Sexual selection under parental choice: the role of parents in the
evolution of human mating
Department of Psychology, University of Warwick, Coventry, CV4 7AL, UK
Initial receipt 5 February 2007; final revision received 23 May 2007
Much of the evolutionary literature on human mating is based on the assumption of extensive female choice during the history of our
species. However, ethnographic evidence from foraging societies reveals that, in societies thought to be akin to those of our ancestors, female
choice is constrained by the control that parents exercise over their daughters. Data from 190 hunting and gathering societies indicate that
almost all reproduction takes place while the woman is married and that the institution of marriage is regulated by parents and close kin.
Parents are able to influence the mating decisions of both sons and daughters, but stronger control is exercised with regard to daughters; male
parents have more say in selecting in-laws than their female counterparts. In light of the fact that parental control is the typical pattern of mate
choice among extant foragers, it is likely that this pattern was also prevalent throughout human evolution. Because daughters' preferences can
be expected not to fully coincide with those of their parents, research to date may thus have simultaneously overestimated the contribution of
female preferences to processes of sexual selection and underestimated the contribution of parental preferences to such processes.
© 2007 Elsevier Inc. All rights reserved.
Keywords: Parental choice; Sexual selection; Female choice; Human mating; Hunters and gatherers
Evolutionary psychology combines evolutionary theory
with evidence from preindustrial societies in an attempt to
reconstruct the ancestral environment and to make valid
claims about the evolution of human behavior (Pinker,
1997). Since most of human evolution took place in an
environment where subsistence was based on hunting and
gathering (Lee & DeVore, 1968), particular emphasis is
placed on evidence from modern foragers. Patterns of
behavior and social organization that are typical among
hunter–gatherers are also assumed to be typical of ancestral
human societies (but see Kelly, 1995). However, much of the
existing theory about the evolution of mating behavior has
not taken into account the typical patterns in hunting and
gathering societies (Ember, 1978). This fact makes many
evolutionary claims problematic.
Over the last few years, a substantial literature on the
evolution of human mating has emerged. Research in this
area is commonly based on the assumption of extensive
female choice during the period of human evolution (e.g.,
Buss, 1995, 2003; Daly & Wilson, 1983; Miller, 2000;
Symons, 1979). However, the ethnographic record indicates
that female mate choice is far from free. To the contrary, it
demonstrates that the mating decisions of females are heavily
controlled by their parents (Broude & Green, 1983; Minturn,
Grosse, & Haider, 1969; Whyte, 1978b). Consequently,
present models that do not incorporate the influence of close
kin in mating decisions are inadequate for the study of
human mating (Cronk, 1991). Accordingly, the first aim of
this article is to provide an evolutionary model that
incorporates the control over mate choice that is exercised
by close kin and better accounts for the mating patterns
observed in foraging societies. Secondly, data from an
extensive sample of modern hunters and gatherers are
surveyed and presented here, and the typical patterns of
mating in these societies are identified.
1.1. The model of parental choice
The theory of parental investment (Bateman, 1948;
Trivers, 1972) states that the female, by investing more in
Evolution and Human Behavior 28 (2007) 403–409
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1090-5138/$ –see front matter © 2007 Elsevier Inc. All rights reserved.
her offspring, becomes a scarce reproductive resource to
which males are seeking access. As a consequence, the
parents of the female find themselves in possession of a
valuable resource that they can manipulate to their own
advantage. By controlling their daughters' mating decisions,
parents can select in-laws with characteristics that maximize
their own inclusive fitness. For example, parents may
choose mates for their daughters based on the male's
willingness to provide resources and long-term support to
the parents and their family in return. The parents can use
these resources to increase the probability of survival and
reproduction for themselves and their kin, including their
daughter. Males also invest in their offspring; thus, parents
have an incentive to control their sons' mating decisions as
well. However, due to the asymmetry in parental invest-
ment, the model predicts that there will be less parental
control aimed at the mating choices made by male versus
female offspring since females are the scarcer commodity.
Note that if parents leave mate selection to their offspring,
the offspring will make choices that maximize their own
(and not necessarily their parents') inclusive fitness.
Because parents and offspring are not genetically identical
and, thus, do not always have identical genetic interests,
parents' and offspring's preferences may differ (Hamilton,
1964; Trivers, 1974).
