BACKGROUND
cooperatively breeding groups often have two defining characteristics: increased productivity over solitary individuals and differential within-group reproductive success or skew  <cit> .
one puzzling feature of reproductive inequality is that subordinate roles appear to be willingly accepted.
kin selection is the dominant evolutionary paradigm for this apparent reproductive altruism  <cit> .
in groups of relatives, an individual reducing its reproduction can be favored if this sufficiently benefits genetic kin.
increasingly, however, the relative importance of genetic relatedness for the evolution of reproductive skew is being questioned  <cit> .
if groups are sufficiently successful, then individual genetic differences creating within-group reproductive skew can be evolutionarily stable  <cit> .
alternatively, parental manipulation can bias offspring to assume otherwise reproductively disadvantageous roles  <cit> .
if such groups remain intact over generations of shared reproduction, then high relatedness may be a consequence and not a cause of cooperation.
indeed, wilson and others argue kin selection acts more often as a 'dissolutive' than a binding force within groups  <cit> .
the proposed alternatives to kin selection for reproductive skew have been challenged on both theoretical and empirical grounds  <cit> .
the importance of kin selection in the evolution of cooperative breeding is argued to be particularly evident in its taxonomic distribution with respect to mating strategy.
by hamilton's rule, helping a relative is selectively favored when relatedness exceeds the cost/benefit ratio, or r >c/b.
with monogamy, helping a parent rear full siblings is as valuable as rearing one's own offspring .
therefore, any reduction in cost or increase in benefit favors helping.
in contrast, polygamy in terms of multiple fathers produces half sibs  and cooperation would require halving costs or doubling benefits.
thus, kin selection predicts the evolution of cooperation ought to be most likely in species preadapted to maintain high relatedness between siblings   <cit> .
monogamy and high relatedness were first proposed to be critical in evolutionary transitions in social insects from cooperative breeding with totipotent individuals, to eusocial systems with morphological queen and worker castes  <cit> .
two recent phylogenetic analyses have extended the monogamy hypothesis to cooperative breeding, per se.
monogamy or lower levels of promiscuity are the most likely ancestral state for evolutionary transitions from solitary to social living in hymenoptera  <cit>  and birds  <cit> .
conversely, lack of monogamy is hypothesized as evolutionarily constraining social degus  from more elaborate sociality as exhibited by other group-living rodents such as naked mole rats  <cit> .
nowak et al.
<cit>  challenged the monogamy hypothesis for social hymenoptera on two grounds.
specifically, the phylogenetic evidence is weak because the ancestral state of the majority of solitary hymenoptera species is likely to be monogamy.
hence, monogamy as an evolutionary preadaptation is indistinguishable from ecological factors favoring cooperation, such as defending nests or sequentially provisioning offspring.
more broadly, the entire approach of inclusive fitness modeling may be rife with simplifying assumptions that produce spurious predictions.
rather than the actor-based approach of kin selection , nowak et al.
<cit>  advocated a gene-based approach .
they derived general cases showing that r values alone may not always accurately predict the evolution of cooperation.
however, they gave no example of a specific behavioral or life history phenomenon where a kin selection model gives an erroneous prediction relative to a gene-based model  <cit> .
the monogamy hypothesis is where kin selection possibly gets it wrong.
if its basic premise of an inclusive fitness advantage to helping with high relatedness is correct, then the same result ought to occur when cooperation is modeled as the spread of a helping allele.
RESULTS
helping allele  is dominant
cooperation evolves under intermediate values of adult survival between offspring cohorts.
if s is less than  <dig>  or  <dig>  for cohort sizes of  <dig> or  <dig> respectively, helping never predominates in the population .
similarly, if s =  <dig> such that mothers do not die between cohorts, there is no selective advantage to making or being a helper.
with no maternal mortality, helping behavior does not invade the population in the model .
under conditions that do favor helping, the monogamy hypothesis is not confirmed by a gene-based approach: helping does not consistently evolve more quickly with monogamy .
under many conditions, the number of mates does not affect how rapidly helping spreads through the population.
the gene-based modeling approach reveals the reason.
any aa female mating with multiple males increases her chances of gaining a helper.
however, helpers aid a relatively smaller fraction of sibs with a. these two probabilities approximately cancel out.
