L P Sepulveda-Rincon

N Islam

P Marsters

K Campbell

N Beaujean

E Maalouf

Dr Walid E Maalouf
email: walid.maalouf@nottingham.ac.uk

EMBRYO CELL ALLOCATION PATTERNS ARE NOT ALTERED BY BIOPSY BUT CAN BE LINKED WITH FURTHER DEVELOPMENT

Keywords: Embryo biopsy, pre-patterning, PGD/PGS, organ development, embryo transfer, implantation

It has been suggested that first embryo cleavage can be related with the embryonic-abembryonic axis at blastocyst stage in mice. Thus, cells of the 2-cell embryo might be already biased to form the inner cell mass or trophectoderm. This study was conducted to observe the possible effects of embryo biopsy on cell allocation patterns during embryo preimplantation in two different mouse strains and the effects of these patterns on further development. First, one blastomere of the 2-cell embryo was injected with a lipophilic tracer and cell allocation patterns were observed at blastocyst stage. Blastocysts were classified into orthogonal, deviant or random pattern. For the first experiment, embryos were biopsied at 8-cell stage and total cell counts (TCC) were annotated. Furthermore, non-biopsied blastocysts were transferred into foster mothers. Then, pups and their organs were weighed two weeks after birth. Random pattern was significantly recurrent (≈60%), against orthogonal (<22%) and deviant (<22%) patterns among groups. These patterns were not affected by biopsy procedure. However, TCC on deviant embryos were reduced after biopsy. Moreover, no differences were found between patterns for implantation rates, litter size, live offspring and organ weights (lungs, liver, pancreas and spleen). However, deviant pups presented heavier hearts and orthogonal pups presented lighter kidneys among the group. In conclusion, these results suggest that single blastomere removal does not disturb cell allocation patterns during pre-implantation. Nonetheless, the results suggest that embryos following different cell allocation patterns present different coping mechanisms against in vitro manipulations and further development might be altered.

INTRODUCTION

Assisted reproductive technologies (ARTs) have been clinically used for more than three decades and the success rates still remain relatively low, with a probability to take home a baby after an IVF cycle of around 33 % in women younger than 35 years old [START_REF] Botros | Metabolomics and its application for non-invasive embryo assessment in IVF[END_REF] and no more than 23 % for women of older age groups [START_REF] Hfea | Fertility treatment in 2011: Trends and Figures[END_REF]. Several factors have been related with pregnancy outcomes after ARTs as gametes/embryos origin and state (autologous or donation and fresh or thawed), female stimulation treatment, patient age, number of previous treatments and day of embryo transfer (D3 or D5) to mention the most common ones [START_REF] Meseguer | Embryo incubation and selection in a time-lapse monitoring system improves pregnancy outcome compared with a standard incubator: a retrospective cohort study[END_REF]. Nevertheless, embryo implantation failure remains the main cause of the low success rates on ARTs [START_REF] Hesters | Impact of early cleaved zygote morphology on embryo development and in vitro fertilization-embryo transfer outcome: a prospective study[END_REF]. Most of embryo implantation failures or pregnancy arrests are caused by embryo chromosomal or genetic abnormalities [START_REF] Simpson | Preimplantation genetic diagnosis to improve pregnancy outcomes in subfertility[END_REF], therefore pre-implantation genetic screening (PGS) or diagnosis (PGD) before embryo transfer is suggested for those cases. The main objectives of PGD are to improve birth rates in those patients presenting any kind of genetic disease or disorder, and to reduce spontaneous abortions [START_REF] Munné | Technology requirements for preimplantation genetic diagnosis to improve assisted reproduction outcomes[END_REF]. Embryo pre-implantation genetic diagnosis/screening (PGD/S) is becoming increasingly applied in fertility clinics. Even though trophectoderm biopsy is currently becoming the preferred method, blastomere biopsy on day 3 remains the most common technique for obtaining the biological material according to the latest ESHRE (European Society for Human Reproduction and Embryology) consortium [START_REF] De Rycke | ESHRE PGD Consortium data collection XIII: cycles from January to December 2010 with pregnancy follow-up to[END_REF]. So far, more than ten thousand babies have been born after a PGD/S cycle [START_REF] Peyvandi | Prenatal diagnosis and preimplantation genetic diagnosis: novel technologies and state of the art of PGD in different regions of the world[END_REF]. Therefore, further research on the potential effect and safety of embryo biopsy on embryo development is needed.

