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What is the relatedness of sisters in a haplodiploid system if you mate virgin queens with 1 of their sons

What is the relatedness of sisters in a haplodiploid system if you mate virgin queens with 1 of their sons



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So I'm having trouble wrapping my head around this. In haplodiploid insects, sisters are related by 75% on average due to all sharing 100% of dad's genetics and 1/2 of mom's. (males are produced from haploid eggs)

The question I have is, if you take a son of a queen and mate her with her own son, what is the genetic relatedness of her resulting daughters to one another?

Here is an illustration of the haplodiploid system in insects.

Thanks in advance!

source: https://en.wikipedia.org/wiki/Haplodiploidy


This question may not be duplicate but I would reconmmend reading the answers of this question first How to calculate relatedness in haplodiploid organisms (mainly full sisters and full brothers)?

I think an image is worth a lot of words so here it is:

To calcul relatedness, I used the formula $ ext{relatedness} = ce{prop_{mother}} imes ce{shared_{mother}} + ce{prop_{father}} imes ce{shared_{father}}$

The little trick here is that we know the father (son of queen) is unique, so we can focus on either of the two possible son of the queen. This gives us a 0.875 relatedness between sisters with a father being the son of the mother. I hope it is clearer now.


Would society be different if humans used Haplodiploid-like sex-determination system? [closed]

Want to improve this question? Update the question so it focuses on one problem only by editing this post.

I'm interested what would be the effects on human society if human sex determination system is different, while everything else is the same thus we still have both men and women.

In particular what if humans used Haplodiploid-like system, similar to ants & bees, where female gender (woman) develops from sperm and egg, while woman could produce sons via something like Parthenogenesis, if she decides to get pregnant.

Please note that ALL women & men are capable of reproduction, no hive/colony Queens ruling over infertile workers.

Edit Would there be any effects on the gender ratio? Would the sisters who share 3/4 of genes & brothers who share

100% of genes be more cooperative with each other and less cooperative with outsiders?


Evolution final exam

______ - Walked upright - Foramen magnum located further forward than in apes. They had a small brain (slightly smaller than a chimpanzee's), a sloping face with very prominent browridges, elongated skull and small canine teeth.

______ - They were approximately the size of a chimpanzee, had small teeth with thick enamel (similar to modern humans). The most important fossil is an upper femur, showing evidence of bone buildup typical of a biped.

______- Closest extinct human relative, 400-40 kya. They had a large middle part of the face, and a large nose for humidifying and warming cold, dry air. Shorter and stockier bodies than H. sapiens, but brains were as large as ours and often larger. They made and used a diverse set of sophisticated tools, controlled fire, lived in shelters, made and wore clothing, were skilled hunters of large animals, ate plant foods, and occasionally made symbolic or ornamental objects. They deliberately buried their dead and marked graves with offerings (e.g. flowers).

____ involves two species changing over time.

_____ is when many species interact and change.

In ____ - The urge to help others emerges from the selection in favor of helping kin and the difficulty to distinguish kin and calculate relatedness.

In ____ - Altruism was selected for because altruistic individuals benefit in the long run from returning favors.

In ____ - Groups without the benefit of altruism were selected against. Groups with many free-loaders were selected against.

In ____ - Genes inside the organisms propagate their copies that are inside other organisms.


Results

Model life history

Suppose a eusocial insect with sterile workers where some (alate) reproductives specialize on dispersal and founding new colonies and other (non-dispersal) reproductives stay in the natal nest to breed. All reproductive individuals thus contribute to producing new generations of dispersing reproductive, but the number of generations of breeding in the same colony varies from one to several (Fig. 1a). In such species sex-asymmetric inbreeding (for example, mother–son and uncle–niece matings) may occur, resulting in male and female founders being unequally efficient as vehicles for genetic contributions to future generations (Fig.1b). If sex-asymmetric inbreeding is common, this should lead to biased sex ratios in favour of the parental sex with the greater genetic contribution.

(a) The typical eusocial breeding system for sex-asymmetric inbreeding. Monogamous founding pairs produce outbred F1 offspring but inbred F2 offspring as the colony grows and both may contribute to founding the next generation of colonies. (b) Mother–son inbreeding resulting in sex-asymmetric genetic contributions, where F2 individuals inherit 0.75 maternal genes and 0.25 paternal genes. (c) Full-sib inbreeding resulting in sex-symmetric genetic contributions, where the grandoffspring (F2) inherit 0.5 maternal genes and 0.5 paternal genes.

Sex-asymmetric inbreeding is expected to occur in eusocial insects whenever the following three conditions are met: (i) A colony is founded by a monogamous pair (one male and one female), (ii) deceased founders are replaced by full-sib reproductive offspring in the nest, resulting in inbreeding among the new cohort of reproductives, and (iii) there is a sex-specific difference in longevity between male and female founders, such that either the male or female consistently outlives its partner and inbreeding occurs between parent and offspring, that is inbreeding is sex-asymmetric.

Recently, a novel breeding system called AQS has been described in two species of subterranean termites—Reticulitermes speratus 19 and Reticulitermes virginicus 20 —that meet all three of these conditions. Termite colonies are typically founded by a monogamous pair of primary reproductives (adult winged forms), one king and one queen. In Reticulitermes termites, neotenics (also called secondary reproductives or supplementary reproductives) are produced from within the colony upon the death of the primary king and/or queen 21,22 . As colonies develop, neotenic queens may differentiate even under the presence of reigning queens to supplement egg production according to the labour needs of the colony. Neotenic individuals can differentiate from either nymphs to become ‘nymphoid’ reproductives with wing pads or from workers to become ‘ergatoid’ reproductives without wing pads (Fig. 2).

Differentiation pathways of primary and neotenic reproductives in the genus Reticulitermes.

In the subterranean termites R. speratus and R. virginicus, queens produce their neotenic replacement reproductives asexually but use normal sexual reproduction to produce other colony members 19,20 . These species undergo typical colony founding by a pair of primary reproductives. Relatively early in the colony life cycle, the primary queen is replaced by numerous secondary queens (female neotenics) that are produced asexually by the primary queen (Fig. 3a). These neotenic queens mate with the primary king and produce workers, soldiers and new primary reproductives through sexual reproduction. On the other hand, primary kings live much longer than primary queens. This AQS system enables founding queens to increase their reproductive output while retaining the same transmission rate of their genes to future generations 19,20,23 (Fig. 3b). Therefore, the founder queen can be considered genetically immortal until the colony dies, because female neotenics are themselves replaced by new cohorts of parthenogenetically produced neotenics. When the founder king dies, he can be replaced by a secondary king that is the son of the founder queen and king, effectively resulting in mother–son inbreeding. AQS colonies with a secondary king should thus be expected to bias sex allocation because their inbreeding is sex asymmetric, and we expect that female bias will be more pronounced when the frequency of mother–son inbreeding is higher.

