AMER. ZOOL., 14:249-264 (1974).

Parent-Offspring Conflict

ROBERT L. TRIVERS

Museum of Comparative Zoology, Harvard University,

Cambridge, Massachusetts 02138

SYNOPSIS. When parent-offspring relation"; in sexually reproducing species are viewed

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from the standpoint of the offspring as well as the parent, conflict is seen to be an
expected feature of such relations. In particular, parent and offspring are expected to
disagree over how long the period of parental investment should last, over the amount
of parental investment that should be given, and over the altruistic and egoistic ten-
dencies of the offspring as these tendencies affect other relatives. In addition, under
certain conditions parents and offspring are expected to disagree over the preferred sex
of the potential offspring. In general, parent-offspring conflict is expected to increase
during the period of parental care, and offspring are expected to employ psychological
weapons in order to compete with their parents. Detailed data on mother-offspring
relations in mammals are consistent with the arguments presented. Conflict in some
species, including the human species, is expected to extend to the adult reproductive
role o£ the offspring: under certain conditions parents are expected to attempt to mold
an offspring, against its better interests, into a permanent nonreproductive.

In classical evolutionary theory parent- tive success (RS) would presumably want
offspring relations are viewed from the more investment than the parent is selected
standpoint of the parent. If parental in- to give. But unlike conflict between unre-
vestment (PI) in an offspring is denned as lated individuals, parent-offspring conflict
anything done by the parent for the off- is expected to be circumscribed by the close
spring that increases the offspring's chance genetic relationship between parent and
of surviving while decreasing the parent's offspring. For example, if the offspring
ability to invest in other offspring (Trivers, garners more investment than the parent
1972), then parents are classically assumed has been selected to give, the offspring
to allocate investment in their young in thereby decreases the number of its sur-
such a way as to maximize the number viving siblings, so that any gene in an off-
surviving, while offspring are implicitly spring that leads to an additional invest-
assumed to be passive vessels into which ment decreases (to some extent) the number
parents pour the appropriate care. Once of surviving copies of itself located in sib-
one imagines offspring as actors in this lings. Clearly, if the gene in the offspring
interaction, then conflict must be assumed exacts too great a cost from the parent,
to lie at the heart of sexual reproduction that gene will be selected against even
itself—an offspring attempting from the though it confers some benefit on the off-
very beginning to maximize its reproduc- spring. To specify precisely how much cost
an offspring should be willing to inflict
I thank I. DeVore for numerous conversations on its parent in order to gain a given bene-
and for detailed comments on the manuscript. For
additional comments I thank W. D. Hamilton, J.
fit, one must specify how the offspring is
Roughgarden, T. W. Schoener, J. Seger, and G. C. expected to weigh the survival of siblings
Williams. For help with the appendix I thank J. D. against its own survival.
Weinrich. Finally, for help with the references I The problem of specifying how an indi-
thank my research assistant, H. Hare, and the Harry vidual is expected to weigh siblings against
Frank Guggenheim Foundation, which provides her
salary. Part of this work was completed under an itself (or any relative against any other) has
N.I.H. postdoctoral fellowship and partly supported been solved in outline by Hamilton (1964),
by N.I.M.H. grant MH-13611 to I. DeVore. in the context of explaining the evolution
249
250 ROBERT L. TRIVERS

of altruistic behavior. An altruistic act can is at all times capable of an active role in
be denned as one that harms the organism its relationship to its parents. The form of
performing the act while benefiting some the argument applies equally well to hap-
other individual, harm and benefit being lodiploid species, but for simplicity the
denned in terms of reproductive success. discussion is mostly limited to diploid spe-
Since any gene that helps itself spread in a cies. Likewise, although many of the
population is, by definition, being selected arguments apply to any sexually repro-
for, altruistic behavior in the above sense ducing species showing parental investment
can be selected only if there is a sufficiently (including many plant species), the argu-

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large probability that the recipient of the ments presented here are particularly rele-
act also has the gene. More precisely, the vant to understanding a species such as the
benefit/cost ratio of the act, times the human species in which parental invest-
chance that the recipient has the gene, must ment is critical to the offspring throughout
be greater than one. If the recipient of the its entire prereproductive life (and often
act is a relative of the altruist, then the later as well) and in which an individual
probability that the recipient has the gene normally spends life embedded in a net-
by descent from a common ancestor can be work of near and distant kin.
specified. This conditional probability is
called the degree of relatedness, r0. For an
altruistic act directed at a relative to have PARENT-OFFSPRING CONFLICT OVER THE
survival value its benefit/cost ratio must CONTINUATION OF PARENTAL INVESTMENT
be larger than the inverse of the altruist's Consider a newborn (male) caribou calf
r0 to the relative. Likewise an individual nursing from his mother. The benefit to
is expected to forego a selfish act if its cost him of nursing (measured in terms of his
to a relative, times the r0 to that relative, chance of surviving) is large, the cost to
is greater than the benefit to the actor. his mother (measured in terms of her ability
The rules for calculating degrees of re- to produce additional offspring) presumably
latedness are straightforward for both small. As time goes on and the calf be-
diploid and haplodiploid organisms, even comes increasingly capable of feeding on
when inbreeding complicates the relevant his own, the benefit to him of nursing de-
genealogy (see the addendum in Hamilton, creases while the cost to his mother may
1971). For example, in a diploid species increase (as a function, for example, of the
(in the absence of inbreeding) an individu- calf's size). If cost and benefit are measured
al's r0 to his or her full-siblings is y2; to in the same units, then at some point the
half-siblings, 14; to children, y2; to cousins, cost to the mother will exceed the benefit
i/g. If in calculating the selective value of to her young and the net reproductive suc-
a gene one not only computes its effect cess of the mother decreases if she continues
on the reproductive success of the indi- to nurse. (Note that later-born offspring
vidual bearing it, but adds to this its effects may contribute less to the mother's eventual
on the reproductive success of related indi- R.S than early-born, because their repro-
viduals, appropriately devalued by the ductive value may be lower [Fisher, 1930],
relevant degrees of relatedness, then one but this is automatically taken into account
has computed what Hamilton (1964) calls in the cost function.)
inclusive fitness. While Hamilton pointed The calf is not expected, so to speak,
out that the parent-offspring relationship to view this situation as does his mother,
is merely a special case of relations between for the calf is completely related to himself
any set of genetically related individuals, but only partially related to his future
he did not apply his theory to such re- siblings, so that he is expected to devalue
lations. I present here a theory of parent- the cost of nursing (as measured in terms
offspring relations which follows directly of future sibs) by his r0 to his future sibs,
from the key concept of inclusive fitness when comparing the cost of nursing with
and from the assumption that the offspring its benefit to himself. For example, if fu-
 PARENT-OFFSPRING CONFLICT 251

ture sibs are expected to be full-sibs, then identical copies of each other. Conflict near
the calf should nurse until the cost to the the end of the period of PI over the con-
mother is more than twice the benefit to tinuation of PI is expected in all such spe-
himself. Once the cost to the mother is cies. The argument applies to PI in general
more than twice the benefit to the calf, or to any subcomponent of PI (such as feed-
continued nursing is opposed by natural ing the young, guarding the young, carry-
selection acting on both the mother and the ing the young) that can be assigned a more
calf. As long as one imagines that the or less independent cost-benefit function.
benefit/cost ratio of a parental act changes Weaning conflict in mammals is an ex-