Parental control over mating is possible in settings where
the offspring are dependent on their parents for food and
protection and where parents are able to use their physical
strength over their offspring to impose their will. Certain
aspects of human sociality, like the long period of parental
investment, potential heritability of resources, and extensive
networks of kinship and reciprocity, also facilitate parental
control (Alexander, 1974; Flinn & Low, 1986; Trivers,
1974). In certain settings, parents have the power to seize
mating control from the hands of their offspring. Further-
more, by means of greater physical strength, exclusive use of
weaponry, and control of political institutions (Flinn & Low,
1986; see also Smuts, 1992, 1995), male parents may have
more influence over offspring mate choice than do their
However, the offspring are not simply pawns in their
parents' hands. Offspring may evolve adaptations to
psychologically manipulate their parents toward their own
ends (Trivers, 1974). On the other hand, parents may also
evolve adaptations to counterbalance such manipulation
(Stamps, Metcalf, & Krishnan, 1978). Consequently, the
balance tilts in favor of the parents, who still control parental
investment and are physically stronger (Dawkins, 1989).
Still, parental control over the offspring's mating has its
limits: parents, for instance, cannot always be present to
guard their offspring. In addition, the successful manipula-
tion of the offspring requires at least some consideration of
their preferences by their parents. Such consideration
reduces conflict and increases the effectiveness of parental
control. However, parental control wanes as offspring grow
older; with age, the offspring become more experienced in
subsistence activities and less dependent upon their parents.
In later marriages, parents and close kin may be absent due to
death or at least less able to impose their choices due to old
age. Likewise, if offspring change their group affiliations
upon marriage, then geographic and social distance may
reduce parental influence in the event of subsequent
remarriage. Since this model predicts that parental control
will be asymmetrically biased toward the female offspring,
increased autonomy with age will have a more noticeable
effect on female versus male mate choice. The precise impact
of such changes will depend on timing. Given that female
residual reproductive potential declines with age, the effects
of increasing autonomy on female reproduction should be
tempered by decreasing fertility. This may be one reason
why control over women is relaxed in their post-childbearing
years (Brown, 1982).
Overall, in this model of human reproduction, mate
choice is controlled by the parents, particularly where female
offspring are concerned. In addition, male parents have more
decision-making power than female parents. Despite par-
ental control, there is still sufficient space in this model for
offspring to exercise some mate choice, either independently
or through their parents. The next step is then to identify the
mating patterns that are typical among foragers and examine
the degree to which this model of parental choice accounts
for the observations.
In cross-cultural research, random sampling is usually
employed for the construction of a sample. However,
random sampling in this case is not appropriate since it
might result in the inclusion of many societies for which
sufficient description is not available, as well as the
exclusion of a number of societies for which rich description
exists (Murdock, 1957). Similarly, certain geographic areas
contain only a small number of foraging societies and a
random sampling process would result in the exclusion or
limited representation of these areas. Therefore, an extensive
sample of 190 societies is employed instead. This sample
includes almost all modern hunting and gathering societies
for which reliable mating pattern data exist.
A society is categorized as a hunting and gathering
group if its people base at least 75% of their subsistence
on hunting and gathering, according to the Ethnographic
Atlas (Murdock, 1967). If a society is not coded in the
Atlas, it is classified as a hunting and gathering society
if it is reported as such in the anthropological sources
employed here. The majority of the societies in the sample
are exclusively hunters and gatherers. Ideally, a geogra-
phically balanced sample of societies is desirable, but since
hunting and gathering societies are not equally distributed
across the globe, this is not possible (Murdock, 1967). For
instance, there are no societies from Europe in the sample,
but North American societies are overrepresented. In all,
404 M. Apostolou / Evolution and Human Behavior 28 (2007) 403–409
the sample consists of 9 African societies, 16 East
Eurasian societies, 19 Insular Pacific societies, 85 North
American societies, 47 Arctic and Sub-Arctic societies, and
14 South American societies. Reference sources were
gathered mainly with the use of Murdock's Atlas of World
Cultures (Murdock, 1981) and Atlas of World Cultures
Ember and Ember's (2001) coding scheme was employed
as a general guideline for the coding process. Coding was
done by two coders. One independent coder was employed
so as to control for possible biases (Ember & Ember, 2001).