(a) Life history of the species with asexual queen succession (AQS). PK, primary king PQ primary queen SQ, secondary queen P, parthenogenesis S, sexual reproduction. (b) Genetic scheme for the breeding system with AQS. Queens are able to reproduce sexually and also asexually. Offspring produced by sexual reproduction develop into workers, soldiers and alates, whereas those produced by parthenogenesis (automixis with terminal fusion) exclusively differentiate into female neotenics and supplement or replace the older queens. Secondary queens also produce the next replacement queens by parthenogenesis. Thus, the primary queens retain their genetic contribution to the next generation even after their death. Squares indicate males and circles indicate females.

Description of the model

Let gf and gm be the proportion of genes in alates derived from the founder female and founder male, respectively. Then, in cases of mother–son mating, the pair producing the F2 offspring consists of the P mother (founder female) and her F1 son (Fig. 1b). Under this mating system gf=0.75, but gm=0.25 so that females contribute three times as many genes as males. In contrast, inbreeding through full-sib matings does not result in such sex-asymmetric genetic contributions, as diploid male and female founders would continue to contribute equally to the gene pool of the next generation of alates, that is, gf=gm=0.5 (Fig. 1c). Thus, not all types of inbreeding result in sex-asymmetric genetic contributions.

To consider the effect of sex-asymmetric inbreeding on sex allocation, let cm and cf be the class reproductive values of male and female founders, respectively. Class reproductive value describes the expected proportion of genes contributed by a class of individuals to a future generation 24,25 . When there are n types of mating that occur over the lifespan of the colony (for example, mating between parental founders, mother–son inbreeding, father–daughter inbreeding, so on.), the class reproductive value of male and female founders, cm and cf, are

where sex is either male (m) or female (f), and pi and gsex,i are the proportion of progeny and the genetic contribution by a founder to the ith-mating type, respectively. Assuming a large enough population in which individuals allocate resources to (invest in) female alates in proportion s, the fitness of a mutant individual who invests in female alates at s* is

to determine the ESS (evolutionarily stable strategy) proportion of females, we take the derivative of W with respect to s*, and set the value equal to zero:

where the sum of cf and cm is unity, so that the ESS proportion of females is s*=s=cf. Thus, the ESS is

in the case where all alates are produced only by mother–son inbreeding, gf=0.75 (Fig. 1b) and pi =1, the resulting s=1.0 × 0.75=0.75. When the proportions of alates produced by mother–son inbreeding (gf=0.75) and outbreeding (gf=0.5) are p and 1−p, respectively, the resulting proportion of females is given by

Empirical test

We found that replacement of the primary king by a secondary king happens in the later stages of colony maturity in R. speratus of 43 colonies, in which kings were recovered, 40 had a single primary king and three had a single secondary king. All of the neotenic reproductives were nymphoid (male neotenics: N=3 female neotenics: N=3,450). In contrast, previous studies indicate that R. virginicus appears to experience king replacement in an earlier stage of colony establishment, so that 40% of colonies are estimated to have a primary king and 60% a secondary king 20 . We can therefore make the following two predictions concerning the sex allocation in Reticulitermes species: sex allocation in species with AQS will be significantly female biased, whereas sex allocation in species without AQS will not be biased sex allocation in R. virginicus should be more female biased than in R. speratus.

We compared sex allocation in two termite species with AQS (R. speratus and R. virginicus) with that of three congeners without AQS (R. flavipes, R. okinawanus and R. yaeyamanus). As predicted by our model, the AQS and non-AQS species showed significant differences in the proportion of alate females produced (generalized linear models , AQS versus non-AQS: likelihood ratio x 2 =30.32, d.f.=1, P<0.0001 species: x 2 =4.90, d.f.=3, P=0.18) and in proportional investment in females (AQS versus non-AQS: x 2 =29.13, d.f.=1, P<0.0001 species: x 2 =3.28, d.f.=3, P=0.35 Fig. 4). The mean proportion of females in R. speratus was 0.562 (±0.017SE), which was significantly skewed towards females (two-tailed t-test, N=107 colonies including 14,445 individuals, t=−3.476, P<0.001). When adjusted for biomass, the proportional investment was even more female biased (0.587±0.017SE t=−4.491, P<0.0001 Fig. 4), because female alates are larger than males from the same nest. Similarly, the mean proportion of females in R. virginicus was 0.642 (±0.060SE), which was significantly skewed toward females (N=16 colonies including 5,620 individuals, t=−2.369, P<0.05). Again, there was greater bias in proportional investment in females (0.655±0.059SE t=−2.585, P<0.05 Fig. 4). We also predicted that sex allocation in R. virginicus would be more female biased compared to R. speratus, as there appears to be a higher proportion of secondary kings and thus a higher percentage of mother–son matings in the former species (estimated at 60% in R. virginicus 20 compared to 7% in R. speratus, a significant difference according to Fisher’s exact probability test, P<0.05). Although we did find that R. virginicus had a greater proportional investment in females than R. speratus (0.655 versus 0.587), this difference was marginally non-significant (one-tailed t-test, t=1.38, d.f.=121, P=0.085). The outcome of this direct test on the two AQS species where we did expect a difference in female bias is thus somewhat more encouraging than the overall 'species' test given above, and might reach significance if the limited sample size in R. virginicus (N=16) could be expanded.

The species with AQS are R. speratus (N=107 colonies) and R. virginicus (N=16) and those without AQS are R. flavipes (N=43), R. okinawanus (N=11) and R. yaeyamanus (N=7). The AQS species (open bars) showed significantly female-biased investment in comparison with non-AQS species (closed bars) (GLM, P<0.0001). Error bars indicate standard errors. The statistics on the bars indicate the significance level of the deviation from equal allocation (two-tailed t-test: ***P<0.001 *P<0.05).

In contrast, the mean proportion of females in R. flavipes was 0.442 (±0.022SE), which was significantly male- biased (N=43 colonies including 7,782 individuals, t=2.63, P<0.05), and the proportional investment in females was 0.455 (±0.023SE), which was not significantly different from 0.5 (t=1.94, P=0.059 Fig. 4). Similarly, the mean proportion of females in R. okinawanus was 0.460 (±0.043SE), and neither this (N=11 colonies including 1353 individuals, t=0.939, P=0.370) nor the proportional investment in females (0.486±0.044SE t=0.315, P=0.759 Fig.4) was significantly different from 0.5. As in R. flavipes and R. okinawanus, the mean proportion of females in R. yaeyamanus was 0.434 (±0.060SE), and neither this (N=7 colonies including 1,184 individuals, t=1.10, P=0.314) nor the proportional investment in females (0.466±0.061SE t=0.563, P=0.594 Fig. 4) deviated significantly from equality.


