ratio
(indeed,
formed part of his Ph.D.
thesis, of
which I was the external examiner),
but I had not seen its relevance to
Price's problem.
A very similar idea was used by the
I developed
at Chicago,
the
While
late G, R. Price in an analysis of an
formal definition of an evolutionari
imal behavior. Price was puzzled by
ly stable strategy which I will give
the evolution of ritualized behavior
in a moment and applied
it to the
in animal contests?that
is, by the
"Dove-Hawk-Retaliator"
and
an
a
in
fact that
animal engaged
"War of Attrition" games. I also re
contest for some valuable
resource
in alized the similarity between these
does not always use its weapons
ideas and the work of Hamilton
of
the most effective way. Examples
1965) on the
(and also MacArthur
such behavior have been discussed
sex
came
I
to write up
ratio.
When
by Lorenz (1966), Huxley (1966),
this work, it was clearly necessary
that
and others. It seems
likely
I was
to quote Price.
somewhat
have
underestimated
ethologists
to
discover
that
taken
aback
he had
the frequency and importance of es
never
was
his
idea
and
published
contests between
all-out
calated,
on something
now working
else.
animals
Geist
(see
particularly
I returned to London
I con
When
1966). Yet display and convention
we
and
tacted
him,
ultimately
are a common enough feature of an
pub
a joint paper
lished
(Maynard
imal contests to call for some expla
Smith and Price 1973) inwhich the
nation. Both Lorenz and Huxley ac
stable
concept of an evolutionarily
selectionist
cepted group
explana
was
con
to
animal
strategy
applied
tions: Huxley,
for example, argued
tests.
that escalated contests would result
inmany animals being seriously in
At this point itwill be convenient to
"this would militate
jured, and
describe some ideas from the theory
against the survival of the species."
of games. By "game" or "contest" is
Similar assumptions are widespread
an encounter between
two
in ethology, although not often so meant
am not concerned
individuals
(I
clearly expressed.
with
in which the
-person games)
outcomes
would
various
was
possible
a
to accept
Price
reluctant
not be placed
in the same order of
oc
selection
It
group
explanation.
preference by the two participants:
curred to him that ifanimals adopt
there is a conflict of interest. By
ed a strategy of "retaliation,"
in
a complete
is meant
"strategy"
an
which
animal normally adopts
of what a contestant
specification
conventional tactics but responds to
an escalated attack by escalating in will do in every situation in which
he might find himself. A strategy
return, this might be favored by se
be "pure" or "mixed"; a pure
may
lection at the individual level. He
states "in situation A, al
strategy
submitted a paper to Nature
argu
do X"; a mixed strategy states
me
was
to
ways
sent
which
this
point,
ing
"in situation A, do X with probabil
to referee. Unfortunately
the paper
was some fifty pages in length and
forNature.
hence quite unsuitable
I wrote a report saying that the
paper contained an interesting idea,
and that the author should be urged
to submit a short account of it to
Nature
and/or to submit the exist
to a more suitable
ing manuscript
42
American
Scientist,
Volume
64
ity
and Y with probabilityQ."
that there are three possi
Suppose
ble strategies, A, B,
and C. A
is then a 3 X 3 ma
"payoff matrix"
trix listing the expected gains to a
contestant
these
three
adopting
strategies, given that his opponent
adopts one of the other strategies.
These
ideas will be made clearer by
an example. Consider the children's
In
"Rock-Scissors-Paper."
game
each contest, a player niust adopt
in ad
one of these "strategies"
vance: then Rock blunts Scissors,
and Paper
cuts Paper,
Scissors
that the win
wraps Rock. Suppose
ner of each contest receives one dol
lar from the loser; if both adopt the
same strategy, no money
changes
hands. The payoff matrix is
R
R
S
S
0
-1
+ 1
+ 1
o
-1
-1
+ 1
o
The payoffs are to the player on the
left.This particular game is a "zero
sum" game, in the sense that what
one player wins the other loses; in
general the games considered below
are not of this kind. Clearly, a play
er adopting
the pure
strategy
"Rock" will lose in the long run, be
cause his opponent will catch on
and play "Paper." A player adopt
ing themixed strategy"% Rock, %
Scissors, % Paper"
will break even.
