Current Biology 23, 2383–2387, December 2, 2013 ª2013 Elsevier Ltd All rights reserved http://dx.doi.org/10.1016/j.cub.2013.10.013 Report Ecology, Not the Genetics of Sex Determination, Determines Who Helps in Eusocial Populations
Laura Ross,1,2,* Andy Gardner,2,3,4 Nate Hardy,5 help. However, other authors have argued that Hamilton’s and Stuart A. West2 ‘‘haplodiploidy hypothesis’’ does not explain variation in the 1School of Biological Sciences, Institute of Evolutionary sex of the helper caste, because haplodiploidy also leads to Biology, University of Edinburgh, Edinburgh, EH9 3JT, UK females being less related to their full brothers (r = ¼) than to 2Department of Zoology, University of Oxford, their sons (r = ½; see the Supplemental Experimental Proce- South Parks Road, Oxford OX1 3PS, UK dures and Figure S3)[4–9]. 3Balliol College, University of Oxford, Broad Street, An alternative explanation for the variation in the sex ratio of Oxford OX1 3BJ, UK the workers across species is variation in the ecological factors 4School of Biology, University of St Andrews, Dyers Brae, that favored the evolution of eusociality [10]. If the main advan- St Andrews KY16 9TH, UK tage of having helpers is to provide care for the young, then we 5Department of Entomology and Plant Pathology, would expect the helpers to be drawn from the sex or sexes Auburn University, Auburn, AL 36849, USA that provided parental care in that species’ solitary ancestor, which is usually females [10, 20–27](Figure 2B). In contrast, if the main advantage of having helpers is to help defend the col- Summary ony and neither sex is preadapted to soldiering, then we would expect the helpers to be drawn equally from both sexes [10, 28, In eusocial species, the sex ratio of helpers varies from 29](Figure 2B). While this ecological explanation provides an female only, in taxa such as the social Hymenoptera (ants, alternative to Hamilton’s haplodiploidy hypothesis, it is fully bees, and wasps) [1], to an unbiased mixture of males and compatible with the theory of kin selection more generally. females, as in most termites [2]. Hamilton suggested that this difference owes to the haplodiploid genetics of the Genetics versus Ecology Hymenoptera leading to females being relatively more Here, we provide the first formal test of the two competing related to their siblings [3]. However, it has been argued hypotheses for which sex should help, with a comparative that Hamilton’s hypothesis does not work [4–9] and that study across all sexual (i.e., nonparthenogenetic) eusocial the sex of helpers could instead be explained by variation taxa. We start by considering all taxa that fit Wilson’s [1] broader in the ecological factors that favor eusociality [10]. Here we definition of eusociality, with cooperative care of young, repro- test these two competing hypotheses, which focus on the ductive division of labor, and overlapping generations (Fig- possible importance of different terms in Hamilton’s rule ure 3). We utilized published DNA sequences to construct a [2, 11], with a comparative study across all sexual eusocial phylogeny of these taxa (Figures 3 and S1). We collected data taxa. We find that the sex ratio of helpers (1) shows no signif- on the helper sex ratio of representative species within each icant correlation with whether species are haplodiploid or origin of eusociality from published sources (see Table S2 for diploid and (2) shows a strong correlation with the ecolog- data and references) and classified the sex ratio of each species ical factor that had favored eusociality. Specifically, when as factor with two levels, either female biased or unbiased (Fig- the role of helpers is to defend the nest, both males and ure 3). No species have a strong male biased helper sex ratio. females help, whereas when the role of helpers is to pro- We found, with a phylogeny based mixed model [30], that vide brood care, then helpers are the sex or sexes that pro- the genetics of sex determination is not significantly correlated vided parental care ancestrally. More generally, our results with the sex ratio of the helpers (pmcmc = 0. 416; Figures 3 and 4 confirm the ability of kin selection theory to explain the and Table S4). Considering haplodiploid species, the Hyme- biology of eusocial species, independently of ploidy, and noptera and haplodiploid ambrosia beetles have predomi- add support to the idea that haplodiploidy has been more nantly female helpers, but the thrips have a mixture of male important for shaping conflicts within eusocial societies and female helpers (Figure 3). Considering the diploid species, than for explaining its origins [6, 12–19]. the termites, sponge-dwelling shrimps, and mole rats have relatively unbiased helper sex ratios, but the spiders and Results and Discussion diploid ambrosia beetles have predominantly female helpers (Figure 3). Hamilton [3] argued that the genetics of sex determination In contrast, we found that the ecological advantage of social explained variation across eusocial species in the sex ratio living is strongly correlated with the sex ratio of the helpers of the helper castes (Figures 1 and 2A and Figure S2 available (pmcmc = 0.001; Figures 3 and 4 and Table S4). For each of online). In haplodiploid species, such as the social Hymenop- the species included, we determined whether