A survey on maximal green sequences

Maximal green sequences appear in the study of Fomin-Zelevinsky's cluster algebras. They are useful for computing refined Donaldson-Thomas invariants, constructing twist automorphisms and proving the existence of theta bases and generic bases. We survey recent progress on their existence and properties and give a representation-theoretic proof of Greg Muller's theorem stating that full subquivers inherit maximal green sequences. In the appendix, Laurent Demonet describes maximal chains of torsion classes in terms of bricks generalizing a theorem by Igusa.Comment: 15 pages, submitted to the proceedings of the ICRA 18, Prague, comments welcome; v2: misquotation in section 6 corrected; v3: minor changes, final version; v4: reference to Jiarui Fei's work added, post-final version; v4: formulation of Remark 4.3 corrected; v5: misquotation of Hermes-Igusa's 2019 paper corrected; v5: reference to Kim-Yamazaki's paper adde

Reproductive specialization in multiple-queen colonies of the ant Formica exsecta

In polygynous (multiple queens per nest) colonies of social insects, queens can increase their reproductive share by laying more eggs or by increasing the proportion of eggs that develop into reproductive individuals instead of workers. We used polymorphic microsatellite loci to determine the genetically effective contribution of queens to the production of gynes (new queens), males, and 2 different cohorts of workers in a polygynous population of the ant Formica exsecta. For this purpose, we developed a new method that can be used for diploid and haplodiploid organisms to quantify the degree of reproductive specialization among breeders in societies where there are too many breeders to ascertain parentage. Using this method, we found a high degree of reproductive specialization among nest-mate queens in both female- and male-producing colonies (sex ratio is bimodally distributed in the study population). For example, a high effective proportion of queens (25% and 79%, respectively) were specialized in the production of males in female- and male-producing colonies. Our analyses further revealed that in female-producing colonies, significantly fewer queens contributed to gyne production than to worker production. Finally, we found significant changes in the identity of queens contributing to different cohorts of workers. Altogether, these data demonstrate that colonies of F. exsecta, and probably those of many other highly polygynous social insect species, are composed of reproductive individuals differing in their investment to gynes, males, and workers. These findings demonstrate a new aspect of the highly dynamic social organization of complex animal societie

Phenotype and individual investment in cooperative foundress associations of the fire ant, Solenopsis invicta

Fire ant (Solenopsis invida) queens founding a colony with unrelated nest mates potentially face a trade-off. Increased individual investment enhances worker production, colony survival, and growth. However, increased investment may reduce a queen's probability of surviving fights that invariably arise after worker eclosion. Indeed, previous studies showed that queens lose less weight (a measure of investment) when initiating colonies with cofoundresses than when alone, and that within associations the queen losing more weight is more likely to die. In this study, we tested whether queens adjust weight loss to social environment and fighting ability and whether restraining weight loss directly increases survival prospects. Experimental manipulation of colonies showed that reduced investment by queens within associations is primarily a response to the presence of a nest mate and not simply a response to per-queen brood-care demands. Differences in head width were associated with relative and combined weight loss of cofoundresses, as well as with queen survival. In contrast, the investment strategies of queens were not significantly influenced by their nest mates' initial weight. Similarly, manipulation of the queens' relative weight by feeding and exposure to contrasting social environment (queens kept alone or in groups) did not significantly affect survivaL These results indicate that head width differences or correlated phenotypic atthbutes of fighting ability influenced both investment strategies and survival probability of queens. That queens with larger heads invested less energy into brood rearing and were more likely to survive reveals more selfish interactions among cofoundresses than has previously been assumed and casts some doubts about the idea that group selection must be invoked to account for the maintenance of cooperation in foundress associations of ant

Lack of inbreeding avoidance in the Argentine ant Linepithema humile

Although workers might increase their inclusive fitness by favoring closer over more distant kin, evidence suggest that nepotism generally does not occur within colonies of social insects. It has been suggested that this may be due to the cost of recognition errors. We tested whether recognition occurs in a system where a better than random ability to recognize kin should be selected for. Using DNA microsatellites, we show that sexuals of the Argentine ant Linepithema humile fail to use genetic cues to avoid sib-mating. When offspring of two queens were allowed to mate, the percentage of matings among siblings was not significantly lower than expected under the hypothesis of random mating. The finding that sexuals fail to use genetic cues to avoid sib-matings cannot be attributed to the cost of recognition errors because any recognition system that would lead to a better than random ability to avoid sib-mating should be selected for when there are costs to inbreeding. These data are thus consistent with the view that kin recognition mediated solely by genetic cues might be intrinsically error prone within colonies of social insect

Fourmidable: a database for ant genomics

BACKGROUND: Fourmidable is an infrastructure to curate and share the emerging genetic, molecular, and functional genomic data and protocols for ants. DESCRIPTION: The Fourmidable assembly pipeline groups nucleotide sequences into clusters before independently assembling each cluster. Subsequently, assembled sequences are annotated via Interproscan and BLAST against general and insect-specific databases. Gene-specific information can be retrieved using gene identifiers, searching for similar sequences or browsing through inferred Gene Ontology annotations. The database will readily scale as ultra-high throughput sequence data and sequences from additional species become available. CONCLUSION: Fourmidable currently houses EST data from two ant species and microarray gene expression data for one of these. Fourmidable is publicly available at http://fourmidable.unil.ch