Until recent years it was believed that during the first round of cleavage, the cells in the mammalian embryo were identical and had the same potential to become ICM or TE. However, the literature reports a theory called the pre-patterning or biased theory, which refers to the different potential of the twin blastomeres at the two-cell stage embryo to become ICM or TE [START_REF] Piotrowska | Blastomeres arising from the first cleavage division have distinguishable fates in normal mouse development[END_REF][START_REF] Piotrowska | Early patterning of the mouse embryo -contributions of sperm and egg[END_REF][START_REF] Fujimori | Analysis of cell lineage in two-and four-cell mouse embryos[END_REF][START_REF] Gardner | The axis of polarity of the mouse blastocyst is specified before blastulation and independently of the zona pellucida[END_REF][START_REF] Torres-Padilla | Histone arginine methylation regulates pluripotency in the early mouse embryo[END_REF][START_REF] Bischoff | Formation of the embryonic-abembryonic axis of the mouse blastocyst: relationships between orientation of early cleavage divisions and pattern of symmetric/asymmetric divisions[END_REF][START_REF] Katayama | The effect of superovulation on the contributions of individual blastomeres from 2-cell stage CF1 mouse embryos to the blastocyst[END_REF][START_REF] Liu | Early patterning of cloned mouse embryos contributes to post-implantation development[END_REF]. Nevertheles, this theory has been debated suggesting that totipotency within the embryo blastomeres is maintained up to the 8-cell stage [START_REF] Alarcón | Deviation of the Blastocyst Axis from the First Cleavage Plane Does Not Affect the Quality of Mouse Postimplantation Development[END_REF][START_REF] Motosugi | Polarity of the mouse embryo is established at blastocyst and is not prepatterned[END_REF][START_REF] Waksmundzka | Allocation of Cells in Mouse Blastocyst Is Not Determined by the Order of Cleavage of the First Two Blastomeres[END_REF][START_REF] Kurotaki | Blastocyst Axis Is Specified Independently of Early Cell Lineage But Aligns with the ZP Shape[END_REF][START_REF] Alarcón | Spatial alignment of the mouse blastocyst axis across the first cleavage plane is caused by mechanical constraint rather than developmental bias among blastomeres[END_REF][START_REF] González | Influence of early fate decisions at the two-cell stage on the derivation of mouse embryonic stem cell lines[END_REF][START_REF] Wennekamp | A self-organization framework for symmetry breaking in the mammalian embryo[END_REF]. It is still unclear if mammalian embryos are pre-patterned or the presence of stochastic development is just a reflex of the great plasticity of mammalian embryos. Research performed on cell allocation patterns suggest that it might be a common characteristic during pre-implantation embryo development of different mammalian species [START_REF] Park | The leading blastomere of the 2-cell stage parthenogenetic porcine embryo contributes to the abembryonic part first[END_REF][START_REF] Hosseini | The Principal Forces of Oocyte Polarity Are Evolutionary Conserved but May Not Affect the Contribution of the First Two Blastomeres to the Blastocyst Development in Mammals[END_REF][START_REF] Sepulveda-Rincon | Random Allocation of Blastomere Descendants to the Trophectoderm and ICM of the Bovine Blastocyst[END_REF]. However, there is a lack of evidence on the mechanism(s) leading to these cell allocation patterns. In this work, the murine model is used to investigate the cell allocation pattern incidence among two different mouse strains and the effects of embryo blastomere removal at the cleavage stage on these patterns. Additionally, we investigated the effect of cell allocation patterns on further embryo development and organ morphometry using the murine model because of its short gestational period.

MATERIALS AND METHODS

All experiments were performed according to the Animals Scientific Procedures Act, 1986 under the Home Office licence 40/3480 and with the approval of the Bio Support Unit at the University of Nottingham. Two different experiments were performed during the present study. First, the effects of single blastomere removal at the 8-cell stage on cell allocation patterns were studied using two different mouse strains. Second, the effects of cell allocation patterns on further embryo development were addressed.