from the helping allele perspective, single mating is a high variance strategy that pays off big, but rarely.
multiple mating is a low variance strategy that works more often, but with reduced effect.
there are associated advantages and disadvantages with mating strategy that are separate from differences in sibling relatedness.
an advantage for single mating is that helpers aid both alleles equally.
for example, all daughters from aa x a matings are aa.
thus, the frequency of a in helpers equals the frequency of a in aided female siblings.
in contrast, if aa females mate multiply with males of both genotypes, then the frequency of a is higher in helping females than in helped ones.
although a can increase in the population due to across-group selection, it decreases in frequency within its own group.
when inter-cohort survival is low, this cost to multiple mating results in helping evolving faster with monogamy .
multiple mating has an advantage that if mothers die, subsequent benefits nonrandomly accrue to a alleles.
only daughters having this allele can inherit nests.
as inter-cohort survival increases, helping becomes more likely to evolve with polygamy and through groups of lower mean relatedness.
interestingly, polygamy is favored over a wider range of values than monogamy .
mating strategy is uniform across females within a population in the above results.
however, when females are randomly assigned a number of mates  within the same population, multiply-mated nests consistently produce more offspring relative to singly-mated nests across a wide range of s values .
the difference is particularly evident when a is the rarer allele.
only when a reaches high frequencies, such as 75% of the population, is nest productivity similar across mating strategies.
when mating strategies are themselves genetically determined, alleles for higher mating frequency are favored .
because polygamous nests produce more helping daughters, this in turn increases lifetime nest productivity  and the potential transmission of alleles for multiple mating.
this advantage disappears at higher frequencies of the helping allele because all mating strategies are likely to produce helpers .
interestingly, with low survival values  cooperation evolves much more rapidly in monogamous rather than polygamous populations , but polygamous nests are on average more productive within populations  and multiple mating alleles are at a selective advantage when helping is not ubiquitous .
therefore, the evolution of helping appears to always have the correlated effect of also favoring mating with multiple potential fathers.
helping allele  is recessive or males are diploid
helping behavior evolves more slowly when a is recessive because the allele must initially drift under neutral selection until its frequency is high enough that aa daughters start being produced.
apart from this, the results are broadly similar to when a is dominant .
monogamy is favored when s is low, equal to polygamy when s is intermediate, and disfavored when s is high.
also similar to when a is dominant, monogamous nests are, on average, less productive when a is rare in the population .
recessive alleles differ in that multiple mating has the greatest relative selective advantage at intermediate frequencies of a. this is again likely due to helping rarely expressed at low frequencies of recessive a alleles.
assuming diploid males has no qualitatively different effects on the results and conclusions .
indirect fitness and multiple helpers
when helpers randomly drift across nests, kin and non-kin are equally likely to benefit from survival insurance.
in the absence of indirect fitness gains for biasing survival insurance towards kin, a does not increase in frequency beyond levels produced by mutation and genetic drift .
across every simulation with all levels of adult survival, the a allele never reached a frequency of 50% or more in the population.
allowing multiple helpers, each of which provides an identical increase in nest survivorship, does not result in helping spreading more rapidly with monogamy than polygamy.
under conditions where a is dominant and offspring come in cohorts of five, the helping allele reaches a population frequency of 50%, on average, in  <dig> ,  <dig>  or  <dig>  generations  with monogamy.
in comparison, the helping allele reaches the 50% criterion in  <dig> ,  <dig>  and  <dig>  generations when females mate with two males.
when mating with five males, the 50% criterion is attained in  <dig> ,  <dig>  and  <dig>  generations.
thus across this range of comparison, the 50% criterion is reached in 39-79% of the number of generations required under monogamy.
contrasted to the results with only one helper , polygamy is even more conducive to the spread of helping behavior when multiple helpers increase nest survival in an additive, linear fashion.
discussion
monogamous behavior on the part of females in mating with only one male does not appear to generally act as a spring-loaded preadaptation for the evolution of cooperative breeding.
to the contrary, polygamy through polyandry is more likely to be particularly beneficial.
although phylogenetic signals may correlate monogamy with eusociality and reproductive skew  <cit> , such relationships are not prima facie support for kin selection theory.
other shared life history traits apart from mating behavior must be reconsidered as predisposing factors for evolution of cooperative breeding  <cit> .