the role of tera, females are more related to their full sisters (life-for-life helpers is either defense only (soldiers) or also includes brood 3 care (workers). In cases where helpers provide brood care, we r = /4 ) than to their own daughters (r = ½), and Hamilton sug- gested that this predisposes females to helping. In contrast, in then determined whether this has evolved from species where diploid species, such as termites, individuals are as related to brood care was either maternal or biparental (Table S2). In all their full siblings as they are to their own offspring, indepen- species where the primary function of helpers is brood care dently of sex, and so both sexes are under equal selection to and care was ancestrally provided by mothers—ambrosia beetles, Hymenoptera, and spiders—the helpers are exclu- sively female. In all other species, where either brood care *Correspondence: [email protected] evolved from biparental care or the primary function of helpers Current Biology Vol 23 No 23 2384
Figure 1. Helper Sex Ratios in Eusocial Societies Some species have an equal number of male and female helpers, such as in (A) the thrips Klado- thrips intermedius (picture by Holly Caravan) and (B) the termite Macrotermes gilvus (picture by Mitsuhiko Imamori). Other species only have female helpers, such as in (C) the ant Leptomyr- mex darlingtoni (picture by Alexander Wild) and (D) the spider Anelosimus eximius (picture by Ken Preston-Mafham).
Conclusions We have provided clear support for the hypothesis that the sex of the helping caste in eusocial species is driven by ecology and not the genetics of sex determination. Why would the genetics of sex determination not matter from a kin selection perspective? While females in monogamous haplodiploid populations are more related to their sisters than to their daughters, they are is colony defense—thrips, termites, sponge-dwelling shrimps, less related to their brothers than to their sons. Overall, these and mole rats—the helpers are a relatively unbiased mixture of factors exactly cancel, so that female helpers are equally males and females. related, on average, to their siblings and their offspring [4–9] We obtained the same results when we repeated our ana- (Supplemental Experimental Procedures). Similarly, while lyses based on the taxa that fit Crespi and Yanega’s [3, 29] males in haplodiploid populations are less related to their sis- and Boomsma’s [16, 18, 19] more strict definition of eusoci- ters than they are to their mate’s daughters, they are more ality. These researchers restrict eusociality to cases in which related to their brothers than they are to their mate’s sons. some or all individuals become irreversibly fixed into castes, Again, this cancels, so that male helpers are equally related, prior to reproductive maturity [16, 18, 19, 29, 31–35]. This ex- on average, to their siblings and their mate’s offspring [4–9] cludes the mole rats, the sponge-dwelling shrimp, and one (Supplemental Experimental Procedures). Consequently, hap- of the ambrosia beetles. Without these taxa, we still found lodiploidy does not, by itself, predispose either sex to altruistic that the genetics of sex determination showed no correlation helping. Haplodiploidy could still matter, if helping was corre- with the sex of helpers (pmcmc = 0.504), whereas the ecological lated with sex ratio variation across colonies, but the empirical advantage of group living did (pmcmc < 0.001; Table S5). The data suggest that this is not common [13–16]. More generally, same pattern holds when we further restrict our analyses to this adds to the growing theoretical and empirical literature the obligate eusocial species, where the breeding and helper that suggests that the major role of haplodiploidy-mediated castes are mutually dependent and helpers provide brood relatedness asymmetries has been to shape conflicts in exist- care [18, 19, 29]: the Hymenoptera evolved female helpers ing eusocial societies, such as over the sex ratio and who pro- from ancestral maternal care, while the higher termites evolved duces males, rather than the evolution of cooperation itself mixed-sex helpers from ancestral biparental care. However, [12–19]. these transitions to obligate eusociality have occurred too infrequently for a useful formal comparative analysis. Taken Experimental Procedures together, these results suggest that ecology is more important than the genetics of sex determination in shaping the sex ratio Data Collection of helpers, however eusociality is defined. The importance of The number of times that eusociality has evolved depends upon how it is ecology in at least some Hymenoptera is further supported defined. Following Wilson’s [1] definition, eusociality has evolved in five orders of insects [2, 16, 32, 35, 42], one order of crustaceans [34], one order by recent experiments and gene expression studies [26, 36], of spiders [43], and one order of mammals [44]. In most cases, multiple which suggest that the nursing behavior of workers in bees transitions have taken place within an order. Figure 2 shows the number and wasps evolved directly from maternal care, which came of independent transitions in each of these orders (based on the published to be directed toward siblings rather than offspring. literature; see Table S2 for references), as well the