Average correlation across variables for the two sets of
coding data was .90. For a number of variables of interest,
data were scarce and information gathering was possible for
only a limited number of cases. It is acknowledged that this
might introduce a potential bias to the conclusions based on
The use of an extensive sample can potentially suffer
from the problems of cultural diffusion and historical
relation (known together as Galton's problem). Cultural
diffusion is the spread of a trait from one culture to another
due to geographic proximity (Mace & Holden, 1999).
However, there are no reasons to believe that the mating-
related traits examined here are picked up from neighbor-
ing cultures simply because of proximity. That is, cultures
do not assume all of the cultural traits that their neighbors
have and still remain as separate cultures (Mace & Holden,
1999). Historical relation is a potential issue with regard to
certain cultures in North America and the Arctic and Sub-
Arctic. That said, Ember (1971) found no evidence that
such historical relation can affect cross-cultural research.
Although this conclusion is probably also valid for mating
patterns, this is tested here with a reanalysis of the data
from North America, the Arctic, and the Sub-Arctic with
the random omission of cases from these subsamples
(Ember & Ember, 2001). This did not produce significantly
different results from the original samples. A potentially
more serious concern is the overrepresentation of certain
geographical areas. An alternative subsample was con-
structed to deal with this problem. The subsample consists
of 54 societies equally distributed across geographical
areas. This sample was created by including the nine
African societies and nine randomly selected societies from
each of the remaining geographical areas. The analysis of
the full sample has also been repeated for the subsample,
and the results are reported along with the results from the
analysis of the entire sample.
3. The anthropological record
3.1. Marriage among hunters and gatherers
Marriage is a universal institution (Murdock, 1949) and
is found in all societies analyzed here. Females in hunter
and gatherer societies remain married throughout their
reproductive years, and hence, most reproduction takes
place while the woman is married. Marriage is therefore
of special importance for understanding human reproduc-
Four main types of marriage are distinguished here:
parental arrangement, close kin arrangement, courtship
subject to parental approval, and courtship. In the parental
arrangement type, parents are predominantly in control of
marriage arrangements but their offspring can also be
consulted. In close kin arrangement, family members other
than parents arrange marriages, but the latter also participate
in the arrangement process. In cases of courtship subject to
parental approval, the individual parties find their own
marriage partners, but their choices are subject to their
parents' approval. Finally, in the courtship type of marriage,
the individual parties are free to choose and marry whomever
they like. It is usually the case that more than one type of
marriage is practiced in each society. When the majority of
marriages in a given society take a specific form (e.g.,
parental arrangement), this type of marriage is classified as
primary for this society. If a marriage type is reported by
anthropologists as present, then this type is classified as
secondary irrespective of its frequency.
As discussed before, the sample is skewed toward an
overrepresentation of North American, Arctic, and Sub-
Arctic societies, and a separate analysis was conducted on a
balanced subsample. The conclusions of the analysis are
based on the results from the entire sample of societies.
However, the results from the analysis of the subsample are
also available and are presented in parentheses next to the
results from the total sample. Unless it is indicated otherwise,
the percentages reported are the percentages of cases that
take a specific value when only cases with nonmissing
values are considered.
The parental arrangement type of marriage, found to be
primary in 130 (32) cases [69.9% (62.7%)], is the most
widespread type of marriage. It is followed by close kin
arrangement in 33 (12) cases [17.7% (23.5%)] and courtship
subject to parental approval in 15 (4) cases [8.1% (7.8%)],
while courtship is the primary form of marriage in only 8 (3)
cases [4.3% (5.9%)] (Fig. 1). Parental and close kin control
of marriage are the most frequent marriage types across all
geographic areas (Fig. 2). In the three most common
categories, parents have a major role in regulating mate
choice. Thus, one can conclude that in roughly 96% of the
societies in the sample, parents play a crucial role in
determining whom their offspring will marry. Parental
arrangement is the secondary marriage type in 145 (41)
cases [52.9% (46.6%)], close kin arrangement in 54 (19)
cases [19.7% (21.6%)], courtship subject to parental
approval in 37 (11) cases [13.5% (12.5%)], and courtship
in 38 (17) cases [13.9% (19.3%)] (Fig. 1).