indeed, the more interesting message in the phylogenetic data may be how often social systems of low relatedness have evolved  from high-relatedness ancestral species.
for example, polyandry appears to have evolved independently from monoandry in  <dig> clades of ants  <cit> .
groups of low relatedness are likely to have correlated benefits arising from increased group-level genetic diversity, and it appears these benefits often exceed the evolutionary advantages of high within-group relatedness  <cit> .
the contradiction of the monogamy hypothesis by a gene-based model supports criticism that inclusive fitness models are potentially inaccurate  <cit> .
there are two reasons, however, why these results do not contradict kin selection, per se.
first, comparing rearing offspring versus rearing full or half sibs in deriving the monogamy hypothesis is overly simplistic.
this fails to include a long chain of probabilities of outcomes.
for example, the true fitness payoff for a daughter in helping must include: the probability of surviving her mother across each potential remaining offspring cohort; if she does survive her mother, the probability that she herself will recruit a helper ; the subsequent probability that she will in turn be superseded by her daughter; etc.
this value must be compared to a similarly extensive calculation of fitness for leaving.
note also that this is from daughter's 'point of view'.
the payoffs would be different if asking whether the mother should manipulate a daughter into helping.
thus a gene-based model might indeed predict the same result as a fully comprehensive inclusive fitness model.
nevertheless, a gene-based approach is clearly a much simpler and more robust approach to this question.
the stochastic simulations include every possible series of outcomes weighted by their probability of occurrence.
none of these have to be calculated a priori.
the model also has no 'point of view' that requires specifying the differential effects on parent and offspring fitness.
if costs to offspring exceed benefits for parents , then reproductive suppression will not be selectively advantageous.
the second reason is more fundamental than a choice of analytical approaches.
although helping often increases more rapidly with lowered relatedness in the gene-based model, positive kin assortment is still required.
even with five fathers, relatedness would not be random .
therefore, helpers can gain both direct fitness from inheriting their mother's position as reproducing adult and indirect fitness through assuring the survival of half and full sibs.
randomly redistributing helpers as if they were drifting to join nests creates a situation where the helpers have a mean expectation of r =  <dig> in terms of kin assortment to the present brood.
helping, therefore, can be selected only through direct fitness gains from future nest inheritance.
removing any potential for kin selection prevents helping from increasing in frequency .
thus, a gene-based approach is also a variation on hamilton's rule.
the basic principle remains unchanged: reproductive altruism evolves only when kin are sufficiently and differentially benefitted.
CONCLUSIONS
gene-based models may be superior to actor-based, kin selection models with variance in outcomes or when fitness consequences vary across interacting individuals.
thus more clearly than an inclusive fitness approach, the gene-based approach demonstrates that monogamy does not intrinsically create conditions predisposed for the evolution of helping.
gene-based approaches have also successfully modeled the evolution of genetic diversity through across-individual epistatic effects .
one must not, however, confuse the utility of a particular mathematical approach with the validity of the underlying evolutionary theory.
showing low relatedness is selectively advantageous to high relatedness is not equivalent to concluding that relatedness is unimportant.
actor-based models of kin selection have had a long and fruitful history of framing interesting evolutionary questions  <cit>  and will undoubtedly continue to be successful in explaining many features of life history.
kin selection theory is important because kinship mattered throughout evolutionary history.
the key point is that genetic relatedness and genetic diversity are inversely correlated and the evolutionary consequences of this correlation are what future modeling endeavors should aim to better understand.