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continuously from some large number to ample of parent-offspring conflict ex-
some very small number near zero, then plained by the argument given here. Such
there must occur a period of time during conflict is known to occur in a variety of
which 1/2<IJ/C<1. This period is one of mammals, in the field and in the labora-
expected conflict between mother and off- tory: for example, baboons (DeVore, 1963),
spring, in the sense that natural selection langurs (Jay, 1963), rhesus macaques (Hinde
working on the mother favors her halting and Spencer-Booth, 1971), other macaques
parental investment while natural selection (Rosenblum, 1971), vervets (Struhsaker,
acting on the offspring favors his eliciting 1971), cats (Schneirla et al., 1963), dogs
the parental investment. The argument (Rheingold, 1963), and rats (Rosenblatt
presented here is graphed in Figure 1. and Lehrman, 1963). Likewise, I interpret
(Note, as argued below, that there are spe- conflict over parental feeding at the time
cialized situations in which the offspring of fledging in bird species as conflict ex-
may be selected to consume less PI than the plained by the present argument: for exam-
parent is selected to give.) ple, Herring Gulls (Drury and Smith, 1968),
This argument applies to all sexually Red Warblers (Elliott, 1969), Verreaux's
reproducing species that are not completely Eagles (Rowe, 1947), and White Pelicans
inbred, that is, in which siblings are not (Schaller, 1964).
Weaning conflict is usually assumed to
occur either because transitions in nature
are assumed always to be imperfect or be-
5 cause such conflict is assumed to serve the
interests of both parent and offspring by
4 informing each of the needs of the other.
In either case, the marked inefficiency of
m weaning conflict seems the clearest argu-
ment in favor of the view that such conflict
results from an underlying conflict in the
way in which the inclusive fitness of mother
1/2
1/4
and offspring are maximized. Weaning con-
0 flict in baboons, for example, may last for
t weeks or months, involving daily competi-
FIG. 1. The benefit/cost ratio (B/C) of a parental tive interactions and loud cries from the
act (such as nursing) toward an offspring as a func- infant in a species otherwise strongly se-
tion of time. Benefit is measured in units of repro- lected for silence (DeVore, 1963). Inter-
ductive success of the offspring and cost in compar- actions that inefficient within a multi-
able units of reproductive success of the mother's
future offspring. Two species are plotted. In species cellular organism would be cause for some
I the benefit/cost ratio decays quickly; in species II, surprise, since, unlike mother and offspring,
slowly. Shaded areas indicate times during which the somatic cells within an organism are
parent and offspring are in conflict over whether identically related.
the parental care should continue. Future sibs are
assumed to be full-sibs. If future sibs were half-sibs, One parameter affecting the expected
the shaded areas would have to be extended until length (and intensity) of weaning conflict
B/C = 1/4. is the offspring's expected r0 to its future
252 ROBERT L. TRIVERS

siblings. The lower the offspring's r0 to its

future siblings, the longer and more in- max net RS
for parent
tense the expected weaning conflict. This
suggests a simple prediction. Other things
being equal, species in which different,
unrelated males commonly father a fe-
male's successive offspring are expected to
show stronger weaning conflict than species
in which a female's successive offspring are

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usually fathered by the same male. As
shown below, however, weaning conflict is
merely a special case of conflict expected
throughout the period of parental invest-
ment, so that this prediction applies to the
intensity of conflict prior to weaning as
well. FIG. 2. The benefit, cost, and half the cost of a
parental act toward an offspring at one moment in
time as a function of the amount the parent invests
CONFLICT THROUGHOUT THE PERIOD OF PI in the act (PI). Amount of milk given during one
OVER THE AMOUNT OF PI day of nursing in a mammal would be an example
of PI. At p the parent's inclusive fitness (B - C) is
maximized; at y the offspring's inclusive fitness
In Figure 1 it was assumed that the (B-C/2) is maximized. Parent and offspring dis-
amount of investment for each day (or mo- agree over whether p or y should be invested. The
ment in time) had already been established, offspring's future siblings are assumed to be full-
and that mother and young were only se- siblings. IF = inclusive fitness.
lected to disagree over when such invest-
ment should be ended. But it can be shown be given. Since parental investment begins
that, in theory, conflict over the amount before eggs are laid or young are born, and
of investment that should at each moment since there appears to be no essential dis-
be given, is expected throughout the pe- tinction between parent-offspring conflict
riod of PI. outside the mother (mediated primarily by
At any moment in the period of PI the behavioral acts) and parent-offspring con-
female is selected to invest that amount flict inside the mother (mediated primarily
which maximizes the difference between by chemical acts), I assume that parent-off-
the associated cost and benefit, where these spring conflict may in theory begin as early
terms are denned as above. The infant is as meiosis.
selected to induce that investment which It must be emphasized that the cost of
maximizes the difference between the bene- parental investment referred to above (see
fit and a cost devalued by the relevant r0. Fig. 2) is measured only in terms of de-
The different optima for a moment in time creased ability to produce future offspring
in a hypothetical species are graphed in (or, when the brood size is larger than one,
Figure 2. With reasonable assumptions decreased ability to produce other off-
about the shape of the benefit and cost spring). To appreciate the significance of
curves, it is clear that the infant will, at this definition, imagine that early in the
each instant in time, tend to favor greater period of PI the offspring garners more
parental investment than the parent is se- investment than the parent has been se-
lected to give. The period of transition dis- lected to give. This added investment may
cussed in the previous section is a special decrease the parent's later investment in
case of this continuing competition, the offspring at hand, either through an
namely, the case in which parent and off- increased chance of parental mortality dur-
spring compete over whether any invest- ing the period of PI, or through a depletion
ment should be given, as opposed to their in parental resources, or because parents
earlier competition over how much should have been selected to make the appropriate
 PARENT-OFFSPRING CONFLICT 253

adjustment (that is, to reduce later invest- will also be a strong difference in the par-
ment below what otherwise would have ent's inclusive fitness, so that both parent
been given). In short, the offspring may and offspring will simultaneously be
gain a temporary benefit but suffer a later strongly motivated to achieve their respec-
cost. This self-inflicted cost is subsumed in tive optimal values of PI. (This technique
the benefit function (B) of Figure 2, because of comparing cost-benefit graphs can be
it decreases the benefit the infant receives. used to make other predictions about
It is not subsumed in the cost function (C) parent-offspring conflict, for example that
because this function refeib only to the such conflict should decrease in intensity