How are these ideas to be applied to
animal contests? A genotype deter
mines the strategy, pure or mixed,
that an animal will adopt. Suppose
an animal adopts strategy / and his
the
then
opponent
strategy J;
payoff to / will be written Ej{I)}
where E stands for "expected gain."
This payoff is the change in J's fit
ness as a result of the contest, fit
ness being the contribution to fu
ture
generations.
Evolutionarily
strategy
stable
We are now in a position to define
an evolutionarily stable strategy, or
ESS for short. Suppose that a popu
lation consists of individuals adopt
ing strategies I ox J with frequen
4- q = 1.What
cies
and q, where
an
individual adopt
is the fitness of
ing strategy /?
Fitness
Fitness
oil
=
??/(/) + q<Ej(I)
of J = p-?,(J)
+ q-Ej(J)
If a particular strategy, say /, is to
it must have the fol
be an ESS,
lowing property. A population of in
dividuals
playing / must be "pro
tected" against invasion by any mu
tant strategy, say J. That is, when I
is common, it must be fitter than
any mutant. That is, / is an ESS
if,
for all J 9^1,
eitherEi(I) > EAJ)
orEjd) = E/(J)
and Ej(I)
> Ej(J)
injured.
(1)
are satisfied,
If these conditions
of individuals
then a population
can
playing J is stable; no mutant
establish itself in such a population.
follows from the fact that
This
when q is small, the fitness of / is
greater than the fitness of J.
It is important to emphasize at this
is not necessari
point that the ESS
as
same
the
the
strategy pre
ly
theorists
for
scribed
by game
human players. There the assump
tion is that a player will adopt that
strategy which minimizes his losses,
given that his opponent plays so as
them. Lewontin
to maximize
(1961)
such "minimax"
strategies
applied
to evolution. He was concerned with
a contest not between
individuals
but between a species and "nature."
The objective of a species is to sur
avoid extinc
vive as a species?to
tion. It should therefore adopt that
its
minimizes
which
strategy
chances of extinction, even ifnature
does its worst. That
is, the species
must adopt the minimax
strategy.
For example, a species should retain
rather than
sexual
reproduction
this will
because
parthenogenesis,
enable it to evolve to meet environ
is clearly a
mental
change. This
group selectionist approach; the ad
vantage is to the species and not to
the individual female. In contrast,
the concept of an evolutionarily sta
ble strategy is relevant to contests
between individuals, not between a
is con
and
species and nature,
individual
ad
cerned solely with
vantage.
us now apply these ideas to a
that
Suppose
problem.
particular
two animals are engaged in a con
test for some indivisible resource
which isworth + V to the victor. An
it can "esca
animal can "display,"
late"?in which case itmay serious
it can re
ly injure its opponent?or
its
treat, leaving
opponent the vic
tor. Serious
injury reduces fitness
?
W
and forces an
(a
"wound")
by
animal to retreat. Finally, a long
contest costs both animals ?T. The
two simplest strategies are
Let
Hawk.
and continue
Escalate,
to do so until injured or until
opponent retreats.
Dove. Display. Retreat if oppo
nent escalates, before getting
We
are
two Hawks
that
suppose
equally likely to be injured or to
that two
also
win. We
suppose
Doves are equally likely to win, but
only after a long contest costing
both of them -T. The payoff ma
trix is then
D
H
H
= V ? tub
payoff to A
= -m?
payoff to
v
0
D
%V-T
If W > V, then there is no pure
is not an ESS,
ESS.
Thus H
be
cause Eh(H)
< Eh(D),
and D is not
an ESS, because ED(D)
< ED(H).
The onlyESS is
with probability (2T + V)/
(2T+W)
D with probability1 (2T + V)/
(2T + W)
at an evolutionary
Thus
equilibri
um the population will consist of a
mixture
of Hawks
and Doves..