Results

Genetic relatedness and social structure

Of the five microsatellite markers studied, one showed null alleles (cc54) and was excluded from the analysis. The other four markers showed no linkage disequilibrium they ranged from 3 to 11 alleles, with a mean observed heterozygosity Ho=0.60 (range: 0.44–0.74) and a mean expected heterozygosity He=0.63 (range: 0.47–0.77). A significant departure from Hardy–Weinberg equilibrium was found in the studied population. The fixation index F was significantly different from 0 (mean±s.e.=0.06±0.02 95% CI: 0.04–0.09). Inbreeding was also supported by the positive, though non-significant, relatedness between the queens and their pedigree-estimated mates rqm=0.16 (two-tailed t-tests, N=29, t=1.778, P=0.086). The frequency of sib-mating reached a value of α=0.20. Fst estimate (0.27±0.03 95% CI: 0.21–0.30) indicated a high genetic divergence between nests. There was no significant correlation between genetic differentiation between pairs of colonies and the geographical distance (Mantel test: matrices correlation r=−0.02 P=0.314), indicating no isolation-by-distance pattern in the study population.

The mean within-colony genetic relatedness rww among nestmate workers was 0.49 (SEjackknife=0.05) and the inbreeding corrected relatedness estimate r* was 0.44. These values were significantly lower than the 0.75 expected under monogyny and monandry (two-tailed t-tests, N=29, both P<0.001).

Number of matrilines per colony

A single queen was found in 20 colonies out of the 29 excavated no queen was collected in the remaining nine colonies. All workers sampled were unambiguously assigned to the queen present in each nest. Similarly, in colonies where queens were not collected, worker genotypes were compatible with single maternity. In line with these results, the average colony relatedness between the workers and the queen rqw equals 0.53 (±0.05 95% CI: 0.43–0.63), not significantly different from 0.5 expected under strict monogyny (two-tailed t-test, t=0.26, N=29, P=0.801).

Mating frequency

Pedigree analyses from both workers and queens collected in the field and from mother–offspring combinations under laboratory conditions were consistent with multiple-mated queens (Table 1). Across the 29 colonies sampled on the field, we found that queens had mated with at least 1–5 males (Figure 1). Similar estimates of queen-mating frequency were obtained from mother–offspring genetic combinations from laboratory-reared colonies. When both field and laboratory results were pooled, the absolute number of patrilines per colony was on average Mp=2.54±0.21, the effective number of patrilines was Me,p=2.30±0.20 and the effective number of patrilines corrected for inbreeding and sampling error was Me,p ,i=2.75±0.22. The average probabilities of non-detection due to two males bearing the same alleles at all loci (Pnon-detect=0.01±0.01) were reasonably low. Mating frequency was not correlated with colony size (Pearson's correlation: rP=−0.003, N=29, P=0.986). The estimated relatedness among the male mates of a single queen was on average rmm=0.11 (SEjackknife=0.03 95% CI: 0.05–0.17), a value significantly different from 0 (two-tailed t-test: t=3.43, N=28, P=0.002). No significant paternity skew was observed in the studied population (Table 1).

Distribution of the absolute number of mating (Mp) per queen (n=29) in C. sabulosa.

Across the 29 colonies sampled, there was a positive and significant association between colony size and total sexual productivity (Spearman rank correlation, rs=0.47, P=0.01 Table 1).

Worker reproduction

Male parentage was investigated in the six colonies that had produced at least four adult males (IS03, IS04, IS11, IS13, IS21, IS22 Table 1). All males typed showed a single allele at each locus, indicating that they were haploid. None of the 97 males examined carried non-queen alleles, suggesting that the workers had not produced them. The average probability of non-detection error, due to worker-derived males carrying queen alleles at all loci, over all colonies, was 0.35. Therefore, sons present in the sample should be detected with a probability of about 65%. Whether workers produce females by thelytokous parthenogenesis cannot be determined by genetic analyses, because worker-produced females are expected to bear the same genotype as queen-offspring (workers and gynes). However, none of the 152 workers dissected had expanded ovaries or developing eggs their ovarioles were reduced and empty. These results are consistent with the complete absence of worker reproduction in queenright colonies of C. sabulosa.

Flow cytometric analyses of the 21 larvae developing from worker-laid eggs in the three orphaned colonies showed that nine larvae were haploid (males 2, 4 and 3 larvae in IS03, IS11 and IS28, respectively) and 12 were diploid (females 3 and 9 larvae in IS03 and IS11, respectively). Thus, workers of C. sabulosa can produce both males by arrhenotokous parthenogenesis and females by thelytokous parthenogenesis. No adults emerged from these worker-produced diploid larvae, so we were unable to determine whether they would have developed into workers or queens.

Thelytokous parthenogenesis by queens

In the seven colonies producing at least four sexual females (IS03, IS07, IS08, IS13, IS19, IS20, IS28 Table 1), the genotype of all such females differed from that of the queen for at least one locus, indicating that new queens are not produced by thelytokous parthenogenesis. Consistent with this result, the relatedness between the queens and their sexual daughters rqf=0.41 (SEjackknife=0.09 95% CI: 0.22–0.60) did not differ from that between the queens and the workers rqw=0.53 (SEjackknife=0.05 95% CI: 0.43–0.63) (paired t-test: t=0.03, N=7, P=0.975).


What is the relatedness of sisters in a haplodiploid system if you mate virgin queens with 1 of their sons - Biology

I redevelop the hypothesis that lifetime monogamy is a fundamental condition for the evolution of eusocial lineages with permanent non-reproductive castes, and that later elaborations — such as multiply-mated queens and multi-queen colonies — arose without the re-mating promiscuity that characterizes non-social and cooperative breeding. Sexually selected traits in eusocial lineages are therefore peculiar, and their evolution constrained. Indirect (inclusive) fitness benefits in cooperatively breeding vertebrates appear to be negatively correlated with promiscuity, corroborating that kin selection and sexual selection tend to generally exclude each other. The monogamy window required for transitions from solitary and cooperative breeding towards eusociality implies that the relatedness and benefit-cost variables of Hamilton's rule do not vary at random, but occur in distinct and only partly overlapping combinations in cooperative, eusocial, and derived eusocial breeding systems.


Contents

P. subnuda belongs to the family Apidae, but far exceed the diversity and habitat distribution in comparison to honeybees. [4] Stingless bees arose as a pivotal force in the Neotropics at the end of the Cretaceous period. [5]

P. subnuda belongs to the Meliponini tribe, which is defined by distinctive phenotypic differences of dorsal vessels. P. subnuda also belongs to the genus Paratrigona found specifically in MesoAmerica. [6]

Morphologically, P. subnuda bees express all the features constituted in the Meliponini tribe. This includes reduction of wing venation, stiff setae or penicillum located on the anterior portion of the hind tibia and reduction of the stinger. As a member of the Meliponini tribe, P. subnuda bees also express distinctive dorsal vessel phenotypes. This includes an arch formed by the dorsal vessels between the thorax longitudinal muscles, creating a forward migrated position of the abdominal ganglia and extended digestive tract. In general, Meliponini members also tend to have a denser hair covering, shorter wings, and are larger than their Trigonini tribe counterparts. [6]