Foreign ant queens are accepted but produce fewer offspring

Understanding social evolution requires us to understand the processes regulating the number of breeders within social groups and how they partition reproduction. Queens in polygynous (multiple queens per colony) ants often seek adoption in established colonies instead of founding a new colony independently. This mode of dispersal leads to potential conflicts, as kin selection theory predicts that resident workers should favour nestmate queens over foreign queens. Here we compared the survival of foreign and resident queens as well as their relative reproductive share. We used the ant Formica exsecta to construct colonies consisting of one queen with workers related to this resident queen and introduced a foreign queen. We found that the survival of foreign queens did not differ from that of resident queens over a period of 136days. However, the genetic analyses revealed that resident queens produced a 1.5-fold higher number of offspring than introduced queens, and had an equal or higher share in 80% of the colonies. These data indicate that some discrimination can occur against dispersing individuals and that dispersal can thus have costs in terms of direct reproduction for dispersing queen

Internest sex-ratio variation and male brood survival in the ant Pheidole pallidula

Sex allocation in social insects has become a general model in tests of inclusive fitness theory, sex-ratio theory, and parent-offspring conflict. Several studies have shown that colony sex ratios are often bimodally distributed, with some colonies producing mainly females and others mainly males. Sex specialization may result from workers assessing their relatedness to male brood versus female brood, relative to the average worker-relatedness asymmetry in other colonies of their population. Workers then adjust the sex ratio in their own interest This hypothesis assumes that workers can recognize the sex of the brood in their colony and selectively eliminate males. We compared the primary sex ratio (at the egg stage) and secondary sex ratio (reproductive pupae and adults) of colonies in the ant Pheidole pallidula. There was a strong bimodal distribution of secondary sex ratios, with most colonies producing mainly reproductives of one sex. In contrast, there was no evidence of a bimodal distribution of primary sex ratios. The proportion of haploid eggs produced by queens was 0.35 in early spring and decreased to about 0.1 in summer. Male eggs also were present in virtually all field colonies sampled in July, although eggs laid at this time of year never give rise to males. All male brood is, therefore, selectively eliminated beginning in July and continue to be eliminated through the rest of the year. Finally, the population sex-ratio investment was female-biased. Together, these results are consistent with the hypothesis that workers control the secondary sex ratio by selectively eliminating male brood in about half the colonies, perhaps those with high relatedness asymmetry.[Behav Ecol 7: 292-298 (1996)

Task-dependent influence of genetic architecture and mating frequency on division of labour in social insect societies

Division of labour is one of the most prominent features of social insects. The efficient allocation of individuals to different tasks requires dynamic adjustment in response to environmental perturbations. Theoretical models suggest that the colony-level flexibility in responding to external changes and internal perturbation may depend on the within-colony genetic diversity, which is affected by the number of breeding individuals. However, these models have not considered the genetic architecture underlying the propensity of workers to perform the various tasks. Here, we investigated how both within-colony genetic variability (stemming from variation in the number of matings by queens) and the number of genes influencing the stimulus (threshold) for a given task at which workers begin to perform that task jointly influence task allocation efficiency. We used a numerical agent-based model to investigate the situation where workers had to perform either a regulatory task or a foraging task. One hundred generations of artificial selection in populations consisting of 500 colonies revealed that an increased number of matings always improved colony performance, whatever the number of loci encoding the thresholds of the regulatory and foraging tasks. However, the beneficial effect of additional matings was particularly important when the genetic architecture of queens comprised one or a few genes for the foraging task's threshold. By contrast, a higher number of genes encoding the foraging task reduced colony performance with the detrimental effect being stronger when queens had mated with several males. Finally, the number of genes encoding the threshold for the regulatory task only had a minor effect on colony performance. Overall, our numerical experiments support the importance of mating frequency on efficiency of division of labour and also reveal complex interactions between the number of matings and genetic architectur

Experimental manipulation of colony genetic diversity had no effect on short-term task efficiency in the Argentine ant Linepithema humile

Genetic diversity might increase the performance of social groups by improving task efficiency or disease resistance, but direct experimental tests of these hypotheses are rare. We manipulated the level of genetic diversity in colonies of the Argentine ant Linepithema humile, and then recorded the short-term task efficiency of these experimental colonies. The efficiency of low and high genetic diversity colonies did not differ significantly for any of the following tasks: exploring a new territory, foraging, moving to a new nest site, or removing corpses. The tests were powerful enough to detect large effects, but may have failed to detect small differences. Indeed, observed effect sizes were generally small, except for the time to create a trail during nest emigration. In addition, genetic diversity had no statistically significant impact on the number of workers, males and females produced by the colony, but these tests had low power. Higher genetic diversity also did not result in lower variance in task efficiency and productivity. In contrast to genetic diversity, colony size was positively correlated with the efficiency at performing most tasks and with colony productivity. Altogether, these results suggest that genetic diversity does not strongly improve short-term task efficiency in L. humile, but that worker number is a key factor determining the success of this invasive specie