 cooperatively breeding groups often have two defining characteristics: increased productivity over solitary individuals and differential within-group reproductive success or skew. one puzzling feature of reproductive inequality is that subordinate roles appear to be willingly accepted. kin selection is the dominant evolutionary paradigm for this apparent reproductive altruism. in groups of relatives, an individual reducing its reproduction can be favored if this sufficiently benefits genetic kin. increasingly, however, the relative importance of genetic relatedness for the evolution of reproductive skew is being questioned. if groups are sufficiently successful, then individual genetic differences creating within-group reproductive skew can be evolutionarily stable. alternatively, parental manipulation can bias offspring to assume otherwise reproductively disadvantageous roles. if such groups remain intact over generations of shared reproduction, then high relatedness may be a consequence and not a cause of cooperation. indeed, wilson and others argue kin selection acts more often as a'dissolutive' than a binding force within groups. the proposed alternatives to kin selection for reproductive skew have been challenged on both theoretical and empirical grounds. the importance of kin selection in the evolution of cooperative breeding is argued to be particularly evident in its taxonomic distribution with respect to mating strategy. by hamilton's rule, helping a relative is selectively favored when relatedness exceeds the cost/benefit ratio, or r >c/b. with monogamy, helping a parent rear full siblings is as valuable as rearing one's own offspring. therefore, any reduction in cost or increase in benefit favors helping. in contrast, polygamy in terms of multiple fathers produces half sibs and cooperation would require halving costs or doubling benefits. thus, kin selection predicts the evolution of cooperation ought to be most likely in species preadapted to maintain high relatedness between siblings. monogamy and high relatedness were first proposed to be critical in evolutionary transitions in social insects from cooperative breeding with totipotent individuals, to eusocial systems with morphological queen and worker castes. two recent phylogenetic analyses have extended the monogamy hypothesis to cooperative breeding, per se. monogamy or lower levels of promiscuity are the most likely ancestral state for evolutionary transitions from solitary to social living in hymenoptera and birds. conversely, lack of monogamy is hypothesized as evolutionarily constraining social degus from more elaborate sociality as exhibited by other group-living rodents such as naked mole rats. nowak et al. challenged the monogamy hypothesis for social hymenoptera on two grounds. specifically, the phylogenetic evidence is weak because the ancestral state of the majority of solitary hymenoptera species is likely to be monogamy. hence, monogamy as an evolutionary preadaptation is indistinguishable from ecological factors favoring cooperation, such as defending nests or sequentially provisioning offspring. more broadly, the entire approach of inclusive fitness modeling may be rife with simplifying assumptions that produce spurious predictions. rather than the actor-based approach of kin selection, nowak et al. advocated a gene-based approach. they derived general cases showing that r values alone may not always accurately predict the evolution of cooperation. however, they gave no example of a specific behavioral or life history phenomenon where a kin selection model gives an erroneous prediction relative to a gene-based model. the monogamy hypothesis is where kin selection possibly gets it wrong. if its basic premise of an inclusive fitness advantage to helping with high relatedness is correct, then the same result ought to occur when cooperation is modeled as the spread of a helping allele.  helping allele is dominant cooperation evolves under intermediate values of adult survival between offspring cohorts. if s is less than or for cohort sizes of or respectively, helping never predominates in the population. similarly, if s = such that mothers do not die between cohorts, there is no selective advantage to making or being a helper. with no maternal mortality, helping behavior does not invade the population in the model. under conditions that do favor helping, the monogamy hypothesis is not confirmed by a gene-based approach: helping does not consistently evolve more quickly with monogamy. under many conditions, the number of mates does not affect how rapidly helping spreads through the population. the gene-based modeling approach reveals the reason. any aa female mating with multiple males increases her chances of gaining a helper. however, helpers aid a relatively smaller fraction of sibs with a. these two probabilities approximately cancel out. from the helping allele perspective, single mating is a high variance strategy that pays off big, but rarely. multiple mating is a low variance strategy that works more often, but with reduced effect. there are associated advantages and disadvantages with mating strategy that are separate from differences in sibling relatedness. an advantage for single mating is that helpers aid both alleles equally. for example, all daughters from aa x a matings are aa. thus, the frequency of a in helpers equals the frequency of a in aided female siblings. in contrast, if aa females mate multiply with males of both genotypes, then the frequency of a is higher in helping females than in helped ones. although a can increase in the population due to across-group selection, it decreases in frequency within its own group. when inter-cohort survival is low, this cost to multiple mating results in helping evolving faster with monogamy. multiple mating has an advantage that if mothers die, subsequent benefits nonrandomly accrue