There is a very obvious size distinction between the queens and the workers of P. subnuda species. The P. subnuda worker is 0.5-0.8 cm in size and have a smaller head and thorax compared to queen bees. A physogastric queen (contains a swollen abdominal) is about double the size of a worker and are about 1.2-1.8 cm in size. [4] Compared to other Neotropical bees, P. subnuda are considered to be small in size. In that way, P. subnuda's small stature is what distinguishes it within the Meliponni tribe. [5]

P. subnuda bees are found in Neotropical moist forests and urban areas in South America. Their distribution overlaps with many other stingless bee species, with an especially large correlation with Tetragonisca angustula distribution. [7] [8] They have been studied in Minas Gerais, Paraná, Rio de Janeiro, Rio Grande do Sul, Santa Catarina and São Paulo within Brazil. They can also be found in south to east regions of Central Brazil. [3] As mentioned above, their nests are in the soft and moist soil of these neotropical environments. This particular species is considered to be common within Brazilian neotropical habitats. [9]

Nest structure Edit

The nests of P. subnuda bees are spherical in shape and are relatively small in size (1000–1500 bees). [3] The nest is protected by several sheets of involucrum, which helps keep the nest insulated in the moist underground environments. Within the outer protective involucrum layer is the helicoid brood comb, which contain eggs’ cells. The comb's cells can either be pear-shaped or larger and normal shaped. [9] The nests also include inlet tubes which are built of wax and are long in length. [10] Within a strong colony, there will be approximately 26 cells. [3] These nests are built underground in moist and soft Neotropical soil, and are normally less than one meter deep. [6] In the Brazilian Atlantic forests, these nests were found about 25–120 cm underground. [9] The underground nests of P. subnuda are comparatively more vulnerable than arboreal stingless bee nests, as the underground nests are easier to see and locate. [11]

Using abandoned ant nests Edit

Excavations of P. subnuda nests showed that their nests were originally occupied and then abandoned by genus Atta (leafcutting ants). This was concluded based on the red and granular soil found around the nests, similar nest design, dark spaces below the P. subnuda nest which correspond to ant chambers, and approximately equal surface of the two species’ nests. [10]

Colony initiation Edit

New colony formation is a progressive process within stingless bee species and have been specifically observed in P. subnuda. The new materials, including those for construction and for food, are transported by workers to the site of the new nests. [6] The P. subnuda workers also depart from the new nests with more than one queen from the mother nest. [10] This process of colony initiation is referred to as swarming and is a long lasting process due to lasting relations with mother nests. [12]

Colony reproduction Edit

Daughter queen bees, also known as gynes, leave the colony for the new colony during nesting. This is partly due to the physogastric queens who are unable to move to swarm to the new colony. There is also contact between the mother queen and the new queen that can last for weeks or months. This phenomenon is a consequence of P. subnuda's single mate behaviors. Under single mating, there is lower conflict between daughter and mother queens. This is due to the fact that there is increased relatedness between daughter queen and the mother queen's progeny. When males are produced by the queen, workers will shift their interest to the daughter queen because they have higher relatedness to the new queen's sons. [4] Unlike other tropical bees, stingless bee colonies only reproduce once a year or sometimes even less. [11]

Colony growth Edit

Once colonies have been established, they usually are contained in a single nest and have a population of about 1000–1500 bees. [3] In P. subnuda, swarming departure occurs on the same day of the resource transport to the new nest and occurs fast. [13]

Dominance hierarchy Edit

Similar to other stingless bees, P. subnuda females are divided into queens and workers. [6] There are two types of queens within a nest, the one, singly mated queen and virgin daughter queens kept in reserve. Workers are the daughters of the one, singly mated queen. [4] Within P. subnuda, there is a power struggle between the queen and the workers. Due to their larger size, queens are able to aggressively push workers, but ultimately workers are successful in laying eggs. It was later found that workers have specific strategies that allow for oviposition. [9]

Oviposition process behavior Edit

Singly mated queens of the P.subnuda will lay eggs within the royal cells and will lay a separate egg in each cell which has been supplied with food. Minutes before the queen lays her egg, the workers will regurgitate their food into the cell. The queen will lay her egg on top of this food and then the cell will be closed rapidly by the workers. [14] Workers have mechanisms to disrupt this process and reproduce male progeny. [9]

Division of labor Edit

Stingless bees, including P. subnuda, have distinctive divisions of labor conducted by different age and in relation of needs. There are four distinctive jobs done at different times in a worker's lifespan. The first is self-grooming which is performed after the first hours emerging from the pupea. After, there is incubation and brood chamber repairs. This is followed by rearing behaviors, including provisioning cells, construction of cells and cleaning. Workers are also responsible for feeding both the young adult bees and the singly mated queen bee. Workers must also participate in reconstruction behaviors. Reconstruction behaviors include reconstructing involucrum, entrance guard duty, cleaning of nest and receiving nectar. Finally, there is also the collection of pollen and nectar that serve as food sources. [6]

Communication Edit

P. subnuda communicates in a similar way as many other species within the Meliponini tribe. Due to the swarming activities of P. subnuda it is essential that the scout bees are able to locate new nests and worker bees can communicate sources of food. This communication is done through jostling and mandibular secretions. When returning with pollen or nectar, bees will bring back small amounts of that resources for the others bees within the nest. But along the way back to the nest they will fly in an irregular zigzag patterns in all directions. The bees will try to jostle bees who are in their way and alert them resources have been found. Because of this zigzag behavior many times the bees will not actually give the out the small amounts of syrup out to other bees. But researchers are able to observe when they do give out syrup based on when there is an interruption in the zigzag pattern, such as a sharp turn in a semicircle. This particular zigzag behavior was seen in all Brazilian Meliponini species studied. The bees also alert one another by secreting mandible glandular secretions. In flight, the bees will rub their mandibles on the surface of blades of grass and stones. P. subnuda contain the tube-shaped mandibular gland which serve as a reservoir for these secretions. These secretions have a particular scent associated with them and are used by scout bees when establishing paths for new paths and food sources. [15]

Mating behaviors Edit

Within a P. subnuda colony, there is a single queen that will have one mate who will fertilize all her eggs. The queen will go into a nuptial flight and the male's genitals will become stuck to the genitals of the female, which is a mating sign. In P. subnuda, the males do not congregate at the front of the entrance of virgin queens newly established colony. [13] Workers do have ovarian development and can lay trophic eggs. [9]

Foraging behaviors Edit

Fight activity is crucial for foraging behaviors of the P. subnuda and is dependent upon many environment factors. These factors include temperature, luminous intensity, relative humidity, rain and wind levels. Their foraging behaviors can also be influenced by biotic factors which include availability of floral resources, their physiology and internal conditions of the colony (food supply and queen productivity). [5] Specifically for P. subnuda, the greatest flight activity was found to arise during temperatures between 24.0 °C and 25.0 °C. They forage for pollen and nectar, which are then stored within nest pots. [16] (cited in Oliveira-Abreu et al. 2014 [17] ). The bee species, Geotrigona mombuca, is found within in the same subterranean habitat and has a similar foraging activity patterns above 22.0 °C. The biogeographical and foraging congruence suggest a possible common history between the two species. [11]