Mouse embryo production

For biopsy experiments B6CBAF1 x B6CBAF1 fresh embryos and B6C3F1 x B6D2F1 frozen/thawed embryos were used. First, 5 to 7 weeks old B6CBAF1 females (Charles River, UK) were superovulated with one peritoneal injection of 5 IU pregnant mare serum gonadotropin (PMSG, Intervet, Buckinghamshire, UK) followed by one peritoneal injection of 5 IU human chorionic gonadotropin (hCG, Intervet, Buckinghamshire, UK) after 48 hours. After hCG injection, females were placed with males of the same strain and vaginal plugs were checked the following morning. Females were sacrificed by cervical dislocation and embryos were collected at one-cell stage at 22 to 24 h post hCG. Embryos were collected in EmbryoMax Hepes medium (Merck Millipore), previously equilibrated at 37°C. In order to compare the obtained results a different mouse strain was used, B6C3F1 x B6D2F1. One cell frozen B6C3F1 x B6D2F1 mouse embryos (Embryotech Laboratories, Inc., Massachusetts, USA) were thawed in EmbryoMax Hepes medium (Merck Millipore) according to supplier's instructions. After embryo thawing, embryos were cultured in KSOM medium (Merck Millipore) under mineral oil (Merck Millipore) at 37°C and 5% CO2. For the second part of the study, the embryo transfer experiment, only frozen/thawed B6C3F1 x B6D2F1 embryos were used.

Non-invasive Cell tracing method

As previously reported [START_REF] Sepulveda-Rincon | Random Allocation of Blastomere Descendants to the Trophectoderm and ICM of the Bovine Blastocyst[END_REF], the lipophilic tracer CM-DiI (Chloromethyl DiI, Molecular probes) was dissolved in olive oil at a final concentration of 2 mg/ml. Prior to labelling, the FemtoTip II (Eppendorf, Germany) was backfilled with the dye. Mouse embryos at 2-cell stage were placed in HEPES buffered medium at 37°C during the micromanipulation. The injections were performed on an inverted microscope (Leica DMI3000 B, Germany) using Eppendorf TransferMan NK 2 micromanipulators with a coupled Eppendorf FemtoJet microinjector. The micropipette was pushed through the zona pellucida and pressed against one of the blastomere membranes, and then a microdrop (≈ 5 pl) was deposited.

Cleavage stage embryo biopsy

Mouse embryos were assessed at 68-72 h post-hCG or 43-45 h post-thawing. Then, 6-to 8-cell embryos were randomised for biopsy. The selected embryos were transferred to a pre-warmed 60 mm ICSI dish (BD Falcon) containing 10 µl drops of G-PGD medium (Vitrolife) under mineral oil (Merck Millipore). Briefly, embryo biopsy was performed using a 40x XYclone laser objective (Hamilton Thorne Biosciences, MA, USA) mounted on a Leica DMI3000 B inverted microscope. A single blastomere was randomly removed and the resulting biopsied embryos were further cultured in culture medium until the blastocyst stage under culture conditions. For morphokinetic analysis embryos were cultured in a time lapse imaging incubator (EmbryoScope, Vitrolife, Denmark).

Blastocyst assessment

Cell allocation patterns

Blastocysts were scored for the different pattern categories as described previously [START_REF] Sepulveda-Rincon | Random Allocation of Blastomere Descendants to the Trophectoderm and ICM of the Bovine Blastocyst[END_REF]. Briefly, blastocysts were placed in 5 µl EmbryoMax Hepes (Merck Millipore) medium drops on 60 mm petri dish and on a Leica DMI3000 B inverted microscope, coupled with red fluorescent filters corresponding to maximum excitation/emission wavelengths of 553 nm and 570 nm respectively. For better visualisation, embryos were rotated in order to place the blastocoel cavity floor and the boundary line between the fluorescent and non-fluorescent cells in the same focal plane. Then, embryos were classified into three categories: orthogonal, if the Em-Ab axis was orthogonal ± 30° to the boundary line between stained and non-stained cells; deviant, if it was ± 30° to the Em-Ab axis and random, if stained cells were intermingled with non-stained cells and more than 2 clusters of cells were observed.

Blastocyst total cell count

Blastocysts were permeabilised in 0.1% Triton-100X/PBS during two minutes at room temperature and then rinsed twice in phosphate buffered saline (PBS). Finally, embryos were mounted on a SuperFrost microscope slide using Vectashield-DAPI as mounting medium and nuclear staining. Total cell count was effectuated on a Nikon Eclipse Ti 90x microscope, along with a Hamamatsu digital camera (C4742-80-12AG) and a fluorescent filter corresponding to the excitation 350 nm and 470 nm of emission for DAPI.