to a alleles. only daughters having this allele can inherit nests. as inter-cohort survival increases, helping becomes more likely to evolve with polygamy and through groups of lower mean relatedness. interestingly, polygamy is favored over a wider range of values than monogamy. mating strategy is uniform across females within a population in the above results. however, when females are randomly assigned a number of mates within the same population, multiply-mated nests consistently produce more offspring relative to singly-mated nests across a wide range of s values. the difference is particularly evident when a is the rarer allele. only when a reaches high frequencies, such as 75% of the population, is nest productivity similar across mating strategies. when mating strategies are themselves genetically determined, alleles for higher mating frequency are favored. because polygamous nests produce more helping daughters, this in turn increases lifetime nest productivity and the potential transmission of alleles for multiple mating. this advantage disappears at higher frequencies of the helping allele because all mating strategies are likely to produce helpers. interestingly, with low survival values cooperation evolves much more rapidly in monogamous rather than polygamous populations, but polygamous nests are on average more productive within populations and multiple mating alleles are at a selective advantage when helping is not ubiquitous. therefore, the evolution of helping appears to always have the correlated effect of also favoring mating with multiple potential fathers. helping allele is recessive or males are diploid helping behavior evolves more slowly when a is recessive because the allele must initially drift under neutral selection until its frequency is high enough that aa daughters start being produced. apart from this, the results are broadly similar to when a is dominant. monogamy is favored when s is low, equal to polygamy when s is intermediate, and disfavored when s is high. also similar to when a is dominant, monogamous nests are, on average, less productive when a is rare in the population. recessive alleles differ in that multiple mating has the greatest relative selective advantage at intermediate frequencies of a. this is again likely due to helping rarely expressed at low frequencies of recessive a alleles. assuming diploid males has no qualitatively different effects on the results and conclusions. indirect fitness and multiple helpers when helpers randomly drift across nests, kin and non-kin are equally likely to benefit from survival insurance. in the absence of indirect fitness gains for biasing survival insurance towards kin, a does not increase in frequency beyond levels produced by mutation and genetic drift. across every simulation with all levels of adult survival, the a allele never reached a frequency of 50% or more in the population. allowing multiple helpers, each of which provides an identical increase in nest survivorship, does not result in helping spreading more rapidly with monogamy than polygamy. under conditions where a is dominant and offspring come in cohorts of five, the helping allele reaches a population frequency of 50%, on average, in, or generations with monogamy. in comparison, the helping allele reaches the 50% criterion in, and generations when females mate with two males. when mating with five males, the 50% criterion is attained in, and generations. thus across this range of comparison, the 50% criterion is reached in 39-79% of the number of generations required under monogamy. contrasted to the results with only one helper, polygamy is even more conducive to the spread of helping behavior when multiple helpers increase nest survival in an additive, linear fashion. discussion monogamous behavior on the part of females in mating with only one male does not appear to generally act as a spring-loaded preadaptation for the evolution of cooperative breeding. to the contrary, polygamy through polyandry is more likely to be particularly beneficial. although phylogenetic signals may correlate monogamy with eusociality and reproductive skew, such relationships are not prima facie support for kin selection theory. other shared life history traits apart from mating behavior must be reconsidered as predisposing factors for evolution of cooperative breeding. indeed, the more interesting message in the phylogenetic data may be how often social systems of low relatedness have evolved from high-relatedness ancestral species. for example, polyandry appears to have evolved independently from monoandry in clades of ants. groups of low relatedness are likely to have correlated benefits arising from increased group-level genetic diversity, and it appears these benefits often exceed the evolutionary advantages of high within-group relatedness. the contradiction of the monogamy hypothesis by a gene-based model supports criticism that inclusive fitness models are potentially inaccurate. there are two reasons, however, why these results do not contradict kin selection, per se. first, comparing rearing offspring versus rearing full or half sibs in deriving the monogamy hypothesis is overly simplistic. this fails to include a long chain of probabilities of outcomes. for example, the true fitness payoff for a daughter in helping must include: the probability of surviving her mother across each potential remaining offspring cohort; if she does survive her mother, the probability that she herself will recruit a helper; the subsequent probability that she will in turn be superseded by her daughter; etc. this value must be compared to a similarly extensive calculation of fitness for leaving. note also that this is from daughter's'point of view'. the payoffs would be different if asking whether the mother should manipulate a daughter into helping. thus a gene-based model might indeed predict the