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mother's future offspring. with increasing age, and hence decreasing
reproductive value, of the parent; see Fig-
THE TIME COURSE OF PARENT ure 3.) In the absence of such day-by-day
OFFSPRING CONFLICT graphs three factors can be identified, all
of which will usually predispose parent and
If one could specify a series of cost-benefit offspring to show greater conflict as the
curves (such as Fig. 2) for each day of the period of PI progresses.
period of PI, then the expected time course 1) Decreased chance of self-inflicted cost.
of parent-offspring conflict could be speci- As the period of PI progresses, the offspring
fied. Where the difference in the offspring's faces a decreased chance of suffering a later
inclusive fitness at the parent's optimum self-inflicted cost for garnering additional
PI (p in Fig. 2) and at the offspring's opti- investment at the moment. At the end of
mum PI (y) is large, conflict is expected to the period of PI any additional investment
be intense. Where the difference is slight, forced on the parent will only affect later
conflict is expected to be slight or non- offspring, so that at that time the interests
existent. In general, where there is a strong of parent and offspring are maximally di-
difference in the offspring's inclusive fitness vergent. This time-dependent change in
at the two different optima (p and y), there the offspring's chance of suffering a self-

mother's net
RS o t y

mother's max
net RS
O
young's ;£
o • max O
m IF 1/2 C m

m m
(a) PI (b) PI
FIG. 3. The benefit and cost of a parental act (as mother: she will produce fewer future offspring
in Fig. 2) toward (a) an offspring born to a young anyway. The difference between the mother's in-
female and (b) an offspring born to an old female. clusive fitness at m and y is greater for (a) than for
One assumes that the benefit to the offspring of a (b). The same is true for the offspring. Conflict
given amount of PI does not change with birth should be correspondingly more intense between
order but that the cost declines as a function of the early born young and their mothers than between
declining reproductive value (Fisher, 1930) of the late born young and their mothers.
254 ROBERT L. TRIVERS

inflicted cost will, other things being equal, example, that weight at birth in a mammal
predispose parent and offspring to increas- such as humans is strongly associated with
ing conflict during the period of PI. the offspring's survival in subsequent
2) Imperfect replenishment of parental weeks, but that the cost to the mother of
resources. If the parent is unable on a daily bearing a large offspring is considerably
basis to replenish resources invested in the greater than some of her ensuing invest-
offspring, the parent will suffer increasing ment. In such circumstances, conflict prior
depletion of its resources, and, as time goes to birth over the offspring's weight at
on, the cost of such depletion should rise birth may be more intense than conflict

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disproportionately, even if the amount of over nursing in the weeks after birth.
resources invested per day declines. For Data from studies of dogs, cats, rhesus
example, a female may give less milk per macaques, and sheep appear to support
day in the first half of the nursing period the arguments of this and the previous
than in the second half (as in pigs: Gill and section. In these species, parent-offspring
Thomson, 1956), but if she is failing conflict begins well before the period of
throughout to replenish her energy losses, weaning and tends to increase during the
then she is constantly increasing her deficit period of PI. In dogs (Rheingold, 1963)
(although at a diminishing rate) and greater and cats (Schneirla et al., 1963) postnatal
deficits may be associated with dispropor- maternal care can be divided into three
tionate costs. In some species a parent does periods according to increasing age of the
not feed itself during much of the period offspring. During the first, the mother ap-
of PI and at least during such periods the proaches the infant to initiate parental
parent must be depleting its resources (for investment. No avoidance behavior or ag-
example, female elephant seals during the gression toward the infant is shown by the
nursing period: LeBoeuf et al., 1972). But mother. In the second, the offspring and
the extent to which parents who feed dur- the mother approach each other about
ing the period of PI fail to replenish their equally, and the mother shows some avoid-
resources is usually not known. For some ance behavior and some aggression in re-
species it is clear that females typically sponse to the infant's demands. The third
show increasing levels of depletion during period can be characterized as the period
the period of PI (e.g., sheep: Wallace, 1948). of weaning. Most contacts are initiated by
3) Increasing size of the offspring. Dur- the offspring. Open avoidance and aggres-
ing that portion of the period of PI in sion characterize the mother.
which the offspring receives all its food Detailed quantitative data on the rhesus
from its parents, the tendency for the off- macaque (Hinde and Spencer-Booth, 1967,
spring to begin very small and steadily 1971), and some parallel data on other
increase in size will, other things being macaques (Rosenblum, 1971), demonstrate
equal, increase the cost to the parent of that the behavior of both mother and off-
maintaining and enlarging it. (Whether spring change during the period of post-
this is always true will depend, of course, natal parental care in a way consistent with
on the way in which the offspring's growth theory. During the first weeks after she
rate changes as a function of increasing has given birth, the rhesus mother's initia-
size.) In addition, as the offspring increases tive in setting up nipple contacts is high
in size the relative energetic expense to it but it soon declines rapidly. Concurrently
of competing with its parents should de- she begins to reject some of the infant's
cline. advances, and after her own initiatives to-
The argument advanced here is only ward nipple contact have ceased, she re-
meant to suggest a general tendency for jects her infant's advances with steadily
conflict to increase during the period of increasing frequency until at the end of
PI, since it is easy to imagine circumstances the period of investment all of the off-
in which conflict might peak several times spring's advances are rejected. Shortly after
during the period of PI. It is possible, for birth, the offspring leaves the mother more
 PARENT-OFFSPRING CONFLICT 255

often than it approaches her, but as time spring is expected to disagree with its par-
goes on the initiative in maintaining ents over whether it should become a male
mother-offspring proximity shifts to the or a female. Since one can not assume that
offspring. This leads to the superficially potential offspring are powerless to affect
paradoxical result that as the offspring be- their sex, sex ratios observed in nature
comes increasingly active and independent, should to some extent reflect the offspring's
spending more and more time away from preferred value as well as the parents'.
its mother, its initiative in maintaining Fisher (1930) showed that (in the ab-
mother-offspring proximity increases (that