Studies have shown that P. subnuda and Scaptotrigona bipunctata are the most numerically dominant stingless bee foragers of flowers found in Cantareira Forest, accounting for more than 80% of all stingless bees found foraging. They were most commonly found in the upper strata (above 7m) in the Neotropics. Yet, P. subnuda were found foraging in the lower strata during shortage of mass flowering or high availability of attractive flowering in the lower strata. P. subnuda is particularly active in the upper strata as they are “pre-adapted” to forage while exposed to direct sunlight due to their large surface to volume ratio. Foraging in the lower strata during shortage periods represents an example of their opportunistic foraging strategies. [5]

Virgin queen behavior Edit

P. subnuda virgin queens find refuge in empty foot pots within the nest. When the virgin queens become “attractive,” they develop tergal and mandibular glands and maintain contact with workers. Yet once their glandular products run out, they will then take refuge in pots and use their mandible to seal the pot. How long they stay in the pot can vary from hours to minutes. Before leaving, they will stick their antennas out of the pot to examine their external environment. Once their glandular product has been replenished, they will circulate around the colony again. This process will continue to happen until she is mature. Throughout her maturation, she will over go many different changes in glandular secretions. At the peak of her “attractiveness” she is secreting pheromones and will try to supersede the queen. [13]

Workers’ behavior towards gynes Edit

P. subnuda and other members of the tribe Meliponini show distinct behavior towards the gynes or royal eggs. It has been observed that new queens are continuously reared and killed by workers bees immediately following their birth. As a result, there is a permeant presence of continuously short-lived gynes. The gynes will be eliminated either by starvation or aggression. Many times the workers will continuously reduce the amount of food donations given to the gyne. As the gynes age, there is a higher risk of being killed due to food deprivation. In periods of intense aggression, the workers can kill a larger number of gynes within a few hours. It is thought that the presence of the queen induces the gynes to discharge their queen pheromones when they are mature enough to do so. The release of their pheromones then initiates the workers to either immediately kill or starve them. [18]

Relatedness Edit

Due to the single mating behavior, P. subnuda show a haplodiploid genetic structure of social Hymenoptera bees. In this system, the workers will be sisters that are 75% related to one another and are 50% related to the queen. If a worker produces a male it will be 50% related to her, but a queen's son is only 25% related to a worker. In this system, a worker should be direct competition with a queen for male production. [4] Workers are 50% related to their own male progeny and 35% related to the progeny of their sisters. Therefore, the workers have the most fitness benefit when they manipulate the sex allocation in such a way that three times more resources in the queen's female progeny than the male progeny. [19]

Worker queen conflict Edit

Due to hymenopteran relatedness, there is a conflict between workers and queen for the production of male progeny. Queens will eat the workers' eggs, and some eggs are trophic eggs, perhaps reflecting an evolutionary history of conflict. [4] With their high relatedness, workers gain an extraordinary indirect fitness benefit from helping the queen rear their sisters. [20] The workers have developed two strategies to oppose the queen's male progeny. One strategy is to lay their eggs in reopened cells that contain the recent eggs from the oviposition process. The other strategy is to open cells that have been provisioned 1–2 days earlier and lay their eggs. The queen has the advantage of size to forcefully push the workers in an attempt to stop worker oviposition, but workers were found to return later to lay eggs. As a result of this conflict, worker bees actually contribute 64% of the male progeny within a single colony. [9]

The main components of P. subnuda’s diet are nectar and pollen. They get their pollen and nectar from over 200 plant species within neotropical environments, including Zanthoxylum hyemale and Baccharis milleflora. [21] As a species, they have been referenced as one of the top three Brazilian Bee species that interact with plant species. [22] P. subnuda are considered to be generalists because their diet consists of pollen and nectar collected from a very large number of floral sources. [11]

P. subnuda are a soft and gentle bee species. It is a species that can be easily handled by humans. [2] The species’ honey is considered to be very tender, flavorful, and possess medicinal qualities. [1]

As of 2006, 26% of stingless bee colonies within the Neotropics of South America have died due to indirect human interference, mainly due to deforestation. [23]


Conclusion

A large body of data is consistent with kin selection having a substantial impact on sex allocation in the social Hymenoptera. Comparisons across species first suggested that workers manipulate sex allocation to match their relatedness asymmetry to males and females. Recently, much stronger evidence that workers manipulate colony sex ratio in their favour arose from studies showing relatedness-induced sex ratio specialization among colonies within single populations, and revealing the proximate mechanisms used in sex ratio biasing.

Lately, it has been suggested that the control of sex allocation by workers might generate surprising and counter-intuitive selection pressures on the mating behaviour of social insects. Queens might be selected to mate with multiple males in order to decrease the relatedness asymmetry in their colonies and induce workers to bias colony sex allocation towards males (Queller, 1993 Ratnieks & Boomsma, 1995). Indeed, a recent study has demonstrated that facultative sex allocation by workers results in higher fitness for double-mated than single-mated queens in field colonies of the ant Formica truncorum (Sundström & Ratnieks, 1998). In contrast, the fitness of the mates of the queens is zero when colonies produce only males (because of haplo-diploidy, males transmit genes through daughters only). This might result in an unusual tug of war between the sexes, with females eager to mate and males showing restraint (Boomsma, 1996). For example, males may avoid mating with queens that have already mated. Alternatively the second male may transfer a small amount of sperm to ensure relatively high relatedness asymmetry and female-biased sex allocation in the future colony (Boomsma, 1996). These new and fascinating theoretical developments now await empirical testing.

Relatedness-induced worker control has been observed frequently in social Hymenoptera, but is not universal. For example, bumblebees are monogynous, but exhibit male-biased population sex investment ratios (Trivers & Hare, 1976 Bourke, 1997). Whether or not worker control is realized depends on multiple parameters, such as the balance of power between queens and workers, the ability of workers to distinguish male and female brood, the level of resources, and the timing of production of reproductive individuals. A particular response may occur in part of this multifactorial space (e.g. when resources are limited), and not in others (e.g. when resources are plentiful). Moreover, the important factors explaining sex ratio variation among colonies within a population may differ from those determining sex ratio variation at the population or species levels. Indeed, long-term studies of population sex investment ratios in ants have revealed variations between years that seem independent of relatedness asymmetry (e.g. Herbers, 1990 Evans, 1996).

Finally, we would like to stress that the large number of factors that can potentially affect sex allocation, and the wealth of alternative hypotheses on sex ratio evolution (Table 1), weaken the conclusions of correlational studies. Basically, any pattern can be explained by one of the numerous alternative hypotheses, or by the effect of various uncontrolled factors. Hence, further manipulative experiments are needed. Controlling for factors such as relatedness asymmetry or resource levels may be difficult and time-consuming, but such experiments are necessary to reveal how multiple factors interact in determining the evolution of sex allocation.