hypothetical evolutionary We have focused on the helper sex ratios and not whether, in relationship between the orders where eusociality occurs (based on our species with helpers of both sexes, there is sex-specific divi- phylogenetic reconstruction described below). Following Crespi and Yanega’s [29] and Boomsma’s [18] definitions, eusociality is restricted to sion of labor. There are too few data at present for a formal the Arthropods and has evolved only in the Hymenoptera, Thysanoptera, analysis of division of labor. Among the termites, where the Araneae (only according to Crespi and Yanega), Isoptera, and Coleoptera. best data are available, it appears that some differences can We collected data from the literature on representative species for each be explained by ecological factors. For example, in those origin of eusociality. These data included (1) helper sex ratio (including termites where females are more involved in defensive tasks both ‘‘soldiers’’ and ‘‘workers’’) with ‘‘unbiased’’ and ‘‘female only’’ as the [37–40], they are often larger, and hence better suited to two levels (as few taxa display male biased helper sex ratios), (2) the type of help (defense, brood care, or both, where we define brood care by the defend the nest [39]. However, in other termite species, sex- presence of direct provisioning of the young, or related behaviors such as linked genes have been shown to be involved in caste determi- cleaning the larva), and (3) genetic system (haplodiploidy versus diploidy) nation and helper behavior [41]. for all obligate and facultative eusocial taxa. Helper Sex in Eusocial Populations 2385
Figure 2. Competing Hypotheses for Who Helps (A) The haplodiploidy hypothesis suggests that, in haplodiploid species, a higher relatedness between sisters (r = 0.75, life-for-life relatedness) favors female helpers. In contrast, in diploid species, there is no relatedness asymmetry, and so both sexes are equally favored to help. This hypothesis focuses on the possible importance of variation in the relatedness (r) term in Hamil- ton’s rule [3, 11]. (B) The ecology and ancestral care hypothesis suggests that the sex of helpers depends upon the ecological (economic) benefit of cooperation and eusociality. Specifically, either the coopera- tive rearing of brood when there is a significant chance that the parent will die before parental care is completed (life insurance) or living in a defendable food resource (fortress defense) [10]. If helpers rear brood, then we would expect the helpers to be drawn from the sex or sexes that provided parental care in the ancestral soli- tary species, which is usually females. In contrast, if helpers defend the colony, and neither sex is preadapted to be a soldier, then we would expect the helpers to be drawn from both sexes. This hypothesis focuses on the possible importance of variation in the benefit (b) and cost (c) terms in Hamilton’s rule [3, 11]. See also Figure S3 and Table S6.
We analyzed the sex ratio as a dichotomous variable with a single data species for which phylogenetic data were available (see below) within point per origin of eusociality, because the continuous estimates of the that origin (we use a single data point per origin, when the traits con- helper sex ratio in the literature are both relatively rare and tend to be biased. sidered do not differ between closely related species). We recon- Specifically, researchers tend to report when sex ratios are biased away structed the most likely ancestral type of parental care by collecting data from equality or only one sex, and not when they are these more usual from the closest noneusocial sister groups, where sister groups were values. For example, in termites, there are many estimates of biased helper assigned by studying recent molecular phylogenies of the relevant taxo- sex ratios (Table S3), while in fact most termites are unbiased [2, 45]. We nomic groups. included the assignment for each origin with their references in the Supple- We excluded three taxa, classified as facultatively eusocial by Crespi and mental Information (Table S2). We also give more detail on the way the data Yanega [29], from our analysis. These are (1) aphids, where the soldiers are were collected, as well as a table with raw data, in the Supplemental Exper- produced parthenogenetically and thus are female by default; (2) polyem- imental Procedures and Table S3. bryonic wasps, where the role of the soldiers is between sex sibling conflict Most traits were not variable between species within an origin—in those [46]; and (3) parasitic Trematodes, as both soldiers as well as reproductives cases, the data in Table S2 represent a randomly selected representative are clones of one diploid larva [47].
Figure 3. The Helping Sex The figure shows a schematic cladogram of the taxa included in our analysis. Open circles and filled squares represent diploid versus haplodi- Mole rats Spiders Shrimp Termites Thrips Hymenoptera Beetles ploid taxa, respectively, while the number within each square/circle shows the number of 2 1 3 12 2 9 1 1 independent origins of eusociality (according to Wilson’s [1] definition of eusociality) within each clade. The color of the icon represents the sex ra- tio of workers—half blue, half pink for unbiased and pink for female only. See also Figure S1 and Tables S1–S3.