Price's
suggestion was that a third
fi, might be
strategy, "Retaliator,"
an ESS; fi plays D against D and
is
against H. The
payoff matrix
H %(V- W)
o
R
d
H
d
One assumption made above?that
can settle a contest?
two Doves
needs some justification. Why don't
the
they go on forever? Consider
following game. Two players, A and
B, can only display. The winner is
the one who goes on for longer; the
only choice of strategy is how long
to go on for. A selects time Ta and
selects Tg. The longer th? contest
actually continues, the more it costs
the costs associated
the players;
with these times are jua and ms. If
Ta > Tb, then we have
v
y2v-T
R %(V- W) %v-
WO
y2v-T
%v
It turns out that Price was right.
a population
Thus
of R is stable
against invasion by mutant H, be
cause Er(R)
> Eft(H). R is not sta
in the ab
ble against D, because
sence of
they are identical. But a
population
consisting initially of a
will evolve
mixture of R, D, and
to fi. This game is analyzed further
inMaynard Smith and Price (1973)
and by Gale
and Eaves
cost of tyia which A was pre
pared to pay is irrelevant, provided
that it is greater than
?. Our
a play
is:
should
How
then
problem
er choose a time, and a correspond
precisely,
ing value of m? More
what choice of m is an ESS? For ob
vious reasons, I have called this the
"War of Attrition." Clearly, no pure
strategy can be an ESS. Any popu
lation playing m, say, could be in
vaded
by a mutant
playing M,
The
whereM > m; ifm > V/2yit could
also be invaded by a mutant playing
0. It can be shown that there is a
mixed ESS givenby
p(x)
=
^e-*<v
(2)
is the probability of
p(x)?x
.
m
4and
between
playing
where
are
There
does this mean?
What
an
ESS
in
which
two possible ways
of this kind could be realized. First,
of the population
all members
identical and
might be genetically
have a behavior pattern which var
ied from contest to contest accord
ing to Eq. 2. Second, the population
might be genetically variable, with
each individual having a fixed be
havior, the frequencies of different
kinds of individuals being given by
Eq. 2. In either case, the population
would be at an ESS.
(1975).
G. A. Parker (1970) has described a
situation which agrees rather well
that we
This
analysis
suggests
would expect to find retaliation a with Eq. 2. Female dung flies of the
feature of actual behavior. One ex
lay their eggs in
genus Scatophaga
cow
mon
The
males
a
must
suffice:
rhesus
stay close to
pats.
ample
cow
with
females
a
the
will
which
loses
mating
pats,
key
passive
fight
to
their
as
arrive
will
but
retal
incisor
bites
eggs.
lay
accept
they
ly
iate viciously if the winner uses its What strategy should a male adopt?
Should he stay with a pat once he
and Gordon
canines
(Bernstein
found one, or should he move
has
1974).
1976
January-February
43
on in search of a fresh pat as soon as
the first one begins to grow stale?
to the choice of
This is comparable
a value of m in theWar of Attrition.
His choice will be influenced by the
fact that females arrive less fre
quently as a pat becomes staler. His
best strategy will depend on what
other males are doing. Thus if other
leave a pat quickly, it would
males
he
pay him to stay on, because
would be certain of mating any fe
males which do come. If other males
stay on, itwould pay him tomove.
tants but have relatively little effect
or on payoff. The obvious
on RHP
example is the asymmetry between
the "owner" of a resource (e.g. a ter
ritory, a female, an item of food)
and a "latecomer." There is no gen
eral reason why an owner should
have a higher RHP
than a latecom
er. The
value of a resource will
often be greater to the owner, but,
no
as I shall show in a moment,
such difference is necessary before
an asymmetry can be used to settle
a contest conventionally.
American
Scientist,
Volume
64
in practice
The
baboon,
Papio
hamadryas
lives in troops com
hamadryas,
of a number of "one-male
posed
groups," each consisting of an adult
one or more
females, and
male,
their babies. The male, who is sub
stantially larger than the females,
prevents "his" females from wan
dering away from his immediate vi
cinity; a female rapidly comes to
It is
this "ownership."
recognize
rare for an owning male to be chal
lenged by another. How is this state
of
affairs maintained?
of
Parker found that the actual length To fix ideas, consider the game
of time males stayed was given by a Hawks and Doves discussed
above,
with the arbitrary values V = 60, W
distribution
2. By
resembling Eq.