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is, it tends to approach the mother more to invest as much in the total of their
often than it leaves her). According to the daughters as in the total of their sons.
theory presented here, this result reflects When each son produced costs on average
the underlying tendency for parent-off- the same as each daughter, parents are
spring conflict to increase during the pe- selected to produce a sex ratio of 50/50.
riod of PI. As the interests of mother and In such species, the expected reproductive
offspring diverge, the offspring must as- success (RS) of a son is the same as that of
sume a greater role in inducing whatever a daughter, so that an offspring should be
parental investment is forthcoming. indifferent as to its sex. But if (for ex-
Data on the production and consump- ample) parents are selected to invest twice
tion of milk in sheep (Wallace, 1948) indi- as much in a typical male as in a typical
cate that during the first weeks of the female, then they will be selected to pro-
lamb's life the mother typically produces duce twice as many females as males, and
more milk than the lamb can drink. The the expected RS of each son will be twice
lamb's appetite determines how much milk that of each daughter. In such a species a
is consumed. But after the fourth week, potential offspring would prefer to be a
the mother begins to produce less than male, for it would then achieve twice the
the lamb can drink, and from that time on RS it would as a female, without suffering
it is the mother who is the limiting factor a comparable decrease in inclusive fitness
in determining how much milk is con- through the cost forced on its parents, be-
sumed. Parallel behavioral data indicate cause the offspring is selected to devalue
that the mother initially permits free ac- that cost by the offspring's expected r0 to
cess by her lamb(s) but after a couple of the displaced sibling. For the example
weeks begins to prevent some suckling at- chosen, the exact gain in the offspring's
tempts (Munro, 1956; Ewbank, 1967). inclusive fitness can be specified as follows.
Mothers who are in poor condition become If the expected RS of a female offspring is
the limiting factor in nursing earlier than defined as one unit of RS, then, in being
do mothers in good condition, and this is made male, the offspring gains one unit of
presumably because the cost of a given RS, but it deprives its mother of an addi-
amount of milk is considerably higher tional daughter (or half a son). This dis-
when the mother is in poor condition, placed sibling (whether a female or half
while the benefit to the offspring remains of a male) would have achieved one unit of
more or less unchanged. Females who pro- RS, but this unit is devalued from the off-
duce twins permit either twin to suckle on spring's standpoint by the relevant r0. If
demand during the first three weeks after the displaced sibling would have been a
birth, but in the ensuing weeks they do full sibling, then this unit of RS is de-
not permit one twin to suckle unless the valued by i/2, and the offspring, in being
other is ready also (Ewbank, 1964; Alexan- made a male, achieves a i/2 unit net increase
der, 1960). in inclusive fitness. If the displaced sibling
would have been a half sibling, the off-
DISAGREEMENT OVER THE SEX OF spring, in being made a male, achieves a
THE OFFSPRING % unit net increase in inclusive fitness.
Under certain conditions a potential off- The parent, on the other hand, experiences
256 ROBERT L. TRIVERS

initially only a trivial decrease in RS, so in the Appendix. Parent and offspring
that initially any gene in the offspring tend- equilibrial sex ratios for different values
ing to make it a male against its parents' of r0 and different values of x (PI in a
efforts would spread rapidly. typical son/PI in a typical daughter) are
As a hypothetical gene for offspring con- plotted in Figure 4. For example, where
trol of sex begins to spread, the number the r0 between siblings is i/2 and where
of males produced increases, thereby lower- parents invest twice as much in a son as in
ing the expected RS of each male. This a daughter (x = 2), the parents' equilibrial
decreases the gain (in inclusive fitness) to sex ratio is 1:2 (males:females) while that

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the offspring of being made a male. If the of-the offspring is 1:1.414.
offspring's equilibrial sex ratio is denned As long as all offspring are fathered by
as that sex ratio at which an offspring is the same male, he will prefer the same sex
indifferent as to whether it becomes a male ratio among the offspring that the mother
or a female, then this sex ratio can be cal- does. But consider a species such as caribou
culated by determining the sex ratio at in which the female produces only one off-
which the offspring's gain in RS in being spring a year and assume that a female's
made a male is exactly offset by its loss in successive offspring are fathered by differ-
inclusive fitness in depriving itself of a sis- ent, unrelated males. If the female invests
ter (or half a brother). The offspring's more in a son than in a daughter, then she
equilibrial sex ratio will depend on both will be selected to produce more daughters
the offspring's expected r0 to the displaced than sons. The greater cost of the son is
siblings and on the extent to which parents not borne by the father, however, who in-
invest more in males than in females (or vests nothing beyond his sperm, and who
vice versa). The general solution is given will not father the female's later offspring,
so the father's equilibrial sex ratio is an
equal number of sons and daughters. The
50 s-
offspring will prefer some probability of
being a male that is intermediate between
its parents' preferred probabilities, because
(unlike the father) the offspring is related
to the mother's future offspring but (unlike
the mother) it is less related to them than
to itself.
In a species such as just described (in
which the male is heterogametic) the fol-
lowing sort of competitive interaction is
possible. The prospective father produces
more Y-bearing sperm than the female
would prefer and she subjects the Y-bearing
sperm to differential mortality. If the ratio
of the sperm reaching the egg has been
reduced to near the mother's optimal value,
FIG. 4. The optimal sex ratio (per cent males) for then the egg preferentially admits the
the mother (m) and the young (y) where the mother Y-bearing sperm. If the mother ovulated
invests more in a son than in a daughter by a factor
of x (and assuming no paternal investment in either
more eggs than she intends to rear, she
sex). Two functions are given for the offspring, de- could then choose which to invest in, ac-
pending on whether the siblings it displaces are cording to the sex of the fertilized egg, un-
full-siblings (ro = 1/2) or half-siblings (ro = 1/4). less a male egg is able to deceive the mother
Note the initial rapid divergence between the moth- about its sex until the mother has com-
er's and the offspring's preferred sex ratio as the
mother moves from equal investment in a typical mitted herself to investing in him. Whether
individual of either sex (x = 1) to twice as much such interactions actually occur in nature
investment in a typical male (x — 2). is at present unknown.
 PARENT-OFFSPRING CONFLICT 257

One consequence of the argument ad- apprize the parent of the offspring's condi-
vanced here is that there is an automatic tion. In short, the offspring cries when
selective agent tending to keep maternal hungry or in danger and the parent re-
investment in a son similar to that in a sponds appropriately. Conversely, the off-
daughter, for the greater the disparity be- spring signals its parent (by smiling or wag-
tween the investment in typical individuals ging its tail) when its needs have been well
of the two sexes, the greater the loss suffered met. Both parent and offspring benefit from
by the mother in competitive interactions this system of communication. But once
with her offspring over their preferred sex such a system has evolved, the offspring can