Diploidy Haplodiploidy N Number of origins Defense Brood care (maternal origin) Brood care (biparental origin) Current Biology Vol 23 No 23 2386
1.0 nonindependence between origins by using the reconstructed molecular Diplodiploidy phylogeny describe above. In order to correct for uncertainty in the phylo- genetic reconstruction, we marginalized over the posterior distribution of 0.8 Haplodiploidy trees [30] by sampling a tree from the posterior at iteration t, running the MCMC comparative analysis for 1,000 iterations, and saving the last 0.6 MCMC sample. The values of the latent variables and variance components were passed as starting values to the analysis at iteration t + 1 for which a 0.4 new tree from the posterior sample was taken. The process was repeated for 1,300 iterations (i.e., t = 1,300), where we disposed of the first 300 runs as burn-in. We used a mixed model with a binary error structure with helper 0.2 sex ratio as the response variable (‘‘unbiased’’ and ‘‘female biased’’). As pre- dictors, we included genetic system (haplodiploidy versus diploidy) and the assumed ‘‘route towards eusociality’’: brood care (either evolved from
Probability of only helpers female 0.0 maternal care or from biparental care) or defense. We used a weakly infor- mative Gelman prior [60, 61] for the fixed effects, an inverse Wishart prior for
Defense random effects, and fixed the residual variance to 1 (as this cannot be Brood care Brood care estimated from binary data). We provided our R code (including the prior (maternal) (biparental) specification) in the Supplemental Experimental Procedures. We report
the significance of our fixed effects in terms of pMCMC, which is twice the posterior probability that the estimate is negative or positive (whichever Figure 4. Helper Sex Ratios probability is smallest). This value can be interpreted as a Bayesian equiva- The probability of having female only helpers, as opposed to an unbiased lent to the traditional p value [30, 61] mixture of males and females (where 0 represents an unbiased helper sex ratio), for haploidiploid and diploid taxa in the different ecological scenarios. Predicted values are derived from the binary phylogenetic mixed model and Supplemental Information were generated using the ‘‘predict’’ function in the R package MCMCglmm. Error bars represent 95% confidence intervals. The probability of female- Supplemental Information includes Supplemental Experimental Proce- biased helpers does not depend on genetic system but differs strongly be- dures, three figures, and six tables and can be found with this article online tween the different role of helpers: brood care derived from maternal care at http://dx.doi.org/10.1016/j.cub.2013.10.013. leads to female biased helpers, while brood care derived from biparental care and colony defense leads to an unbiased mixture of male and female Acknowledgments helpers. See also Figures S1 and S2 and Tables S1–S5. We would like to thank Jarrod Hadfield for his help with the analysis, three anonymous reviewers for their comments, and the ERC, the Royal Society, Phylogenetic Reconstruction and Balliol College for funding. We estimated phylogenetic relationships among eusocial lineages to con- trol for nonindependence caused by shared ancestry in the comparative analysis. 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Ecology, Not the Genetics of Sex Determination, Determines