Most of the societies practice polygyny, which is usually
reported to be the privilege of few men. Polygyny is found in
140 (41) societies [73.7% (75.9%); missing values are
considered], while it is reported as common in 17 (5)
societies [21.5% (21.7%)] and rare in 62 (18) societies
405M. Apostolou / Evolution and Human Behavior 28 (2007) 403–409
[78.5% (78.3%)]. Polyandry is also present and is reported in
23 (10) cases [12.1% (18.5%); missing values are consid-
ered], always as very rare.
3.2. Who does the choosing?
The choice of a marriage partner for a given individual is
predominantly made by his or her parents. Parental choice
can be subdivided into two components: the choice exercised
by female parents and the choice exercised by male parents.
One can then analyze whether the opinions of individual
parents carry equal weight or whether one parent's influence
dominates the other's. In this sample, males are predomi-
nantly in control of the marriage negotiations with little or no
influence from their female spouses in 53 (20) cases [43.8%
(54.1%)]. Both parents participate equally in negotiations in
38 (9) cases [31.4% (24.3%)]. Both parents participate in
negotiation, but males have more say than females in 19 (5)
cases [15.7% (13.5%)] while both parents participate but
females have more say than males in 10 (3) cases [8.3%
(13.5%)]. Finally, females dominate marriage negotiations
with little or no influence from their female spouses in one
(zero) case [0.8% (0%)] (Fig. 3).
When females have more say or dominate the negotia-
tions, it is almost exclusively the mother who is the decision
maker. When males dominate negotiations exclusively or
have more say, fathers are the decision makers in 52 (19)
societies [77.6% (76%)] followed by brothers of the bride in
11 (4) societies [16.4% (16%)] and her uncles in 4 (2)
societies [6% (8%)].
3.3. Parental control
One way for parents to exercise effective control over
their female offspring is to ensure that their daughters are
married as soon as they reach puberty or even earlier (Goody,
1959). In such cases, daughters do not have time to start
relationships of their own. In addition, parents can impose
their choices more easily upon their female offspring, who
are still dependent on them. According to a Sama Bajau
saying, “fish and daughters are alike; both must be disposed
of quickly lest they spoil”(Sather, 1997, p. 252). In this
sample, the primary female age at first marriage is at onset of
puberty in 66 (19) cases [86.8% (86.4%)], followed by
marriage in childhood in 6 (3) cases [7.9% (13.6%)], and
finally, marriage in adulthood in 4 (0) cases [5.3% (0%)].
Marriage at the onset of puberty is reported as secondary in
76 (22) cases [69.7% (68.8%)], marriage in childhood in 20
(9) cases [18.3% (28.1%)], and finally, marriage in
adulthood in 13 (1) cases [11.9% (3.1%)]. However, males
are not forced into early marriage, and as a consequence,
females are usually married to men older than they are. This
is the case in 55 (16) societies [88.7% (94.1%)]. Only in 7 (1)
societies [11.3% (5.9%)] are females married to a man of the
same age. Infant or child betrothal is found in 63 (20) cases
[33.1% (37%); missing values are considered]. In this
arrangement, parents betroth their children when they are
very young, but these betrothals rarely constitute an absolute
commitment for later marriage.
Arranged marriages usually take the form of parents or
close kin “giving away”their female relative after
Fig. 3. The distribution of decision makers according to sex.
Fig. 2. Marriage types by geographical area: (A) Africa, (E) East Eurasia, (I)
Insular Pacific, (N) North America, (S) South America, (R) Arctic and Sub-
Fig. 1. Total number of cases by primary and secondary types of marriage in
406 M. Apostolou / Evolution and Human Behavior 28 (2007) 403–409
negotiations with the male or his relatives. As such, males
are allowed much more autonomy to exercise mate choice
than females. Men are reported to ask for a woman in
marriage from her parents in 49 (15) cases [25.8% (27.8%);
missing values are considered], while there is no case where
women are allowed to take such initiative. Also, the groom's
parents take the initiative in arranging the marriage with the
bride's parents in 52 (15) cases [86.7% (83.3%)], both sets of
parents can take the initiative in 7 (3) cases [11.7% (16.7%)],
and only in 1 (0) case [1.7% (0%)] are the bride's parents
reported to take the initiative.