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and in producing a sex ratio further skewed begin to employ it out of context. The off-
away from her preferred ratio (see Fig. 4). spring can cry not only when it is famished
This automatic selection pressure may but also when it merely wants more food
partly account for the apparent absence than the parent is selected to give. Like-
of strongly size-dimorphic young (at the wise, it can begin to withhold its smile
end of PI) in species showing striking adult until it has gotten its way. Selection will
sexual dimorphism in size. then of course favor parental ability to dis-
The argument presented here applies to criminate the two uses of the signals, but
any tendency of the parent to invest dif- still subtler mimicry and deception by the
ferentially in the young, whether according offspring are always possible. Parental ex-
to sex or some other variable, except that perience with preceding offspring is ex-
in many species sex is irreversibly deter- pected to improve the parent's ability to
mined early in ontogeny and the offspring make the appropriate discrimination. Un-
is expected at the very beginning to be able less succeeding offspring can employ more
to discern its own sex and hence the pre- confusing tactics than earlier ones, parent-
dicted pattern of investment it will receive, offspring interactions are expected to be
so that, unlike other forms of differential increasingly biased in favor of the parent
investment, conflict is expected very early, as a function of parental age.
namely, at the time of sex determination. In those species in which the offspring
is more helpless and vulnerable the younger
THE OFFSPRING AS PSYCHOLOGICAL it is, its parents will have been more
MANIPULATOR strongly selected to respond positively to
signals of need emitted by the offspring,
How is the offspring to compete effec- the younger that offspring is. This suggests
tively with its parent? An offspring can that at any stage of ontogeny in which the
not fling its mother to the ground at will offspring is in conflict with its parents, one
and nurse. Throughout the period of par- appropriate tactic may be to revert to the
ental investment the offspring competes gestures and actions of an earlier stage of
at a disadvantage. The offspring is smaller development in order to induce the invest-
and less experienced than its parent, and its ment that would then have been forthcom-
parent controls the resources at issue. Given ing. Psychologists have long recognized
this competitive disadvantage the offspring such a tendency in humans and have given
is expected to employ psychological rather it the name of regression. A detailed func-
than physical tactics. (Inside the mother tional analysis of regression could be based
the offspring is expected to employ chemical on the theory presented here.
tactics, but some of the analysis presented The normal course of parent-offspring
below should also apply to such competi- relations must be subject to considerable
tion.) It should attempt to induce more in- unpredictable variation in both the condi-
vestment than the parent wishes to give. tion of the parent and (sometimes inde-
Since an offspring will often have better pendently) the condition of the offspring.
knowledge of its real needs than will its Both partners must be sensitive to such
parent, selection should favor parental at- variation and must adjust their behavior
tentiveness to signals from its offspring that appropriately. Low investment coming
258 ROBERT L. TRIVERS

from a parent in poor condition has a dif- the infant was removed for 6 days from
ferent meaning than low investment coming its mother, leaving her in the home cage,
from a parent in good condition. This sug- and the same behavioral data were gath-
gests that from an early age the offspring ered (see point 3 below). The main findings
is expected to be a psychologically so- can be summarized as follows:
phisticated organism. The offspring should 1) Separation of mother from her off-
be able to evaluate the cost of a given spring affects their relationship upon re-
parental act (which depends in part on union. After reunion with its mother, the
the condition of the parent at that moment) infant spends more time on the mother

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and its benefit (which depends in part on than it did before separation—although,
the condition of the offspring). When the had the separation not occurred, the infant
offspring's interests diverge from those of would have reduced its time on the mother.
its parent, the offspring must be able to This increase is caused by the infant, and
employ a series of psychological maneuvers, occurs despite an increase in the frequency
including the mimicry and regression men- of maternal rejection (Hinde and Spencer-
tioned above. Although it would be ex- Booth, 1971). These effects can be detected
pected to learn appropriate information at least as long as 5 weeks after reunion.
(such as whether its psychological maneu- These data are consistent with the assump-
vers were having the desired effects), an tion that the infant has been selected to
important feature of the argument pre- interpret its mother's disappearance as an
sented here is that the offspring cannot rely event whose recurrence the infant can help
on its parents for disinterested guidance. prevent by devoting more of its energies to
One expects the offspring to be pre-pro- staying close to its mother.
grammed to resist some parental teaching 2) The mother-offspring relationship prior
while being open to other forms. This is to separation affects the offspring's be-
particularly true, as argued below, for havior on reunion. Upon reunion with its
parental teaching that affects the altruistic mother, an infant typically shows distress,
and egoistic tendencies of the offspring. as measured by callings and immobility.
If one event in a social relationship pre- The more frequently an infant was re-
dicts to some degree future events in that jected prior to separation, the more distress
relationship, the organism should be se- it shows upon reunion. This correlation
lected to alter its behavior in response to holds for at least 4 weeks after reunion. In
an initial event, in order to change the addition, the more distressed the infant is,
probability that the predicted events will the greater is its role in maintaining prox-
occur. For example, if a mother's lack of imity to its mother (Hinde and Spencer-
love for her offspring early in its life pre- Booth, 1971). These data support the
dicts deficient future investment, then the assumption that the infant interprets its
offspring will be selected to be sensitive to mother's disappearance in relation to her
such early lack of love, whether investment predeparture behavior in a logical way:
at that time is deficient or not, in order to the offspring should assume that a rejecting
increase her future investment. The best mother who temporarily disappears needs
data relevant to these possibilities come more offspring surveilance and interven-
from the work of Hinde and his associates tion than does a nonrejecting mother who
on groups of caged rhesus macaques. In a temporarily disappears.
series of experiments, a mother was re- 3) An offspring removed from its mother
moved from her 6-month-old infant, leav- shows, upon reunion, different effects than
ing the infant in the home cage with other an offspring whose mother has been re-
group members. After 6 days, the mother moved. Compared to an infant whose
was returned to the home cage. Behavioral mother had been removed, an infant re-
data were gathered before, during, and moved from its mother shows, upon re-
after the separation (see points 1 and 2 be- union, and for up to 6 weeks after reunion,
low). In a parallel series of experiments, less distress and more time off the mother.
 PARENT-OFFSPRING CONFLICT 259

In addition, the offspring tends to play a discouragement.

smaller role in maintaining proximity to This parent-offspring disagreement is ex-
its mother, and it experiences less frequent pected over behavior directed toward other
maternal rejections (Hinde and Davies, relatives as well. For example, the offspring
1972a,b). These data are consistent with is only selected to perform altruistic acts
the expectation that the offspring should toward a cousin (related through the
be sensitive to the meaning of events af- mother) when B>8C. But the offspring's
fecting its relationship to its mother. The mother is related to her own nephews and
offspring can differentiate between a sepa- nieces by r0 = 14 and to her offspring by