Who Helps in Eusocial Populations Laura Ross, Andy Gardner, Nate Hardy, and Stuart A. West
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Lasioglossum
Halictus
Augochlorella
Allodape
Melipona
Vespula
Liostenogaster
Formica
Austroplatypus
Xyleborinus
Oncothrips_tepperi
Oncothrips_habrus
Oncothrips_waterhousei
Oncothrips_morrisi
Kladothrips_hamiltoni
Kladothrips_harpophyllae
Zootermopsis
Hodotermes
Macrotermes
Mastotermes
Reticulitermes
Prorhinotermes
Cryptotermes
Synalpheus_chacei
Synalpheus_regalis
Anelosimus
Heterocephalus
Fukomys
40.0
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! @J993'*',&+3!6K9'()*',&+3!#($8'1J('%L! ! F%%)I,*',&!$7!D'39'(!%'K!(+&)$!+,1!D'39'(!&+%M! ! )+$#+,(-+.(,*/"%( J9!0&9&2#%F!<&!6-9,/=&2!+;&!;&%7&2!,&>!2#+/-!.&4#%&!-9%5!/.!4-2&!+;#9!KGM!-.!;&%7&2,!#2&! .&4#%&!A,&>!2#+/-!-.!G:HE!-2!/.!4#%&,!;#8&!9&8&2!$&&9!-$,&28&=!7&2.-24/90!6--7&2#+/8&! $&;#8/-12,:!J9!,-4&!,7&6/&,F!+;&2&!#2&!-9%5!6-%-95O%&8&%!&,+/4#+&,!-.!+;&!,&>!2#+/-F!/9!<;/6;! 6#,&!<&!1,&!+;&,&!&,+/4#+&,:!J9!,-4&!+#>#F!$-+;!<-2Z&2!#9=!2&72-=16+/8&,!,&>!2#+/-,!#2&! ;/0;%5!,Z&<&=F!/9!<;/6;!6#,&!<&!#,,/09!.&4#%&O$/#,&=!;&%7/90!-9%5!<;&9!+;&!,&>!2#+/-!-.! +;&!;&%7&2,!/,!4-2&!.&4#%&O$/#,&=!+;#9!+;#+!-.!+;&!2&72-=16+/8&,:!";&!-9%5!&>6&7+/-9!+-! +;&,&!21%&,!#2&!.-2!=&+&24/9/90!+;&!#,,/094&9+,!.-2!+;&!+;2/7,!#9=!+;&!+&24/+&,:!'-%=/&2!,&>! 2#+/-!/9!$-+;!02-17,!#77,!+-!$&!8#2/#$%&F!5&+!/9!$-+;!6#,&,!+;/,!8#2/#+/-9!;#,!#77&=! #.+&2!+;&!-2/0/9!-.!&1,-6/#%/+5:!J9!+;2/7,!4#%&!,-%=/&2!#2&!72&,&9+!/9!#%%!,7&6/&,!,+1=/&=!$1+! +;&!,&>!2#+/-!-.!,-%=/&2,!/,!$/#,&=!A/9!6-47#2/,-9!+-!+;&!2&72-=16+/8&,E!/9!#!.&#!#9=!6#9!$&! 19=&2,+--=!/9!+&24,!-.!<-2Z&2!2&72-=16+/-9!#9=!%-6#%!4#+&!6-47&+/+/-9!X'HQF!'QGF!'QQF! '(TY:!a/Z&!2#+/-!#,!19$/#,&=:! ! )+$#+,(/*-0( b&%7&2,!/9!&1,-6/#%!,-6/&+/&,!-.+&9!&90#0&!/9!$-+;!$2--=6#2&!#9=!=&.&9,&:!b-<&8&2!+;&! /47-2+#96&!-.!+;&,&!+<-!+57&,!-.!$&;#8/-12,!#+!+;&!-2/0/9!-.!&1,-6/#%/+5!=/..&2!A2&.&22&=!+-! #,!.-2+2&,,!=&.&9,&!8,:!%/.&!/9,12#96&F!I2&,7/F!c1&%%&2E:!3-2!&>#47%&!,-%=/&2,!#77&=!#+!+;&! -2/0/9!-.!&1,-6/#%/+5!/9!+;2/7,!#9=!+&24/+&,F!#9=!72/4/+/8&!+&24/+&,!#9=!+;2/7,!=-!9-+!=/,7#5! #%%-7#2&9+#%!$2--=6#2&F!<;/%&!#%%!&1,-6/#%!b54&9-7+&2#!72-8/=&!,-4&!.-24!-.!#%%-7#2&9+#%! 6#2&:!@&!&>7&6+!#%%-7#2&9+#%!6#2&!+-!$&!,&>O%/9Z&=!/.!+;&2&!/,!#!72&O&>/,+/90!$/#,!+-<#2=! 4#+&29#%!6#2&F!<;/%&!<&!=-!9-+!&>7&6+!,16;!$/#,!.-2!=&.&9,/8&!+#,Z,:!@&!;#8&!+;&2&.-2&! =/8/=&=!+;&!&1,-6/#%!+#>#!/9!+;-,&!+;#+!HE!1+2+,!72-8/=&!$2--=6#2&!#9=!+;-,&!+;#+!NE!&%! 72-8/=&!,-4&!.-24!-.!$2--=6#2&!A&8-%8/90!&/+;&2!.2-4!4#+&29#%!-2!7#+&29#%!6#2&E:!!@&! 2&6-09/d&!+;2&&!=/..&2&9+!$&;#8/-2,!#,!#%%-7#2&9+#%!6#2&)!AHE!=/2&6+!72-8/,/-9/90!-.!+;&! 5-190e!ANE!6#2&!.-2!+;&!&00,e!#9=!AQE!+2#9,7-2+!-.!&00,!#9=!5-190:!@&!/9=/6#+&!+;&!72&,&96&! -.!+;&,&!$&;#8/-12,!/9!+#$%&!'Q! ! !