Sex-biased dispersal, haplodiploidy and the evolution of helping in social insects

In his famous haplodiploidy hypothesis, W. D. Hamilton proposed that high sister–sister relatedness facilitates the evolution of kin-selected reproductive altruism among Hymenopteran females. Subsequent analyses, however, suggested that haplodiploidy cannot promote altruism unless altruists capitalize on relatedness asymmetries by helping to raise offspring whose sex ratio is more female-biased than the population at large. Here, we show that haplodiploidy is in fact more favourable than is diploidy to the evolution of reproductive altruism on the part of females, provided only that dispersal is male-biased (no sex-ratio bias or active kin discrimination is required). The effect is strong, and applies to the evolution both of sterile female helpers and of helping among breeding females. Moreover, a review of existing data suggests that female philopatry and non-local mating are widespread among nest-building Hymenoptera. We thus conclude that Hamilton was correct in his claim that ‘family relationships in the Hymenoptera are potentially very favourable to the evolution of reproductive altruism’.

1. Introduction

Bees, wasps and ants (Hymenoptera) have haplodiploid sex determination, whereby males arise from unfertilized eggs and are haploid, whereas females arise from fertilized eggs and are diploid. One consequence of haplodiploidy is that females are more closely related to sisters (r = 0.75) than is the case in diploids (r = 0.5). W. D. Hamilton suggested that this difference might help to explain the large number of origins of sociality and reproductive altruism among females in the Hymenoptera [1]. More recent work, both theoretical and empirical, cast doubt on this theory. Genetic models suggest that because a female's relatedness to her brothers is lower under haplodiploidy (r = 0.25) than under diploidy (r = 0.5), haplodiploidy can promote altruism only if altruists help to produce young among whom females are more common than in the general population [2] although there are conditions under which this may occur, it is questionable how often they are met [3]. In addition, empirical studies have shown that active kin discrimination is rare in the social Hymenoptera [4]. Such findings have led to a shift in focus from genetic to ecological factors favouring hymenopteran eusociality [5], although the two are not necessarily mutually exclusive.

Here, we show that haplodiploidy is in fact favourable to the evolution of reproductive altruism on the part of females, provided only that dispersal is male-biased—it is not necessary to invoke sex-ratio bias or active kin discrimination. Several previous analyses of altruism in viscous populations (with limited dispersal) have considered the impact of haplodiploidy, but none have explored the interaction between haplodiploidy and sex-biased dispersal as we do. In his seminal model of local helping, Taylor [6] explicitly showed that haplodiploidy does not alter the conditions for the evolution of helping among adult breeders, given the assumption that males mate on their natal patch and females then disperse (carrying their partner's genes with them—effectively ensuring identical dispersal rates for both sexes) Queller [7] subsequently suggested that sex-biased dispersal might alter this conclusion, but did not formally analyse this possibility. More recently, Johnstone & Cant [8] showed that sex-biased dispersal can favour helping among adult breeders, but considered only the diploid case. Lastly, Lehmann et al. [9] showed that population viscosity can favour the evolution of sterile workers (as opposed to helping among breeders). They explicitly demonstrate, as Taylor [6] did, that haplodiploidy does not affect the conclusions of their model when dispersal is identical for both sexes (and both males and females become workers). Unlike Taylor [6], they also briefly consider the impact of sex differences in dispersal, but do not explore in detail the interaction between sex-biased dispersal and haplodiploidy.

Below, we build on the analyses of Lehmann et al. [9] and Johnstone & Cant [8] to show that when dispersal is male-biased, haplodiploidy does favour female reproductive altruism, whether this takes the form of the evolution of sterile female workers or of helping among reproductive females. Since both analyses make very similar assumptions about population structure, we treat them as variants of a single model, distinguished chiefly by their focus on the evolution of sterile female helpers or of helping among adult reproductive females, respectively.

2. Model

We focus on an infinite, sexually reproducing population divided into discrete groups or colonies, each comprising n breeding females or queens, possibly assisted by a variable number of sterile female workers. The population cycles through a series of steps: queens in a colony (with the assistance of local workers) each produce a large number of offspring. Some fraction of female young develop as sterile workers the remaining females and all males are reproductively capable, with a primary sex ratio of f reproductive female to (1 − f) reproductive male young. Reproductively capable female and male offspring then disperse with probability (1 − hf) and (1 − hm) we assume that workers always remain in their natal colony. Dispersal is followed by random mating among reproductively capable offspring present in a patch (if a female remains in her natal colony with probability hf, then with probability hm she mates with a male from the same colony who has not dispersed otherwise, she mates with a non-local male). Following mating, all queens and workers of the parental generation die, as do reproductively capable males of the offspring generation. Lastly, queens of the offspring generation compete for breeding spots vacated by the death of queens of the parental generation. Those queens who fail to obtain a breeding position die, while those that survive will, with the assistance of local workers, go on to produce a new generation of young.

We consider the evolution of two forms of altruism. First, following Lehmann et al. [9], we focus on an allele of small effect that causes a slight increase of c in the proportion of female offspring that become sterile workers (assuming that development as a worker or as a reproductive is under offspring control). This entails a reduction of c in the fraction of female offspring bearing the allele that become reproductively capable, but the additional workers are assumed later to increase the number of reproductively capable offspring produced by their colony by a fraction b.

Second, following Johnstone & Cant [8] (an extension of Taylor [6]), we consider an allele that causes a queen bearing it to engage (after dispersal and mating, just before reproduction) in helping behaviour, which again entails a proportional reduction of c in the number of reproductively capable young she produces, but confers an immediate proportional fecundity gain of b on other queens in the same colony.

3. Analysis

To derive the inclusive fitness effects of helping alleles, we adopt the terminology of Lehmann et al. [9], and will write Qi for the probability of identity between two homologous genes randomly sampled with replacement from the same individual of sex i, Qij for the probability of identity between a gene sampled in a reproductive adult of sex i and another homologous gene randomly sampled from a distinct reproductive adult of sex j in the same colony (immediately after dispersal), and for the probability of identity between two genes sampled with replacement from same-sex reproductive individuals in the same colony at the adult stage. We will also write for the probability of identity between a gene sampled in a juvenile of sex i and another homologous gene randomly sampled from a distinct juvenile of sex j in the same colony (immediately prior to dispersal), and for the probability of identity between a gene sampled in an adult worker of sex i and another homologous gene randomly sampled from a reproductive adult of sex j in the same colony (immediately after dispersal). Given our assumptions above, it is straightforward to determine these probabilities of genetic identity under either diploidy or haplodiploidy (see appendix A). We can then use these values to determine the inclusive fitness effects of the alleles with which we are concerned. Our analysis follows the direct fitness method of Taylor & Frank [10] and Rousset [11], whereby we focus on the effect of all actors expressing a mutant helping allele on the fitness of a focal adult bearing the allele in question (including the effect of the focal adult on itself).