Blastocyst expansion grading

Blastocysts for embryo transfer were graded according to their blastocoel expansion according to the Gardner and Schoolcraft grading system. Blastocysts which the blastocoel cavity was half or it completely fills the embryo were classified as Grade ≤ 3; Grade 4 blastocysts were those which the blastocoel cavity fully fills the embryo and this was bigger than the original volume and zona pellucida thinning was observed; Grade 5 blastocysts which some cells are herniating through the zona pellucida.

Non-surgical embryo transfer

Nine to eleven weeks old CD1 female mice were placed with > 10 weeks old vasectomised CD1 males. Then, 2.5 days post coitus (dpc) pseudo-pregnant females were used as surrogates for embryo transfer. The protocol suggested on the non-surgical embryo transfer (NSET) device (ParaTechs, USA) was followed. Briefly, after cell allocation pattern classification, embryos were transferred by groups to 15 µl drops of KSOM previously equilibrated at 37°C. Then, 13 to 18 blastocysts were loaded into the NSET device and it was inserted into the mouse cervix where embryos were released. After embryo transfer, foster females were caged individually and pregnancy was visually assessed on day 14 after embryo transfer.

Offspring assessment

Pups were weighed and sexed at 1 week after birth. Furthermore, pups were culled 2 weeks after birth by cervical dislocation, weighed and dissected. Different organs (spleen, pancreas, kidneys, liver, lungs and heart) were carefully dissected and weighed immediately after harvesting. Relative organ weights were calculated dividing organ weight by total body weight. Foster mothers were also sacrificed by cervical dislocation. Then, uteri were harvested and implantation sites were noted.

Statistical analysis

Data distribution was checked for normality by Shapiro-Wilk test and using SPSS v23 (IBM Software Services, Hamshire, UK). Presented values are mean value ± standard error of mean. For values reporting cell allocation pattern incidence, SEM was calculated based on number of repetitions of the experiment. Whereas, for values reporting TCC, SEM was calculated based on total number of embryos analysed. Statistical significance was set at p < 0.05 for all analyses. Blastocysts incidence rates within the different cell allocation patterns were compared using ANOVA test for single or two factor as needed. Post Hoc Bonferroni test was used when adequate. Non parametric test, Kruskal Wallis, was used to determine any differences among groups for pregnancy, pregnancy loss, mean live birth, live offspring rates as well as litter size comparison. Also, non-parametric test Kruskal Wallis was used to determine any differences on relative organ weights among groups; when adequate Mann Whitney U test was used to compare groups against each other.

RESULTS

Cleavage stage embryo biopsy does not disturb cell allocation patterns

A total of 287 B6CBAF1 x B6CBAF1 blastocysts in the control group and 214 blastocysts in the biopsied group were successfully classified according to their cell allocation pattern as previously reported on (Sepulveda-Rincon et al. 2016) (Figure 1). Orthogonal embryos represented 21 ± 5.4% and 19% ± 3.6 of the blastocysts within the control and the biopsied group respectively. The deviant group represented 21 ± 3.9% and 23 ± 3.6% and the random group 58 ± 4.8% and 59 ± 4.6% for the control and biopsied group respectively (Figure 2a). Univariate two way ANOVA showed no significant differences between treatment: control and biopsied groups (p = 0.973). However, there is a significant difference on the incidence of the cell allocation patterns (p < 0.001). Post Hoc Bonferroni test revealed that this difference is mainly attributed to the difference between the incidence of the random group compared with the orthogonal (p < 0.001) and deviant (p < 0.001). Morphokinetic analysis after blastomere removal (Supplementary Table 1) revealed that there are no differences between patterns among the control group (p < 0.05); however there is not the case among the biopsied group (p = 0.012). Orthogonal embryos spend longer time on the interval from 8-cell stage to 9-cell stage (p = 0.011) when compared with deviant embryos. Also, orthogonal embryos spend longer time between compaction and the start of cavitation when compared with deviant (p = 0.003) and random embryos (p = 0.012).