! E!0$1'!+,1!9()$(!J%'1!7$(!&D'!+,+34%)%!),!&D'!:0:0I3**!9+8M+I'!X'((Y!
library(MCMCglmm)
eus<-read.table("/Users/lauraross/ eusoc_analysis_dataframe.txt",header=T) tree1300.eus <- read.tree("/Users/lauraross/ eusocial_1300.trees")
INtree.eus<- inverseA(tree1300.eus[[1]], nodes="TIPS")
gelmanprior<-list(B=list(mu=c(0,0,0,0),V=gelman.prior(~ecology+genetic.sys, data=eus, scale=1+1+pi^2/3)), R=list(V=1,fix=1),G=list(G1=list(V=diag(1)*0.1, nu=1)))
mphylMCMC.start<-MCMCglmm(helper.sex~ecology+genetic.sys, random=~animal, data=eus, ginverse=list(animal=INtree.eus$Ainv), family="categorical", prior=gelmanprior, pl=TRUE,slice=TRUE, nitt=1000, thin=1, burnin=0)
mphylMCMC<-mphylMCMC.start
for(i in 1:1300){
INtree.eus<- inverseA(tree1300.eus[[i]],nodes="TIPS")
start<-list(Liab=mphylMCMC$Liab[1,], R=1, G=list(G1=mphylMCMC$VCV[1,1]))
mphylMCMC<-MCMCglmm(helper.sex~ecology+genetic.sys, random=~animal, data=eus, family="categorical", prior=gelmanprior, ginverse=list(animal=INtree.eus$Ainv), pl=TRUE,slice=TRUE, nitt=1000, thin=1, burnin=999, start=start, verbose=FALSE)
if(i>300){ mphylMCMC.start$VCV[i-300,]<-mphylMCMC$VCV[1,] mphylMCMC.start$Sol[i-300,]<-mphylMCMC$Sol[1,] mphylMCMC.start$Liab[i-300,]<-mphylMCMC$Liab[1,] }
print(i) } summary(mphylMCMC.start) hist(mphylMCMC.start$Liab) hist(mphylMCMC.start$VCV[,1]/(rowSums(mphylMCMC.start$VCV)+pi^2/3)) mean(mphylMCMC.start$VCV[,1]/(rowSums(mphylMCMC.start$VCV)+pi^2/3)) HPDinterval(mphylMCMC.start$VCV[,1]/(rowSums(mphylMCMC.start$VCV)+pi^2/3)) write.table(predict(mphylMCMC.start, interval = "confidence"),"/Users/lauraross/ eusoc_analysis_predictions.csv",sep = ",") !
F,+34%)%!,$&'%L!@&!4#20/9#%/d&=!-8&2!+;&!7-,+&2/-2!=/,+2/$1+/-9!-.!+2&&,!$5!,#47%/90!#!+2&&!.2-4! +;&!7-,+&2/-2!#+!/+&2#+/-9!+F!2199/90!+;&!`I`I!6-47#2#+/8&!#9#%5,/,!.-2!HGGG!/+&2#+/-9,!#9=!,#8/90!