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ration from its mother caused by its own ro = i/2, so that she would like to see any
behavior or some accident (infant removed altruistic acts performed by her offspring
from group) and a separation which may toward their maternal cousins whenever
have been caused by maternal negligence B>2C. The same argument applies to sel-
(mother removed from group). In the for- fish acts, and both arguments can be made
mer kind of separation, the infant shows for more distant relatives as well. (The
less effects when reunited, because, from father is unrelated to his mate's kin and,
its point of view, such a separation does not other things being equal, should not be
reflect on its mother and no remedial action distressed to see his offspring treat such in-
is indicated. A similar explanation can be dividuals as if they were unrelated.)
given for differences in the mother's be- The general argument extends to inter-
havior. actions with unrelated individuals, as long
as these interactions have some effect, how-
PARENT OFFSPRING CONFLICT OVER THE ever remote and indirect, on kin. Assume,
BEHAVIORAL TENDENCIES OF THE OFFSPRING for example, that an individual gains some
immediate benefit, B, by acting nastily to-
Parents and offspring are expected to ward some unrelated individual. Assume
disagree over the behavioral tendencies of that the unrelated individual reciprocates
the offspring insofar as these tendencies in kind (Trivers, 1971), but assume that the
affect related individuals. Consider first reciprocity is directed toward both the
interactions among siblings. An individual original actor and some relative, e.g., his
is only expected to perform an altruistic sibling. Assuming no other effects of the
act toward its full-sibling whenever the initial act, the original actor will be se-
benefit to the sibling is greater than twice lected to perform the nasty act as long as
the cost to the altruist. Likewise, it is only B>Ci -f. 1/2 (Co), where Cx is the cost to the
expected to forego selfish acts when C>2B original actor of the reciprocal nastiness he
(where a selfish act is defined as one that receives and C2 is the cost to his sibling of
gives the actor a benefit, B, while inflicting the nastiness the sibling receives. The actor's
a cost, C, on some other individual, in this parents viewing the interaction would be
case, on a full-sibling). But parents, who expected to condone the initial act only if
are equally related to all of their offspring, B>C t -f- C2. Since there ought to exist sit-
are expected to encourage all altruistic acts uations in which Cx -j- i/ 2 (C 2 )<B<C 1 -f C2,
among their offspring in which B>C, and one expects conflict between offspring and
to discourage all selfish acts in which C>B. parents over the offspring's tendency to per-
Since there ought to exist altruistic situa- form the initial nasty act in the situation
tions in which C<B<2C, parents and off- described. A similar argument can be made
spring are expected to disagree over the for altruistic behavior directed toward an
tendency of the offspring to act altruistically unrelated individual if this behavior in-
toward its siblings. Likewise, whenever for duces altruism in return, part of which
any selfish act harming a full-sibling benefits the original altruist's sibling. Par-
B<C<2B, parents are expected to dis- ents are expected to encourage such altru-
courage such behavior and offspring are ism more often than the offspring is
expected to be relatively refractory to such expected to undertake on his own. The
260 ROBERT L. TRIVERS

argument can obviously be extended to be- would be expected to overemphasize their

havior which has indirect effects on kin role as teachers in order to minimize re-
other than one's sibling. sistance in their young. According to this
As it applies to human beings, the above view then, the prevailing concept of sociali-
argument can be summarized by saying that zation is to some extent a view one would
a fundamental conflict is expected during expect adults to entertain and disseminate.
socialization over the altruistic and egoistic Parent-offspring conflict may extend to
impulses of the offspring. Parents are ex- behavior that is not on the surface either
pected to socialize their offspring to act altruistic or selfish but which has conse-

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more altruistically and less egoistically than quences that can be so classified. The
the offspring would naturally act, and the amount of energy a child consumes during
offspring are expected to resist such sociali- the day, and the way in which the child
zation. If this argument is valid, then it is consumes this energy, are not matters of in-
clearly a mistake to view socialization in difference to the parent when the parent is
humans (or in any sexually reproducing supplying that energy, and when the way
species) as only or even primarily a process in which the child consumes the energy
of "enculturation," a process by which par- affects its ability to act altruistically in the
ents teach offspring their culture (e.g., future. For example, when parent and
Mussen et al., 1969, p. 259). For example, child disagree over when the child should
one is not permitted to assume that parents go to sleep, one expects in general the
who attempt to impart such virtues as parent to favor early bedtime, since the
responsibility, decency, honesty, trust- parent anticipates that this will decrease
worthiness, generosity, and self-denial are the offspring's demands on parental re-
merely providing the offspring with useful sources the following day. Likewise, one
information on appropriate behavior in expects the parent to favor serious and
the local culture, for all such virtues are useful expenditures of energy by the child
likely to affect the amount of altruistic (such as tending the family chickens, or
and egoistic behavior impinging on the studying) over frivolous and unnecessary
parent's kin, and parent and offspring are expenditures (such as playing cards)—the
expected to view such behavior differently. former are either altruistic in themselves,
That some teaching beneficial to the off- or they prepare the offspring for future
spring transpires during human socializa- altruism. In short, we expect the offspring
tion can be taken for granted, and one to perceive some behavior, that the parent
would expect no conflict if socialization favors, as being dull, unpleasant, moral, or
involved only teaching beneficial to the any combination of these. One must at
offspring. According to the theory pre- least entertain the assumption that the
sented here, socialization is a process by child would find such behavior more en-
which parents attempt to mold each off- joyable if in fact the behavior maximized
spring in order to increase their own in- the offspring's inclusive fitness.
clusive fitness, while each offspring is
selected to resist some of the molding and CONFLICT OVER THE ADULT REPRODUCTIVE
to attempt to mold the behavior of its ROLE OF THE OFFSPRING
parents (and siblings) in order to increase
its inclusive fitness. Conflict during sociali- As a special case of the preceding argu-
zation need not be viewed solely as conflict ment, it is clear that under certain condi-
between the culture of the parent and the tions conflict is expected between parent
biology of the child; it can also be viewed and offspring over the adult reproductive
as conflict between the biology of the par- role of the offspring. To take the extreme
ent and the biology of the child. Since case, it follows at once from Hamilton's
teaching (as opposed to molding) is ex- (1964) work that individuals who choose
pected to be recognized by offspring as not to reproduce (such as celibate priests)
being in their own self-interest, parents are not necessarily acting counter to their
 PARENT-OFFSPRING CONFLICT 261

genetic self-interest. One need merely as- plained in terms of the present argument.
sume that the nonreproducer thereby in- Assuming that parent and offspring agree
creases the reproductive success of relatives that the offspring should reproduce, dis-
by an amount which, when devalued by the agreement is still possible over the form of
relevant degrees of relatedness, is greater that reproduction. Whether an individual
than the nonreproducer would have attempts to produce few offspring or many
achieved on his own. This kind of explana- is a decision that affects that individual's
tion has been developed in some detail to opportunities for kin-directed altruism, so
explain nonreproductives in the haplo- that parent and offspring may disagree over