In order to address if the biopsy procedure has an effect on the size of the embryo at blastocysts stage, total cell counts (TCC) of blastocysts were calculated. Embryos from the orthogonal group presented a TCC of 45.8 ± 0.2 cells and 41.2 ± 0.5 cells within the control and biopsied group respectively. Deviant embryos presented a TCC of 50.4 ± 0.6 and 42.0 ± 0.4 for control and biopsied group; while random embryos presented a TCC of 47.9 ± 0.2 and 43.5 ± 0.2. Univariate test showed no significant difference on the TCC among the three patterns (p = 0.490). Still, there was a significant difference on the TCC between the control and the non-biopsied groups (p = 0.002). Post Hoc Bonferroni test suggested that this difference is mainly attributed to the effect of biopsy on the TCC of the deviant group (p = 0.028).

Similar results were obtained when repeating the above experiment on B6C3F1 x B6D2F1 frozen/thawed embryos. A total of 69 blastocysts in the control group and 82 blastocysts in the biopsied group were classified where 23 ± 2.9% and 26 ± 4.2% were orthogonal in the control and biopsied groups respectively, 26 ± 3.4% and 23 ± 0.7% were deviant, and 51 ± 3.5% and 50 ± 3.9% were random (Figure 2b). No significant differences were found on the incidence of the different cell allocation patterns between treatment groups (p > 0.05). However, random embryos remained more predominant (p < 0.001) when compared with orthogonal and deviant embryos in both treatment groups. Morphokinetic analysis did not show any difference among cell allocation patterns in control and biopsied groups (p < 0.05) and even though a tendency of orthogonal embryos spending longer time between the 8-cell stage to the 9-cell stage, significance was not reached (p = 0.056, Supplementary Table 1). TCC at blastocyst stage were similar among cell allocation patterns in the control group (p = 0.683) or the biopsied group (p = 0.932). Again, significant difference was found on the TCC between control and biopsied group (p = 0.002) and it was attributed to the decreased of TCC of deviant embryos after biopsy (p = 0.030). Orthogonal embryos presented 49.8 ± 2.8 cells and 45.5 ± 1.4 cells for control and biopsied groups respectively, deviant embryos presented 52.1 ± 2.6 cells and 45.6 ± 1.5 cells and random embryos presented 50.0 ± 1.9 cells and 46.3 ± 1.2 cells respectively.

Body weight and organ development might be affected by cell allocation patterns during preimplantation embryo development

As cell allocation patterns were not disturbed by cleavage stage embryo biopsy, further analysis on the effect of these patterns without the biopsy procedure was investigated. During three repetitions of the experiment, a total of 323 blastocysts were successfully classified into orthogonal, deviant or random accordingly to their cell allocation pattern with an incidence of 27.0 ± 4.7%, 28.3 ± 5.2% and 52.3 ± 7.2% respectively.

In order to observe if there was the same distribution on blastocysts size within groups, blastocyst expansion grades were noted. Expansion grades were similar between orthogonal (n = 83), deviant (n = 85) and random (n = 157) groups (p = 0.717 for grade ≤ 3, p = 0.917 for grade 4 and p = 0.734 for grade 5 among groups by ANOVA test). The majority of the blastocysts were graded as grade 4; 57.8% for orthogonal, 60% for deviant and 57.3% for random groups. Smaller proportions of blastocysts grade 5 and ≤ 3 were found within the groups; 21.7% and 20.5% for orthogonal, 23.5% and 16.5% for deviant, 24.9% and 17.8% for random groups respectively. Seventeen 2.5 dpc pseudo-pregnant females were used to transfer a total of 275 blastocysts. Due to the higher incidence of embryos classified as random, more foster mothers were used in this group. Nevertheless, the transferred blastocyst number within the three repetitions of the experiment remained constant within the three groups (18, 13 and 16 blastocysts per female for the first, second and third repetition respectively). No significant differences were found between groups for pregnancy rates, implantation rates, pregnancy loss rate, litter size or live offspring rates (Table 1) (p > 0.05 by Kruskal Wallis test).

Significant difference was found (p = 0.028) among groups when 7 days old pups weights were compared. Mann Whitney U test revealed that pups from deviant group were significantly lighter (5.60 ± 0.3 g) when compared with pups from random group (p = 0.015, 6.55 ± 0.1 g), but not when compared to orthogonal group (p = 0.230, 6.28 ± 0.3 g). Fourteen days old pups weights did not vary between groups where orthogonal, deviant and random pups weighed 11.10 ± 0.4 g, 9.77 ± 0.4 g and 10.8 ± 0.2 g respectively. It is worth noting that within the deviant group male pups (n = 5) were significantly heavier than female ones (n = 3, p < 0.05, Mann Whitney U test) during the first and second week measurements (6.2 ± 0.2 g, 10.4 ± 0.3 g and 4.6 ± 0.1 g, 8.56 ± 0.2 g respectively).