3.4. What parents want
When choosing a son-in-law, parents look for someone
who is hardworking and a good provider in 20 (4) cases
[45.5% (33.3%)], a good hunter in 19 (5) cases [43.2%
(41.7%)], and from a good family in 5 (3) cases [11.4%
(25%)]. When parents do explicitly express a dominant
preference, it is usually for a good hunter in 15 (4) cases
[60% (57.1%)], followed by someone who is hardworking
and a good provider in 8 (2) cases [32% (28.6%)], and from a
good family in 2 (1) cases [8% (14%)]. The groom's parents
are looking for a hardworking daughter-in-law in 22 (4)
cases [75.9% (66.7%)] and one from a good family in 7 (2)
cases [24.1% (33.3%)]. Being hardworking is reported as the
dominant preference in 16 (4) cases [84.2% (100%)] and
coming from a good family in 3 (0) cases [15.8% (0%)]. Of
interest here is that traits such as physical attractiveness are
not reported as contributing to parents' assessments of
Being selected by a mate's parents gives an individual
male far more reproductive advantages than acquiring a
single female. Through the institution of sororal polygyny, a
male is likely to receive his first wife's sisters as additional
wives. The sororate, a common practice across cultures
(Murdock, 1949), also mandates that if a man's wife dies,
he can receive one of her sisters as a wife. The sororate is
found in 81 (15) [42.6% (27.8%); missing values are
considered] of the societies presented here. Sororal polygyny
and the sororate are heavily regulated by the families of the
3.5. Female choice
Despite strong parental control over mating, female
choice may still be exercised. The institution of divorce
offers this possibility. Divorce is almost as frequent as
marriage, being found in 125 (33) societies [65.8% (61.1%);
missing values are considered]. It is reported as common in
32 (8) societies [59.3% (57.1%)] and as rare in 22 (6) of them
[40.7% (42.9%)]. For the Chinookans and the Sarsi, divorce
is reported to be a male privilege; in the rest of the sample,
divorce is obtained at will by both sexes. Incompatibility is
given as reason for marriage dissolution by both parties in 23
(6) societies [21.9% (21.4%)]. Husbands may also initiate
marriage dissolution due to female barrenness in 30 (6)
societies [28.6% (21.4%)]. Finally, laziness is given as a
reason for divorce by both partners in 20 (6) cases [19%
When arranging their daughters' marriages, parents
usually consult the daughters themselves. This is the case
in 35 (7) societies [18.4% (13%); missing values are
considered]. A daughter's consent is not always a pre-
requisite for a marriage to proceed, and the females are
usually reported to submit to their parents' wishes.
Extramarital relations are another way for women to
exercise choice, but this carries a heavy price. Adultery is
punished severely in 20 (2) cases [60.6% (25%)]. Severe
punishment includes mutilation and often death. Moderate
punishment, which involves beating the wife, is reported in
12 (5) cases [36.4% (62%)]. No punishment for adultery is
reported only in 1 (1) case [3% (12.5%)]. Although severe
punishment is more frequent in the total sample than in the
subsample, no punishment for adultery is the minority in
both. Women also risk permanently destroying their
marriage by engaging in extramarital relations; adultery is
given as reason for divorce in 32 (10) cases [30.5% (35.7%)].
Finally, elopement is another manifestation of female
choice. Elopement may or may not lead to marriage.
Elopement is found in 45 (15) societies [23.7% (27.8%);
missing values are considered]. In all these cases, elopement
is reported as rare, one of the reasons being that parents often
react severely, forcing their daughter to return or withholding
support from her.
An exhaustive review of the ethnographic record
indicates that parents in foraging societies have a central
role in selecting the long-term spouses of their offspring,
although offspring can still exercise some mating choice
through various means, including divorce and extramarital
relations. These conclusions also hold for the subsample
examined here, which is balanced across geographical areas.