! +;&!%#,+!`I`I!,#47%&:!";&!8#%1&,!-.!+;&!%#+&9+!8#2/#$%&,!#9=!8#2/#96&!6-47-9&9+,!<&2&!7#,,&=!#,! ,+#2+/90!8#%1&,!+-!+;&!#9#%5,/,!#+!/+&2#+/-9!+fH!.-2!<;/6;!#!9&7%-/+!#%0-2/+;4,!.-2!,-%8/90!,7#2,& %/9!,5,+&4,!2#+;&2!+;#9!#!9&6&,,/+5!.-2!8#%/=!/9.&2&96&F! <&!2#9!4-=&%,!/9!<;/6;!+;&!7#2#4&+&2!,7#6&!<#,!9-+!#104&9+&=!+#9+!+#>#!<;/6;!6-1%=!$&!=&./9&=!6-9,/,+&9+%5!$&+<&&9! +2&&,:!!3-2!%#20&!7;5%-0&9/&,!+;/,!4#5!72-8&!+-!$&!+--!,%- ! ?D'$(4L!ND4!1$'%,O&!&D'!I','&)8%!$7!%'K!1'&'(*),+&)$,!*+&&'(P! ! J96%1,/8&!./+9&,,!/,!0#/9&=!$5!,&9=/90!6-7/&,!-.!-9&D,!0&9&,!/9+-!.1+12&!0&9&2#+/-9,:!b&96&F! #9!#6+-2!8#%1&,!#!2&6/7/&9+!#66-2=/90!+-!;-+&9+!+-!<;/6;!+;&!#6+-2!#9=!2&6/7/&9+!,;#2&!0&9&,!/9!6-44-9e! #9=!+;&!2&6/7/&9+D,!2&72-=16+/8&!8#%1&!A2EF!/:&:!+;&!&>+&9+!+-!<;/6;!+;&5!+2#9,4/+!+;&/2!-<9! 0&9&,!+-!.1+12&!0&9&2#+/-9,!X'(ROLGY:!";&!6-9,#901/9/+/&,!.-2!=/7%-/=!#9=!;#7%-=/7%-/=! .#4/%5!4&4$&2,!#2&!,144#2/d&=!/9!"#$%&!'T:!";&!2&72-=16+/8&!8#%1&,!#2&!2! = H_AHO3E!.-2! .&4#%&,!#9=!2" = H_3!.-2!4#%&,!19=&2!=/7%-/=5F!#9=!2! = N_AHO3E!.-2!.&4#%&,!#9=!2" = H_3! .-2!4#%&,!19=&2!;#7%-=/7%-/=5F!<;&2&!3!/,!+;&!7-71%#+/-9!,&>!2#+/-!A72-7-2+/-9!4#%&E:!! ! ";1,F!/9!#!=/7%-/=!7-71%#+/-9F!#!.&4#%&!<;-!2#/,&,!4!&>+2#!,/$%/90,!#+!#!6-,+!-.!5!+-!;&2!-<9! 2&72-=16+/-9!/962&#,&,!;&2!/96%1,/8&!./+9&,,!$5!#9!#4-19+!4!!!A3!!!#^2-i! !!2" f!AHO3E!!!#'/,i! !!2!E![!5!!!A3!!!#'-9i! !!2" f!AHO3E!!!#]#1i! !!2!EF!<;/6;!/,!7-,/+/8&!/.!5_4!\!j:!3-2!#!4#%&F!+;&! 6#%61%#+/-9!/,(4!!!A3!!!#^2-i" !!2" f!AHO3E!!!#'/,i" !!2!E![!5!!!A3!!!#'-9i" !!2" f!AHO3E!!!#]#1i" !! 2!EF!<;/6;!/,!#%,-!7-,/+/8&!/.!5_4!\!j:!J9!#!;#7%-=/7%-/=!7-71%#+/-9F!+;&!6#%61%#+/-9!.-2!#! .&4#%&!/,!4!!!A3!!!#^2-i! !!2" f!AHO3E!!!#'/,i! !!2!E![!5!!!A3!!!#'-9i! !!2" f!AHO3E!!!#]#1i! !!2!EF! 5/&%=/90!&>#6+%5!+;&!,#4&!6-9=/+/-9!5_4!\!j:!?9=!.-2!#!4#%&!+;&!6#%61%#+/-9!/,!4!!!A3!!!#^2-i" !!2" f!AHO3E!!!#'/,i" !!2!E![!5!!!A3!!!#'-9i" !!2" f!AHO3E!!!#]#1i" !!2!EF!<;/6;!#%,-!5/&%=,!+;&! 6-9=/+/-9!5_4!\!j:!Hence, the genetics of sex determination neither predisposes haplodiploid versus diploids to eusociality nor predisposes females versus males to altruistic helping in haplodiploid societies X'HF!'LHOLLY.! ! ";&!#$-8&!#2014&9+!;#,!$&&9!.2#4&=!/9!+&24,!-.!6-9,#901/9/+5!#9=!2&72-=16+/8&!8#%1&:! b-<&8&2F!+;&!6-96&7+!-.!%/.&O.-2O%/.&!2&%#+&=9&,,F!<;/6;!6-4$/9&,!+;&,&!B1#9+/+/&,!/9+-!#! ,/90%&!4&#,12&!-.!8#%1&F!/,!4-2&!6-44-9%5!&96-19+&2&=!/9!+;&!,-6/#%!/9,&6+!%/+&2#+12&:!a/.&O .-2O%/.&!2&%#+&=9&,,&,!#2&!2&6-8&2&=!