Table 1 summarizes the inclusive fitness effects of an allele that increases the proportion of female offspring who become workers. This is equivalent to table 3 of Lehmann et al. [9], but differs for three reasons: (i) we have assumed that only female offspring become workers (ii) we have assumed that workers do not disperse and (iii) we have allowed for different rates of female and male dispersal among reproductively capable young we have also partitioned terms slightly differently. The table lists inclusive fitness effects through daughters and through sons, the four rows in the former case corresponding to (i) the immediate loss of reproductive daughters due to a greater proportion of them becoming workers, (ii) the gain in reproductive daughters attributable to reduced local competition caused by the former loss, (iii) the gain in reproductive daughters owing to the positive impact of increased worker numbers on colony productivity and, lastly, (iv) the loss of reproductive daughters attributable to increased local competition caused by this greater productivity. Since the worker allele is not expressed in males, there are only two rows for effects through sons, corresponding to (i) the gain in reproductive sons owing to the positive impact of increased worker numbers on colony productivity and (ii) the loss of reproductive sons attributable to increased local competition caused by this greater productivity. These fitness effects are calculated taking into account the possibility that the focal helping allele may reside in an adult male or queen, with the sexes weighted according to tij, the probability that a gene randomly taken in an individual of sex i descends from an individual of sex j effects through sons and daughters are also weighted according to the reproductive value vi of an individual of sex i (see appendix A).

Table 1. Inclusive fitness effects of female worker allele.

Lehmann et al. [9] observe, in their analysis, that the population female-to-male sex ratio f (among reproductive young) does not affect the evolution of the helping allele (see also [6,8]), because the relative expected reproductive success of individual females compared with males is inversely proportional to the female-to-male sex ratio, so that a queen obtains equal reproductive success through sons and daughters regardless of the value of f. In our case, however, it is only females that become workers, as in the social Hymenoptera. Under these circumstances, although a queen's loss of fitness owing to a given proportion of her daughters becoming workers is unaffected by f, the absolute number of workers produced as a result, and the benefit to colony productivity they provide, is proportional to f. Consequently, the population sex ratio does affect the fate of a sex-specific worker allele.

Table 2 summarizes, in a similar way to table 1, the inclusive fitness effects of an allele that promotes helping by adult queens. These are equivalent to the effective costs and benefits derived in Johnstone & Cant [8] for ease of comparison, we have split them into similar components as in table 1, and expressed them in a more general form valid for both diploids and haplodiploids, using the notation of Lehmann et al. [9].

Table 2. Inclusive fitness effects of adult female helping allele.

Summing up the elements of table 1 or table 2, and inserting the equilibrium values for the relevant probabilities of identity derived in the appendix, we obtain conditions for invasion of alleles that cause an increased proportion of female offspring to become workers, or that promote helping by adult reproductive females, in diploids or haplodiploids.

4. Results: worker evolution

We consider first the conditions for the invasion of an allele that leads to an increased proportion of female offspring becoming workers. When hf = hm, implying that there is no sex-bias in dispersal, we find (as did Taylor [6] and Lehmann et al. [9]) that haplodiploidy does not influence the conditions for invasion in both diploids and haplodiploids the allele can invade when

Now consider the impact of sex-biased dispersal. When hf = 1 and hm = 0, implying that males all disperse to mate while females all remain on their natal patch, the invasion conditions are for diploids and for haplodiploids. The critical ratio of c to b below which invasion is possible (a simple measure of the strength of selection for helping) is thus (for any positive value of f) three times greater in haplodiploids than in diploids when there is a single breeding queen per colony (i.e. when n = 1), as is often the case in social Hymenoptera. As the number of queens per colony, n, increases, the relative strength of selection under haplodiploidy compared with diploidy declines, but always remains substantial, tending to precisely 50 per cent greater in haplodiploids than in diploids as n becomes large. By contrast, when hf = 0 and hm = 1, implying that it is females who disperse and males who stay put, the invasion conditions are for diploids and for haplodiploids. In this case, the critical ratio of c to b below which invasion is possible is (for any positive value of f) smaller for haplodiploids than for diploids, tending to 25 per cent smaller as n becomes large. To sum up, haplodiploidy favours the evolution of helping when dispersal is completely male-biased, but is unfavourable when dispersal is completely female-biased.

Figure 1 shows the relative strength of selection for female workers in haplodiploids compared with diploids, for the full range of values of hf and hm (for the illustrative case of n = 5 breeding queens per colony other values of n yield qualitatively similar results, although the effects are more pronounced with fewer queens per colony) as above, the relative strength of selection for workers under haplodiploidy compared with diploidy is independent of the population sex ratio. The graph confirms the general pattern suggested by the extreme cases considered above. Haplodiploidy generally favours the evolution of female workers when dispersal is male-biased (and inhibits the evolution of female workers when dispersal is female-biased), and does so more strongly the greater the degree of bias.

Figure 1. Relative strength of selection for female workers under haplodiploidy compared with diploidy. Strength of selection is measured as the critical ratio of c/b below which selection favours an allele that causes an increased proportion of female offspring to become workers. Results are shown as a function of the levels of male philopatry (hm) and of female philopatry (hf). In all cases, n = 5 breeding queens per colony (other values of n yield qualitatively similar results, with haplodipoidy becoming relatively more favourable to the evolution of female workers under male-biased dispersal for smaller values of n) note that the relative strength of selection for female workers under haplodiploidy compared with diploidy is independent of the population sex ratio (i.e. is unaffected by the proportion of female offspring f).

Although the relative strength of selection for female workers under haplodiploidy compared with diploidy does not change with the sex ratio, the absolute strength of selection under either genetic system does change. Moreover, the stable sex ratio itself changes according to the extent of sex-difference in dispersal. To illustrate this effect, figure 2 shows the absolute strength of selection for female workers in haplodiploids and in diploids, as female and male dispersal vary in opposition to one another, assuming that the sex ratio has evolved to its stable value (under maternal control) given the rates of female and male dispersal. Results are shown for four different values of n, the number of breeding queens per colony (n = 1, 2, 4 and 8). It is constructive to compare these results with those previously shown. As figure 1 revealed, the relative strength of selection for helping under haplodiploidy, compared with under diploidy, is greatest when dispersal is completely male-biased (i.e. when hm = 0 and hf = 1). By contrast, figure 2 shows that the absolute strength of selection for helping under haplodiploidy attains a maximum when dispersal is somewhat (but not completely) male-biased. This is because an extreme male-bias in dispersal selects for a male-biased sex ratio, which tends to reduce the strength of selection for female helping. The effect is most pronounced when there is a single breeding female per colony (i.e. when n = 1), because the lack of female–female competition within a colony means that strongly male-biased dispersal can then favour a very skewed sex ratio, leading to a collapse in the strength of selection for female helping to zero as dispersal approaches the extreme of complete male-bias. Nevertheless, despite the effects of sex-ratio evolution, helping always evolves more easily under haplodiploidy than under diploidy when dispersal is female-biased, and the maximum strength of selection for helping (as one ranges from female- to male-biased philopatry) is greater under haplodiploidy than under diploidy.