Therefore, it may be productive to modify previous models
of human mating, which assume free female choice, so as
to take into consideration the role of parental control in
As described in Section 2, steps have been taken to
control for Galton's problem, coder bias, and the over-
representation of certain geographical areas. However, the
best guard against these biases is the replication of the results
presented here. It is therefore revealing that previous studies,
although with findings less comprehensive than those
reported here and/or not limited to foraging societies, arrive
at similar conclusions. Minturn et al. (1969) report that the
courtship type of marriage was the least frequent type of
marriage in their sample. Similarly, Broude and Green
(1983) use a subsample from the standard cross-cultural
sample and find that arranged marriages were the most
common marriage type, with more control exercised over the
marriage of females. Moreover, Whyte (1978b) concluded
407M. Apostolou / Evolution and Human Behavior 28 (2007) 403–409
that in the majority of the preindustrial societies considered,
marriage arrangements are dominated by males. It was also
found that, in the vast majority of cases, divorce was equally
available as an option for both husband and wife. Frayser
(1985) reported that, in the majority of the societies in his
sample, parents consider the offspring's opinion when
selecting an in-law. Finally, Betzig (1989) found that
adultery and incompatibility are frequent causes of divorce
Although there is agreement that patriarchy is the norm in
preindustrial societies, and thus it is reasonable to expect
male dominance over marriage decisions (Collier &
Rosaldo, 1981; Goldberg, 1973; Leach, 1951; Levi-Strauss,
1969), this may be exaggerated in the ethnography. Men,
having a passion for prestige and public display, may have
less control than is apparent (Daly & Wilson, 1988). Whyte
(1980) found that in almost half of the preindustrial societies
in his sample, ethnographers report that women have more
influence than is reflected in their society's formal norms.
According to Brown (1982), the influence of older women in
marriage arrangements is often underestimated by many
anthropologists. It has also been argued that most anthro-
pological studies are undertaken by men, and this can lead to
a bias in understanding the position of women in a given
society (see also Endicott, 1999). Although Whyte (1978a)
found no evidence for this claim, this is still a worrying
concern. Overall, female parents may have more decision-
making power over marriage decisions than is evident in
The findings presented here will not come as a surprise
to many scholars familiar with the ethnographic literature.
However, this may be less true for psychologists who,
perhaps constrained by time demands imposed by
discipline-based specialization, are less well acquainted
with the ethnographic record. For instance, Miller (2000,
p.180) assumes that arranged marriages and patriarchy are
recent inventions associated with the onset of agriculture
and animal domestication. While other evolutionary
psychologists accept that, in many societies, the marital
decisions of the offspring rest with the parents (Buss,
2003,p.91;Daly & Wilson, 1983, p. 288), they
nevertheless proceed to assume extensive female choice
in their analyses. Thus, many scholars may benefit from
incorporating anthropological evidence into the study of
Sexual selection arises from differences in the reproduc-
tive success caused by competition over mates (Darwin,
1871). Since males compete for access to females, who, in
turn, are controlled by their parents, it is possible that certain
mating adaptations are best understood as the evolutionary
product of parental rather than female choice. More
complexly, since both parents and offspring are able to
exercise some control over mate choice, the evolution of
individual and parental mate choice behavior can be seen as
the outcome of coevolution between parental and offspring
choice. This renders the exploration of parent–offspring
conflict over mating particularly important. The theory of
parent–offspring conflict (Trivers, 1974) predicts that some
conflict exists, but the extent to which parental and offspring
mating preferences overlap or clash requires further
investigation. However, even if parents and offspring do
have identical interests, the evolutionary path of mating
adaptations may still be different if mating is disproportio-
nately controlled by parents. For example, it has been
hypothesized that males have evolved adaptations for honest
signaling that reliably communicates their otherwise unob-
servable properties to females (Miller, 2000; Zahavi &
Zahavi, 1997). As honest signaling adaptations are con-
tingent upon the receiver's psychology (Guilford &
Dawkins, 1991; Row, 1999), evolution may take one path
if the receiver is a female and a different path if the receiver is
a female and male pair (the parents).
To date, the evolutionary literature on human mating has
often been inconsistent, or incomplete, in its attention to
ethnographic evidence such as that studied here. Perhaps this
is because data on mating patterns among foraging societies
are scattered across individual studies (e.g., the !Kung; Lee,
1979) or presented along with evidence from nonforaging
societies (e.g., Whyte, 1978b), or perhaps this is because
much human mating research takes place within a Western
context where parents have little direct role in the choices of
their offspring. Regardless, taking into account the role of
parents in manipulating the mating choices of their offspring
may broaden our understanding of human mating, enabling
us to more accurately reconstruct the evolution of human
I am in debt to Lia Mexa for her help and advice during
the preparation of this article. I would also like to thank
William Jimenez for his useful advice. Finally, I would like
to thank Daniel Fessler and two anonymous reviewers for
their comments and feedback, which substantially contrib-
uted to the improvement of this work.
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