same result as a fully comprehensive inclusive fitness model. nevertheless, a gene-based approach is clearly a much simpler and more robust approach to this question. the stochastic simulations include every possible series of outcomes weighted by their probability of occurrence. none of these have to be calculated a priori. the model also has no'point of view' that requires specifying the differential effects on parent and offspring fitness. if costs to offspring exceed benefits for parents, then reproductive suppression will not be selectively advantageous. the second reason is more fundamental than a choice of analytical approaches. although helping often increases more rapidly with lowered relatedness in the gene-based model, positive kin assortment is still required. even with five fathers, relatedness would not be random. therefore, helpers can gain both direct fitness from inheriting their mother's position as reproducing adult and indirect fitness through assuring the survival of half and full sibs. randomly redistributing helpers as if they were drifting to join nests creates a situation where the helpers have a mean expectation of r = in terms of kin assortment to the present brood. helping, therefore, can be selected only through direct fitness gains from future nest inheritance. removing any potential for kin selection prevents helping from increasing in frequency. thus, a gene-based approach is also a variation on hamilton's rule. the basic principle remains unchanged: reproductive altruism evolves only when kin are sufficiently and differentially benefitted.  gene-based models may be superior to actor-based, kin selection models with variance in outcomes or when fitness consequences vary across interacting individuals. thus more clearly than an inclusive fitness approach, the gene-based approach demonstrates that monogamy does not intrinsically create conditions predisposed for the evolution of helping. gene-based approaches have also successfully modeled the evolution of genetic diversity through across-individual epistatic effects. one must not, however, confuse the utility of a particular mathematical approach with the validity of the underlying evolutionary theory. showing low relatedness is selectively advantageous to high relatedness is not equivalent to concluding that relatedness is unimportant. actor-based models of kin selection have had a long and fruitful history of framing interesting evolutionary questions and will undoubtedly continue to be successful in explaining many features of life history. kin selection theory is important because kinship mattered throughout evolutionary history. the key point is that genetic relatedness and genetic diversity are inversely correlated and the evolutionary consequences of this correlation are what future modeling endeavors should aim to better understand. 
the monogamy hypothesis may be the first case of such a flawed calculation. the key question, therefore, is not whether kin selection occurs, but how best to elucidate the differing evolutionary advantages of genetic relatedness versus genetic diversity. nevertheless, cooperation only evolves when benefits are provided for kin: helping alleles did not increase in frequency in the absence of potential gains in indirect fitness. examining this tradeoff showed that under a wide range of conditions polygamy, rather than monogamy, allowed helping to spread more rapidly through populations. because monogamy creates high-relatedness family groups, kin selection has been concluded to drive the evolution of cooperative breeding. although kin selection is criticized as inappropriate for modeling and predicting the evolution of cooperation, there are no examples where specific inclusive fitness-based predictions are intrinsically wrong.
 phylogenetic analyses strongly associate nonsocial ancestors of cooperatively-breeding or eusocial species with monogamy. because monogamy creates high-relatedness family groups, kin selection has been concluded to drive the evolution of cooperative breeding. although kin selection is criticized as inappropriate for modeling and predicting the evolution of cooperation, there are no examples where specific inclusive fitness-based predictions are intrinsically wrong. the monogamy hypothesis may be the first case of such a flawed calculation.  a simulation model mutated helping alleles into non-cooperative populations where females mated either once or multiply. although multiple mating produces sibling broods of lower relatedness, it also increases the likelihood that one offspring will adopt a helper role. examining this tradeoff showed that under a wide range of conditions polygamy, rather than monogamy, allowed helping to spread more rapidly through populations. further simulations with mating strategies as heritable traits confirmed that multiple-mating is selectively advantageous. although cooperation evolves similarly regardless of whether dependent young are close or more distant kin, it does not evolve if they are unrelated.  the solitary ancestral species to cooperative breeders may have been predominantly monogamous, but it cannot be concluded that monogamy is a predisposing state for the evolution of helping behavior. monogamy may simply be coincidental to other more important life history characteristics such as nest defense or sequential provisioning of offspring. the differing predictive outcome from a gene-based model also supports arguments that inclusive fitness formulations poorly model some evolutionary questions. nevertheless, cooperation only evolves when benefits are provided for kin: helping alleles did not increase in frequency in the absence of potential gains in indirect fitness. the key question, therefore, is not whether kin selection occurs, but how best to elucidate the differing evolutionary advantages of genetic relatedness versus genetic diversity. 