$5!41%+/7%5/90!+;&!6-9,#901/9/+5!-.!#6+-2!#9=!2&6/7/&9+! $5!+;&!2&6/7/&9+D,!2&72-=16+/8&!8#%1&F!#9=!=/8/=/90!$5!+;&!72-=16+!-.!+;&!#6+-2D,! 6-9,#901/9/+5!+-!,&%.!#9=!+;&!#6+-2D,!-<9!2&72-=16+/8&!8#%1&:!3-2!&>#47%&F!+;/,!2&6-8&2,!+;&! .#4/%/#2!k!2&%#+&=9&,,!$&+<&&9!;#7%-=/7%-/=!,/,+&2,)!6'/,i!!g!A#'/,i! ! v!)/A#'&%i! ! v!) = #. Assuming an even sex ratio, the other consanguinities are: 6^2-i!!g!lF!6]#1i!!g!jF!6'-9i!!g!jF! 6'/,i"!g!jF!6^2-i"!g!jF!6]#1i"!g!HF!6'-9i"!g!G!19=&2!;#7%-=/7%-/=5e!#9=!6'/,i!!g!6^2-i!!g!6]#1i!!g! 6'-9i!!g!6'/,i"!g!6^2-i"!g!6]#1i"!g!6'-9i"!g!j!19=&2!=/7%-/=5:!";&!6-9,&B1&9+!&B1#%!8#%1#+/-9! -.!,/$%/90,!#9=!-..,72/90!19=&2!$-+;!0&9&+/6!4-=&,!/,!/%%1,+2#+&=!/9!3/012&!'QF!#9=!+;&!#$-8&! #2014&9+!.2#4&=!/9!+&24,!-.!6-9,#901/9/+5!#9=!2&72-=16+/8&!8#%1&!2&8&#%,!+;#+!+;/,!2&,1%+! 6-9+/91&,!+-!;-%=!&8&9!<;&9!,&>!2#+/-,!#2&!$/#,&=:!!!!!!!!!! ! ! ! ! ! ! ! ! ! ! @J993'*',&+3!E'7'(',8'%L! ! 'H:! "2/8&2,F!*:!a:F!#9=!b#2&F!b:!AHKPTE:!b#7%-/=7%-/=5!#9=!+;&!&8-%1+/-9!-.!+;&!,-6/#%! /9,&6+,:!'6/&96&!787F!N(K[NTQ:! 'N:! b10;&,F!@:!m:!b:F!m%=2-5=F!^:!C:F!^&&Z4#9F!`:F!#9=!*#+9/&Z,F!3:!a:!@:!ANGGRE:!?96&,+2#%! `-9-0#45!';-<,!n/9!'&%&6+/-9!J,!n&5!+-!+;&!o8-%1+/-9!-.!o1,-6/#%/+5:!'6/&96&!9:;F! HNHQ[HNHT:! 'Q:! bp%%=-$%&2F!^:F!#9=!@/%,-9F!o:!m:!AHKKGE:!";&!#9+,!AI#4$2/=0&F!`#,,#6;1,&++,)! ^&%Z9#7!C2&,,E:! '(:! "-+;F!?:!a:F!q#2#%#F!n:F!r&<4#9F!":!I:F!`/01&dF!3:!o:F!b1+6;/,-9F!':!n:F!@/%%-10;$5F!]:!?:F! '/4-9,F!s:!3:F!o0;-%4F!`:F!b19+F!s:!b:F!b1=,-9F!`:!o:F!&+!#%:!ANGGPE:!@#,7!h&9&! o>72&,,/-9!'177-2+,!#9!o8-%1+/-9#25!a/9Z!^&+<&&9!`#+&29#%!^&;#8/-2!#9=! o1,-6/#%/+5:!'6/&96&!97 'L:! ?4=#4F!h:!q:F!I,-9=&,F!?:F!3-9=2ZF!`:!n:F!#9=!C#0&F!*:!o:!ANGGTE:!I-47%&>!,-6/#%! $&;#8/-12!=&2/8&=!.2-4!4#+&29#%!2&72-=16+/8&!+2#/+,:!r#+12&!=98F!PT[PR:! 'T:! sc&F!*:!a:!AHKRGE:!o8-%1+/-9!-.!,-6/#%!$&;#8/-2!/9!+;&!q&,7/=#&:!?991:!*&8:! o9+-4-%:!:>F!QPH[QKT:! 'P:! *&&8&F!b:!n:!AHKKQE:!b#7%-=/7%-/=5F!o1,-6/#%/+5!#9=!?$,&96&!-.!`#%&!C#2&9+#%!#9=! ?%%-7#2&9+#%!I#2&!/9!b54&9-7+&2#)!?!t9/.5/90!h&9&+/6!b57-+;&,/,!]/,+/96+!.2-4!n/9! '&%&6+/-9!";&-25:!C;/%-,!"!*-5!'-6!^!9=:F!QQL[QLN:! 'R:! 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