Relative organ weights from 2 week old mice showed no significant differences (p > 0.05) among groups for lungs, liver, pancreas and spleen (Figure 3). However, a significant difference was found between groups (p < 0.05) for heart and kidneys relative weights (Figure 3). Pups within the deviant group presented significantly heavier relative heart weight when compared with orthogonal (p = 0.025) and random (p = 0.036) groups. The pups from the orthogonal group presented the lightest relative kidneys weight when compared with deviant (p = 0.043) and random (p = 0.025) groups. Mann Whitney U test was applied to determine if gender has an effect on relative organ weights within each group. The results showed no significant difference between genders within the three different groups (p > 0.05).

DISCUSSION

In the present study different cell allocation patterns during preimplantation development were not disturbed by single blastomere removal at 8-cell stage. These patterns might trigger different compensatory mechanism(s) against in vitro embryo manipulation and this may result in short and long term consequences for foetus or offspring born after embryo transfer; particularly in deviant embryos. This study raises some questions about the cardiovascular system and kidneys development during foetal development and how this might be affected or predisposed since early preimplantation embryo stages.

Pre-patterning in mouse embryos has been previously reported [START_REF] Gardner | The early blastocyst is bilaterally symmetrical and its axis of symmetry is aligned with the animal-vegetal axis of the zygote in the mouse[END_REF][START_REF] Piotrowska | Blastomeres arising from the first cleavage division have distinguishable fates in normal mouse development[END_REF][START_REF] Piotrowska | Early patterning of the mouse embryo -contributions of sperm and egg[END_REF][START_REF] Fujimori | Analysis of cell lineage in two-and four-cell mouse embryos[END_REF], Piotrowska-Nitsche & Zernicka-Goetz 2005[START_REF] Plusa | The first cleavage of the mouse zygote predicts the blastocyst axis[END_REF][START_REF] Zernicka-Goetz | Cleavage pattern and emerging asymmetry of the mouse embryo[END_REF]. In the present study, we confirm the presence and a comparable distribution of the three different cell allocation patterns in mouse blastocysts irrespective of mouse strain or embryo cryopreservation at 1-cell stage. These resuls are also in agreement with those previously reported in mouse, bovine and ovine embryos [START_REF] Hosseini | The Principal Forces of Oocyte Polarity Are Evolutionary Conserved but May Not Affect the Contribution of the First Two Blastomeres to the Blastocyst Development in Mammals[END_REF][START_REF] Sepulveda-Rincon | Random Allocation of Blastomere Descendants to the Trophectoderm and ICM of the Bovine Blastocyst[END_REF]. Embryo biopsy at the 8-cell stage, whether the biopsied cell is stained or not stained (data not shown), does not seem to alter the cell allocation patterns in mouse embryos similar to what we have previously reported in bovine embryos [START_REF] Sepulveda-Rincon | Random Allocation of Blastomere Descendants to the Trophectoderm and ICM of the Bovine Blastocyst[END_REF]. Assuming that intermingling of cells on the random patterned embryos starts around the fourth cell cycle as in bovine embryos, then these results suggest that cell allocation patterns might be established earlier in development than the 8-cell stage in mammalian embryos. Even though, cell allocation patterns were unaffected by the biopsy procedure, TCC at blastocyst stage were significantly affected in deviant embryos among two different mouse strains and also as previously reported in bovine embryos [START_REF] Sepulveda-Rincon | Random Allocation of Blastomere Descendants to the Trophectoderm and ICM of the Bovine Blastocyst[END_REF]. Hence, cell allocation patterns could be related with different compensatory mechanisms after cell removal. With still an increasing proportion of PGS and PGD procedures and more than ten thousand babies born after embryo biopsy procedures [START_REF] Peyvandi | Prenatal diagnosis and preimplantation genetic diagnosis: novel technologies and state of the art of PGD in different regions of the world[END_REF], further understanding of the effects of early embryo micromanipulation and follow up assessment is needed in order to establish the safety of ARTs in short and long term of development. Therefore, we investigated the effect of cell allocation patterns and its possible impact on further development.