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diploid Hymenoptera (Hamilton, 1972). the optimal reproductive effort of the off-
What is clear from the present argument, spring. Since in humans an individual's
however, is that it is even more likely that choice of mate may affect his or her ability
the nonreproducer will thereby increase to render altruistic behavior toward rela-
his parents' inclusive fitness than that he tives, mate choice is not expected to be a
will increase his own. This follows because matter of indifference to the parents. Par-
his parents are expected to value the in- ents are expected to encourage their off-
creased reproductive success of kin rela- spring to choose a mate that will enlarge
tively more than he is. the offspring's altruism toward kin. For
If the benefits of nonreproducing are example, when a man marries his cousin,
assumed, for simplicity, to accrue only to he increases (other things being equal) his
full siblings and if the costs of nonrepro- contacts with relatives, since the immediate
ducing are defined as the surviving offspring kin of his wife will also be related to him,
the nonreproducer would have produced and marriage will normally lead to greater
had he or she chosen to reproduce, then contact with her immediate kin. One
parent-offspring conflict over whether the therefore might expect human parents to
offspring should reproduce is expected show a tendency to encourage their off-
whenever C<B<2C. Assuming it is some- spring to marry more closely related indi-
times possible for parents to predict while viduals (e.g., cousins) than the offspring
an offspring is still young what the cost would prefer. Parents may also use an off-
and benefit of its not reproducing will be, spring's marriage to cement an alliance with
the parents would be selected to mold the an unrelated family or group, and insofar
offspring toward not reproducing whenever as such an alliance is beneficial to kin of
B>C. Two kinds of nonreproductives are the parent in addition to the offspring it-
expected: those who are thereby increasing self, parents are expected to encourage such
their own inclusive fitness (B>2C) and marriages more often than the offspring
those who are thereby lowering their own would prefer. Finally, parents will more
inclusive fitness but increasing that of their strongly discourage marriage by their off-
parents (C<B<2C). The first kind is ex- spring to individuals the local society de-
pected to be as happy and content as living fines as pariahs, because such unions are
creatures ever are, but the second is ex- likely to besmirch the reputation of close
pected to show internal conflict over its kin as well.
adult role and to express ambivalence over Because parents may be selected to em-
the past, particularly over the behavior ploy parental investment itself as an incen-
and influence of its parents. I emphasize tive to induce greater offspring altruism,
that it is not necessary for parents to be parent-offspring conflict may include situa-
conscious of molding an offspring toward tions in which the offspring attempts to
nonreproduction in order for such molding terminate the period of PI before the par-
to occur and to increase the parent's in- ent wishes to. For example, where the
. elusive fitness. It remains to be explored to parent is selected to retain one or more off-
what extent the etiology of sexual prefer- spring as permanent "helpers at the nest"
ences (such as homosexuality) which tend (Skutch, 1961), that is, permanent nonre-
to interfere with reproduction can be ex- productives who help their parents raise
262 ROBERT L. TRIVERS

additional offspring (or help those offspring ing the benefits and costs associated with
to reproduce), the parent may be selected some offspring behavior, both the parent
to give additional investment in order to and the offspring are selected to alter the
tie the offspring to the parent. In this situ- offspring's behavior appropriately. That is,
ation, selection on the offspring may favor the parent is selected to mold the appro-
any urge toward independence which over- priate change in the offspring's behavior,
comes the offspring's impulse toward addi- and if parental molding is successful, it
tional investment (with its hidden cost of will strongly reduce the selection pressure
additional dependency). In short, in species on the offspring to change its behavior

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in which kin-directed altruism is important, spontaneously. Since the parent is likely to
parent-offspring conflict may include situ- discover the changing circumstances as a
ations in which the offspring wants less result of its own experience, one expects
than the parent is selected to give as well tendencies toward parental molding to ap-
as the more common situation in which pear, and spread, before the parellel tenden-
the offspring attempts to garner more PI cies appear in the offspring. Once parents
than the parent is selected to give. commonly mold the appropriate offspring
Parent-offspring relations early in on- behavior, selection still favors genes lead-
togeny can affect the later adult reproduc- ing toward voluntary offspring behavior,
tive role of the offspring. A parent can since such a developmental avenue is pre-
influence the altruistic and egoistic tenden- sumably more efficient and more certain
cies of its offspring whenever it has influ- than that involving parental manipulation.
ence over any variable that affects the costs But the selection pressure for the appropri-
and benefits associated with altruistic and ate offspring genes should be weak, and if
egoistic behavior. For example, if becoming circumstances change at a faster rate than
a permanent nonreproductive, helping this selection operates, there is the possi-
one's siblings, is more likely to increase bility of continued parent-offspring con-
one's inclusive fitness when one is small in flict resulting from the greater experience
size relative to one's siblings (as appears of the parent.
to be true in some polistine wasps: Eber- If the conflict described above actually
hard, 1969), then parents can influence the occurs, then (as mentioned in an earlier
proportion of their offspring who become section) selection will favor a tendency for
helpers by altering the size distribution of parents to overemphasize their experience
their offspring. Parent-offspring conflict in all situations, and for the offspring to
over early PI may itself involve parent- differentiate between those situations in
offspring conflict over the eventual repro- which greater parental experience is real
ductive role of the offspring. This theo- and those situations in which such experi-
retical possibility may be relevant to human ence is merely claimed in order to manipu-
psychology if parental decision to mold an late the offspring.
offspring into being a nonreproductive in-
volves differential investment as well as APPENDIX: THE OFFSPRING'S EQUILIBRIAL
psychological manipulation. SEX RATIO

THE ROLE OF PARENTAL EXPERIENCE IN Let the cost of producing a female be

PARENT-OFFSPRING CONFLICT one unit of investment, and let the cost of
producing a male be x units, where x is
It cannot be supposed that all parent- larger than one. Let the expected repro-
offspring conflict results from the conflict ductive success of a female be one unit of
in the way in which the parent's and the RS. Let the sex ratio produced be 1 :y (males:
offspring's inclusive fitnesses are maximized. females), where y is larger than one. At
Some conflict also results, ironically because this sex ratio the expected RS of a male is
of an overlap in the interests of parent and y units of RS, so that, in being made a male
young. When circumstances change, alter- instead of a female, an offspring gains
 PARENT-OFFSPRING CONFLICT 263

y—1 units of RS. But the offspring also REFERENCES

thereby deprives its mother of x—1 units
of investment. The offspring's equilibrial Alexander, G. 1960. Maternal behaviour in the
sex ratio is that sex ratio at which the off- Merino ewe. Anim. Prod. 8:105-114.
DeVore, I. 1963. Mother-infant relations in free-
spring's gain in RS in being made a male ranging baboons, p. 305-335. In H. Rheingold
(y—1) is exactly offset by its loss in inclu- [ed.], Maternal behavior in mammals. Wiley, N.Y.
sive fitness which results because it thereby Drury, W. H., and W. J. Smith. 1968. Defense of
deprives its mother of x—1 units of in- feeding areas by adult Herring Gulls and intru-
vebUiient. The mother would have allo- sion by young. Evolution 22:193-201.