Figure 2. Absolute strength of selection for female workers under haplodiploidy and under diploidy, given a stable sex ratio. Strength of selection (under haplodiploidy, dashed line under under diploidy, solid line) is measured as the critical ratio of c/b below which selection favours an allele that causes an increased proportion of female offspring to become workers. Results are shown as a function of the levels of male philopatry (hm) and of female philopatry (hf), assuming that these vary in opposition to one another (i.e. that hm = 1 − hf) thus, the left-hand side of each graph corresponds to female philopatry and male dispersal (hm = 0, hf = 1), and the right-hand side to female dispersal and male philopatry (hm = 1, hf = 0). In all cases, the sex ratio is assumed to have evolved to the equilibrium value (under maternal control) given the levels of female and male dispersal. Results are shown for different numbers of breeding queens per colony (n).

5. Results: helping by adult females

When hf = hm = h, implying that there is no sex-bias in dispersal, an allele for adult female helping cannot invade (assuming c > 0) under either diploidy or haplodiploidy—this is simply a restatement of Taylor's [6] seminal result. However, when hf = 1 and hm = 0, implying that males all disperse to mate while females all remain on their natal patch, the invasion conditions are

Figure 3 shows the strength of selection for adult female helping and/or harming in haplodiploids and in diploids, over the full range of hf (the frequency of female philopatry), for different degrees of male-bias in dispersal (i.e. for different ratios of hm to hf the figure uses the illustrative case of n = 5 breeding queens per colony other values of n yield very similar results) note that because selection sometimes favours helping and sometimes harming, the results are more complex than was the case in our analysis of a worker allele, and we cannot simply present the strength of selection for female helping in haplodiploids compared with diploids in a single graph as we did in figure 1. Nevertheless, the figure demonstrates that selection will only favour helping among adult queens when dispersal is male-biased, and that it is generally more likely to do so, and to do so more strongly, in haplodiploids than in diploids.

Figure 3. Strength of selection for helping or harming by adult queens under haplodiploidy (light line) compared with diploidy (dark line). Strength of selection is measured as the critical magnitude of the ratio of c/b below which an allele is favoured, with positive values representing selection for helping and negative selection for harming. Results are shown as a function of the level of female philopatry (hf). Successive panels correspond to increasingly male-biased dispersal (i.e. to lower ratios of male philopatry compared with female philopatry). In all cases, n = 5 breeding queens per colony (other values of n yield qualitatively similar results).

6. Discussion

Our analysis suggests that haplodiploidy is favourable to the evolution of female helping, when combined with male-biased dispersal. This applies both to the evolution of helping by adult, breeding females and to the evolution of a sterile caste of worker females. In the former case, haplodiploidy can lead to selection for helping where harming would be favoured in diploids, while in the latter it simply leads to stronger selection for helping. The quantitative effect of haplodiploidy is pronounced—in the case of worker production, the critical ratio of c to b below which invasion is possible is more than 50 per cent greater in haplodiploids than in diploids, and rises, as the number of queens per colony falls, to three times greater in haplodiploids than in diploids for a single breeding queen per colony.

Why does haplodiploidy favour helping when dispersal is male-biased? Philopatry leads to positive local relatedness among females on a patch, which can potentially favour helping behaviour. At the same time, it leads to local competition among the offspring of females on a patch, potentially favouring harming. The net effect of philopatry thus depends on the balance between these two effects. Under haplodiploidy, however, the unusually high relatedness between sisters leads to higher local relatedness within a patch than would be the case under diploidy, for the same level of female philopatry. When dispersal is male-biased, this high local relatedness is not diluted to the same extent by the low relatedness of haplodiploid females to their brothers, because males are more likely to leave their natal patch. The result is that helping yields greater kin-selected benefits in haplodiploids, while the intensity of local competition remains the same as in diploids, leading to stronger selection for helping.

But how common are female philopatry and male dispersal to mate among hymenopterans? Female philopatry is thought to be widespread in eusocial hymenopterans and their non-social sister lineages [12–14], but male dispersal has been less well studied. In primitively eusocial paper-wasps (Polistes), new queens each mate with a single male, then overwinter before initiating new nests in spring, often in groups where one queen dominates reproduction while the others act as helpers. Overwintered queens are philopatric, so that associations usually consist of close relatives (r life-for-life > 0.6 [15–17]). However, in three species where it has been measured, relatedness between the mates of joint-nesting queens is zero, so that mating is effectively non-local [15–17]. Similarly, in two species of Myrmica ants, the queens sharing a nest were relatives whereas their mates were probably unrelated [18,19], while in three additional studies there was no evidence of sex-biased dispersal [20–22]. A second way of testing whether dispersal is sex-biased is from studies in which gene flow has been estimated separately using mitochondrial and nuclear genes. In seven of nine such tests, including four Formica ant species, and in three other ant lineages in which tests have been conducted, gene flow was inferred to be male-biased [23–26]. Similarly, Clarke et al. [27] showed that Africanization of honeybees of the Yucatan initially involved mainly paternal gene flow, with negligible maternal gene flow.

In ants, there has been repeated evolution of a complex social organization known as ‘polygyny’, in which many queens share a nest. New queens are philopatric, commonly being readopted by their natal colonies after mating, or ‘budding off’ to start new nests adjacent to their natal colonies. Interestingly, there is some evidence that dispersal is more male-biased in polygynous populations than in conspecific monogynous populations, in which queens do not live in cooperative groups (so that there is only one queen per nest) [28,29]. Thus, while further tests for sex-biased dispersal are required, the data available imply that male-biased dispersal is widespread in the Hymenoptera.

To conclude, while our results do not call into question the importance of ecological factors for the evolution of eusociality [30], they indicate that haplodiploidy can also play a significant role. Hamilton [1] did not explicitly consider the significance of sex-specific dispersal for the evolution of altruism, but our results show that when dispersal is male-biased, he was indeed right to claim that ‘family relationships in Hymenoptera are potentially very favourable to the evolution of reproductive altruism’ (p. 28 of [1]).


Conclusions

Living things are complex, but this complexity is of two broad types. Organisms show complexity of apparent purpose, with all of the parts acting for the whole. Groups, however, are usually dominated by the complexities of cross-purpose the parts seem goal-directed, but the goals are not shared, and the result is often anything but elegant. The most spectacular exceptions, at the group level, are social insect societies, in which the individuals usually do seem to act toward a common goal.

Any scientific theory purporting to account for biological complexity ought to account for this special nature of social insects. Why do their colonies show a degree of apparent purpose lacking in other aggregations, herds, and flocks? The kin selection extension of natural selection theory does explain this cooperation results from the opportunity to give sufficiently large benefits to kin.

More importantly, kin selection theory has successfully predicted new findings. Although social insect colonies have clock-like design in many respects, kin selection theory predicts who is throwing sand into the clockworks, as well as which gears might be slipped and which springs sprung. Many of the predicted findings, such as sex ratio conflict and policing, were otherwise completely unexpected. The success of this approach shows that the Darwinian paradigm is capable of explaining not just the adaptations of organisms but also how new kinds of organismal entities come into being.