Pregnancy rates in the present study were comparable between groups and in agreement with previously reported studies using NSET device obtaining pregnancy rates higher than 60% [START_REF] Cui | Transcervical embryo transfer in mice[END_REF]). However, there was no statistical difference between groups. It is worth noting that all surrogate females with transferred random blastocysts became pregnant. A possible theory is that random embryos might produce more hyaluronan promoting cell movements, which is released to the endometrium and cell migration and implantation might be facilitated [START_REF] Gardner | Lactate production by the mammalian blastocyst: Manipulating the microenvironment for uterine implantation and invasion?[END_REF]. Also, in the present study, two of the females carrying deviant embryos, presumably committed cannibalism due to problems at delivery or poor offspring health [START_REF] Wuensch | Cross-species fostering affects meat preferences of wild house mice[END_REF].

Similarly, embryo implantation rates were comparable between the three groups (around 40%) and are similar to those reported after surgical embryo transfer in mice [START_REF] Hemkemeyer | Effects of embryo culture media do not persist after implantation: a histological study in mice[END_REF]. On the other hand, the literature only reports two embryo classifications according to their cell allocation pattern: orthogonal and deviant. The results obtained in the present study are similar reporting no significant differences between groups regarding implantation rates [START_REF] Alarcón | Deviation of the Blastocyst Axis from the First Cleavage Plane Does Not Affect the Quality of Mouse Postimplantation Development[END_REF][START_REF] Liu | Early patterning of cloned mouse embryos contributes to post-implantation development[END_REF]). Nevertheless, our results differ from those in cloned mouse embryos where orthogonal embryos presented higher implantation rates in comparison with deviant ones [START_REF] Liu | Early patterning of cloned mouse embryos contributes to post-implantation development[END_REF]. Molecular pathways occurring during implantation and crosstalk between embryo and uterus are not clearly understood [START_REF] Wang | Roadmap to embryo implantation: clues from mouse models[END_REF][START_REF] Cha | Mechanisms of implantation: strategies for successful pregnancy[END_REF]. It is believed that some embryos do not survive embryo transfer procedure due to microenvironment changes and their inability to adapt [START_REF] Hemkemeyer | Effects of embryo culture media do not persist after implantation: a histological study in mice[END_REF]. Moreover, further research is needed in order to determine at which stage the implanted embryos were lost. Pregnancy loss rates in the present study were > 50% among groups. Pregnancy loss might be due to aberrant decidualisation; giving rise to placental defects [START_REF] Chen | Assisted reproduction causes placental maldevelopment and dysfunction linked to reduced fetal weight in mice[END_REF] and therefore affecting foetal growth [START_REF] Cha | Mechanisms of implantation: strategies for successful pregnancy[END_REF].

Total body weights at 7 days after birth were different among groups, where the pups from the deviant group presented the lowest weight. While some studies have reported low birth weight after ART when compared with natural conceived babies [START_REF] Ceelen | Growth during infancy and early childhood in relation to blood pressure and body fat measures at age 8-18 years of IVF children and spontaneously conceived controls born to subfertile parents[END_REF][START_REF] Bay | Is subfertility or fertility treatment associated with longterm growth in the offspring? A cohort study[END_REF], others have reported only a tendency [START_REF] Pontesilli | Subfertility and assisted reproduction techniques are associated with poorer cardiometabolic profiles in childhood[END_REF]. In mice, low birth weight has been linked to metabolic syndromes as type 2 diabetes, obesity and hypertension in adults [START_REF] Chen | Assisted reproduction causes placental maldevelopment and dysfunction linked to reduced fetal weight in mice[END_REF]. Fourteen days after birth, pups among the three groups presented similar total body weights. In humans, it has been reported that babies born with low weight "catch up" within the first 6 months of life [START_REF] Ceelen | Growth during infancy and early childhood in relation to blood pressure and body fat measures at age 8-18 years of IVF children and spontaneously conceived controls born to subfertile parents[END_REF][START_REF] Bay | Is subfertility or fertility treatment associated with longterm growth in the offspring? A cohort study[END_REF]. Moreover, no differences were found between male and female pups for orthogonal and random groups, only for deviant group. Gender differences have been reported for birth weights in babies after unassisted and assisted conception [START_REF] O'neill | Sex-related growth differences are present but not enhanced in IVF pregnancies[END_REF]. Further investigations on the long term health between females and males must be addressed as it has been suggested that mouse male offspring might present a higher risk of developing glucose intolerance after ART [START_REF] Donjacour | In Vitro Fertilization Affects Growth and Glucose Metabolism in a Sex-Specific Manner in an Outbred Mouse Model[END_REF]. In turn, glucose intolerance can develop into cardiovascular diseases which might affect males or females in a different way [START_REF] Vlasov | Dependence of the Heart Weight on the Body Weight in Patients with Cardiovascular Diseases[END_REF].