Downloaded from https://academic.oup.com/icb/article/14/1/249/2066733 by guest on 05 October 2020

Eberhard, M. j . W. 1969. The social biology of pel-
cated these units in such a way as to istine wasps, Misc. Publ. Mus. Zool. Univ. Mich.
achieve a l:y sex ratio, that is, she would 140:1-101.
have allocated x/(x-(-y) of the units to Elliott, B. 1969. Life history of the Red Warbler.
males and y/(x-(-y) of the units to females. Wilson Bull. 81:184-195.
Ewbank, R. 1964. Observations on the suckling
In short, she would have produced (x—1)/ habits of twin lambs. Anim. Behav. 12:34-37.
(x-)-y) sons, which would have achieved Ewbank, R. 1967. Nursing and suckling behaviour
RS of y(x—l)/(x-|-y), and she would have amongst Clun Forest ewes and lambs. Anim.
produced y(x—l)/(x-j-y) daughters, which Behav. 15:251-258.
would have achieved RS of y(x—l)/(x-|-y). Fisher, R. A. 1930. The genetical theory of natural
selection. Clarendon, Oxford.
The offspring is expected to devalue this Gill, J. C, and W. Thomson. 1956. Observations on
loss by the offspring's r0 to its displaced sib- the behavior of suckling pigs. Anim. Behav. 4:
lings. Hence, the offspring's equilibrial sex 46-51.
ratio results when Hamilton, W. D. 1964. The genetical evolution of
social behavior. J. Theoret. Biol. 7:1-52.
x _ r0 y (x — 1) r0 y (x — I) Hamilton, W. D. 1971. The genetical evolution of
social behavior, p. 23-39. Reprinted, with adden-
xx-fy
f y x +y dum. In G. C. Williams [ed.]. Group selection.
Aldine-Atherton, Chicago.
Hamilton, W. D. 1972. Altruism and related phe-
nomena, mainly in social insects. Annu. Rev.
Rearranging gives Ecol. Syst. 3:193-232.
Hinde, R. A., and Y. Spencer-Booth. 1967. The be-
y2 -f y (x — 2rox -f 2r0 — 1) — x = 0 haviour of socially living rhesus monkeys in their
first two and a half years. Anim. Behav. 15:169-
y3+(x_l)(l_2ro)y-x = 0 196.
The general solution for this quadratic Hinde, R. A., and Y. Spencer-Booth. 1971. Effects
of brief separation from mother on rhesus mon-
equation is keys. Science 173:111-118.
Hinde, R. A., and L. M. Davies. 1972a. Changes in
y = mother-infant relationship after separation in
rhesus monkeys. Nature 239:41-42.
Hinde, R. A., and L. M. Davies. 1972b. Removing
V(x - 1)2 (1 - 4x infant rhesus from mother for 13 days compared
2 with removing mother from infant. J. Child Psy-
chol. Psychiat. 13:227-237.
Where r0 = i/2, the equation reduces to Jay, P. 1963. Mother-infant relations in langurs,
y = \/x. In other words, when the offspring p. 282-304. In H. Rheingold [ed.], Maternal be-
haviour in mammals. Wiley, N.Y.
displaces full siblings (as is probably often Le Boeuf, B. J., R. J. Whiting, and R. F. GantL
the case), the offspring's equilibrial sex 1972. Perinatal behavior of northern elephant seal
ratio if 1 : \/x, while the parent's equilib- females and their young. Behaviour 43:121-156.
rial sex ratio is l:x. These values, as well Munro, J. 1956. Observations on the suckling be-
as the offspring's equilibrial sex ratio where haviour of young lambs. Anim. Behav. 4:34-36.
r0 = 14, are plotted in Figure 4. The same Mussen, P. H., J. J. Conger, and J. Kagan. 1969.
Child development and personality. 3rd ed. Har-
general solution holds if parents invest per and Row, N.Y.
more in females by a factor of x, except Rheingold, H. 1963. Maternal behavior in the dog,
that the resulting sex ratios are then re- p. 169-202. In H. Rheingold [ed.], Maternal be-
versed (e.g., y/x : 1 instead of 1 : V x )- havior in mammals. Wiley, N.Y.
264 ROBERT L. TRIVERS

Rosenblatt, J. S., and D. S. Lehrman. 1963. Maternal mals. Wiley, N.Y.

behavior of the laboratory rat, p. 8-57. In H. Skutch, A. F. 1961. Helpers among birds. Condor
Rheingold [ed.], Maternal behavior in mammals. 63:198-226.
Wiley, N.Y.
Struhsaker, T. T. 1971. Social behaviour of mother
Rosenblum, L. A. 1971. The ontogeny of mother- and infant vervet monkeys (Cercopithecus aethi-
infant relations in macaques, p. 315-367. In H. ops). Anim. Behav. 19:233-250.
Moltz [ed.], The ontogeny of vertebrate behavior.
Academic Press, N.Y. Trivers, R. L. 1971. The evolution of reciprocal
Rowe, E. G. 1947. The breeding biology of Aquita altruism. Quart. Rev. Biol. 46:35-57.
verreauxi Lesson. Ibis 89:576-606. Trivers, R. L. 1972. Parental investment and sexual
Schaller, G. B. 1964. Breeding behavior of the White selection, p. 136-179. In B. Campbell [ed.], Sex-
Pelican at Yellowstone Lake, Wyoming. Condor ual selection and the descent of man, 1871-1971.
Aldine-Atherton, Chicago.

Downloaded from https://academic.oup.com/icb/article/14/1/249/2066733 by guest on 05 October 2020

66:3-23.
Schneirla, T. C, J. S. Rosenblatt, and E. Tobach. Wallace, L. R. 1948. The growth of lambs before
1963. Maternal behavior in the cat, p. 122-168. In and after birth in relation to the level of nutri-
H. Rheingold [ed.], Maternal behavior in mam- tion. J. Agri. Sci. 38:93-153.