= 10. The
it is = 100, and
itself this means
little, because
payoff ma
the distribution one would expect if trix for the symmetrical case is then
every male had the same constant
probability of leaving per unit time.
D
H
It is the typical negative exponen
for the
+50
tial distribution
-20
expected
"survivors" of a population
suffer
0
+20
D
ing a constant "force of mortality."
What
is significant is that Parker
that an animal may be ei
Suppose
was able to show that the expected
owner
of the resource or a
the
ther
was
same
for
number ofmatings
the
latecomer, for a particular animal is
males which left early as for those
equally likely to find himself
which stayed on. This means
that
now
playing either role. Consider
the males are adopting an ESS; nat
are
if
the
/:
you
"Play
strategy
ural
selection
the
has
adjusted
D ifyou are latecomer."
owner;
play
of
unit
time
leaving per
probability
Then, since an animal is owner and
to bring this about.
latecomer with equal frequency,
It is not known whether contests
Ej(I) = % X 50 + % X 0 = +25
between pairs of animals, in which
only display is employed, show the
let J be a strategy which ig
in length. It Now
variation
appropriate
nores
the asymmetry and plays
to
out.
find
will be interesting
and D with prob
with probability
Then
(1
A major
in
ability
p).
applying
complication
these ideas in practice arises be
Ei(J) = %[50p + 20(1 p)] +
cause most contests are asymmetri
=
Smith
cal (Parker 1974; Maynard
5p + 10
%[-20p]
and Parker, in press), either in the
> Ei(J).
For any value of p, Ej(I)
fighting ability of the contestants
in
"re
amounts
has
the
which
Thus
what
called
Parker
(i.e.
strategy J,
or
to
of
the
conventional
acceptance
RHP),
source-holding potential,"
or in the value of the resource to the
is an ESS
ownership,
against any
contestants
(i.e. in payoff). Clearly,
strategy which
ignores ownership.
can only affect
these asymmetries
(Notice that the game permits the
if you are
alternative ESS, "play
if they are
the strategies adopted
Thus
known to the contestants.
latecomer; play D ifyou are owner."
raises difficulties which are
suppose two animals differ in size, This
Smith and
discussed
and hence in RHP, but have no way
by Maynard
short of escalation of detecting the Parker, in press.)
difference. Then the difference can
It follows that conventional
to esca
not alter their willingness
accep
late (i.e. their strategy), although it tance of ownership can be used to
settle contests even when there is
would affect the outcome of an es
no asymmetry in payoff or RHP,
calated contest.
is unam
that ownership
provided
In some cases an asymmetry may be
Some
actual
biguous.
examples will
help to illustrate this point.
clearly perceived
by both contes
44
The ESS
the fol
(1971) describes
lowing experiment. Two males, pre
to each other,
viously unknown
were placed in an enclosure; male A
was free to move about the enclo
was shut in a
sure whereas male
see what
from
which
he
could
cage
was happening but not interfere. A
female strange to both males was
then
loosed
into the enclosure.
Within 20 minutes male A had con
vinced the female of his ownership,
so that she followed him about.
was then released into the
Male
He
did not challenge
enclosure.
male A, but kept well away from
him, accepting A's ownership.
Kummer
ex
can be
observations
in
two
male
ways. First,
plained
may have been able to detect that
male A would win an escalated con
test if challenged;
there
second,
acceptance
may be a conventional
of ownership, for the reasons out
lined above. Kummer was able to
is
show that the second explanation
correct. Two weeks later, he repeat
ed the experiment with the same
two males but with a different fe
male, but on this occasion male
was loose in the enclosure and male
A
confined. Male
established
of the female and was
ownership
not challenged by A.
These
One last observation is relevant. If a
male
is removed from a troop, his
females will be taken over by other
males. If after some weeks the origi
nal male is reintroduced, an escalat
ed fight occurs; both males now be
have
It
as
"owners."
that
be argued
is a
there
baboon
hamadryas
ence in payoff, because when
first takes over a new female
to invest time and energy
could
in the
differ
a male
he has
in per
on conventional
based
acceptance
suading her to accept his owner
is probably
of ownership. Gilbert showed that
correct, al
ship. This
is correct by
the
the latter explanation
theoretical
though
analysis
an experiment analogous
to that of
shows that no such difference is re
a
an
male
of
for
the
establishment
hamadryas baboon
removing
quired
from a troop and then restoring it.
ESS
based on conventional
accep
tance of ownership. An asymmetry
He allowed two male butterflies to
in payoff is less likely in the anubis
occupy a hilltop on alternate days,
In this
baboon
(Packer
1975).
keeping each in the dark on their
off days. After two weeks, when
species, there is a fairly stable male
had come to regard
dominance
both males
hierarchy for food but
not for females. Females are not the
themselves as owners of the same
them on the
permanent
property of particular
hilltop, he released
same day. A contest lasting many
instead, a male "owns" a fe
males;
for minutes and causing damage to the
male only for a single day?or
ensued.
contestants
several days if he can prevent her
from moving away during the night.
in temporary possession
of a Much
has been left out of these
Once
in which
is not challenged,
Contests
female, a male
simple models.
even by those above him in the
information
about
partial
only
con
to
is
the
available
should
dominance
asymmetries
hierarchy. Why
contests about food and females be
testants, or in which information is
in the course of a contest,
settled differently? One possible ex
acquired
are discussed
Smith
is that the ownership
by Maynard
planation
same
not
to
The
settle
could
be
used
and
Parker
(in press).
principle
the possibility
of
contests over food, because
itmust
paper discusses
of
"bluff'?that
often be the case that two animals
is, the possession
see a food item almost
structures such as manes, ruffs, or
simulta
am
increase
would
be
crests, which
apparent
neously. Ownership
re
an
in
two
both
RHP
without
animals
would
equivalent
biguous;
as
owners
crease
in
of
actual
the
themselves
ability.
fighting
gard
same item, and escalated
contests
I suggested at the beginning of this
would ensue.
is
article that the concept of an ESS
This last possibility is beautifully il
also relevant to the evolution of
this idea is developed
lustrated by the work of L. Gilbert
ecosystems;
Smith and Lawlor
(in
by Maynard
(pers. comm.) on the swallowtail
It
zelicaon.
is
Because
butterfly, Papilio
impossible to do more
press).
here than indicate the nature of the
this is a relatively rare butterfly, the
In nature, animals
and
problem.
finding of a sexual partner presents
a problem. This problem
is solved
plants compete for resources?food,
Males
establish
space, light, etc. Genetic changes in
by "hilltopping."
an individual can alter its "choice"
territories at or near the tops of
of resources: for example, the food
hills, and virgin females fly uphill to
mate. There
items taken by an animal, or the
are, however, more
time of year a plant puts out its
males than hilltops, so most males
leaves. Individuals will choose their
must accept territories lower down
resources so as to maximize
the slopes. They attempt to waylay
their
fitness. The best choice will depend
females on their way up and, al
on what other individuals, of the
though they sometimes succeed, the
same and other species, are doing. If
evidence suggests that the male ac
it
everyone else is eating spinach
tually at the hilltop mates most
will pay to concentrate on cabbage;
often. Gilbert marked
individual
since most forest trees put out their
males and observed that a strange
arrive at a
leaves late in spring, it pays forest
male
did occasionally
herbs to put out leaves early.
hilltop and challenge the owner, but
retreated
the stranger
invariably
after a brief "contest."
Since the appropriate
strategy for
an individual depends on what oth
ers are doing, we are again con
As in Rummer's
experiments with
cerned with the search for an ESS.
baboons, we have to choose between
that two
and I conclude
two explanations. Either the owner
Lawlor
of a hilltop is a particularly strong
competing species will tend to be
on different re
come specialists
butterfly, and this fact is perceived
a
even
brief
the
sources,
by
challenger during
though in isolation
each species would be a generalist.
contest, or there is again an ESS
This conclusion
is not a new one: it
accords with a good deal of observa
tional data and has received several
previous theoretical treatments. We
would claim, however, that we have
clarified a familiar idea and set it in
a wider context. That wider context
the best
is simply this: whenever
an
for
individual
depends
strategy
on what others are doing, the strat
will be an
egy actually
adopted
ESS.
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