Organ morphometry assessment revealed significant differences among groups for relative weights of heart and kidneys. It is poorly understood why kidneys, blood vessels and the heart are the most affected by early life events [START_REF] Thornburg | The programming of cardiovascular disease[END_REF]. Relative heart weights within the deviant group were higher when compared with other groups. The increase of heart weight has been related with hyperfunction of the myocardium in humans [START_REF] Vlasov | Dependence of the Heart Weight on the Body Weight in Patients with Cardiovascular Diseases[END_REF] and with an increase on systolic blood pressure and ventricular mass in mice [START_REF] Donjacour | In Vitro Fertilization Affects Growth and Glucose Metabolism in a Sex-Specific Manner in an Outbred Mouse Model[END_REF]. Thus, our results on deviant pups might reflect further consequences on this cardiovascular phenotype and additional investigations could shed some light on how embryo preimplantation development influences the cardiovascular system. Among the long term effects of ART, cardiovascular problems are the most concerning health issue as an increased risk of developing cardiovascular diseases in comparison with naturally conceived babies has been reported [START_REF] Padhee | The Periconceptional Environment and Cardiovascular Disease: Does In Vitro Embryo Culture and Transfer Influence Cardiovascular Development and Health?[END_REF][START_REF] Pontesilli | Subfertility and assisted reproduction techniques are associated with poorer cardiometabolic profiles in childhood[END_REF].

One of the major limitations of this study is the small number of embryo transfers performed. Thus, although the results showed some evidence of effects of preimplantation cell behaviour on subsequent development, further studies are needed to reassure the presented data. Furthermore, it is suggested that a follow up offspring study is conducted in order to investigate in more depth the consequences of the obtained organ morphometry. Likewise, this work was carried out in mice and caution should be taken when translating the reported results in to humans.

In conclusion, the present study supports the theory that cell allocation patterns during pre-implantation embryo development could be a conserved mechanism in mammalian species at least in two different mouse strains. In addition, a latent concern has been rising about the effects of ART in further offspring health, especially long term effects. A better understanding on the effects of in vitro embryo micromanipulation on further development is paramount not only to improve success rates in ART, but also to ensure the health of resulting offspring.

FUNDING

PhD studies of LPSR are funded by CONACyT Mexico. 1. Morphokinetic analysis after blastomere removal. After cell tracing at the two-cell stage, single blastomere removal was performed at the 8-cell stage on the biopsied group, while the control group remained intact. At blastocyst stage embryos were classified into Orthogonal, Deviant and Random groups according to their cell allocation patterns. t8 to t9 interval correspond to the 8-to 9-cell stage during preimplantation, the interval of compaction to cavitation refers to the start of embryo compaction up to the start of cavitation and tB corresponds to the first sign of blastocoel formation.

Values are expressed in hours ± SEM (n). A: mouse strain B6CBAF1 x B6CBAF1, B: mouse strain B6C3F1 x B6D2F1 ▫ hours post-hCG, + hours post-thawing Different superscripts denote statistical significance (p<0.05) by two-way ANOVA and Bonferroni test between treatment groups and cell allocation patterns within the same mouse strain.

Figure 1 .

 1 Figure 1. Mouse embryo cell allocation patterns at blastocyst stage. a) Orthogonal embryos, the boundary (doted yellow line) of the stained and non-stained cells is orthogonal to the embryonicabembryonic (Em-Ab) axis (blue line); b) Deviant embryos, the boundary of stained and non-stained cells is parallel to the Em-Ab axis; and c) Random embryos, stained and non-stained cells are randomly distributed and no boundary line between them can be seen.

Figure 2 .

 2 Figure 2. Incidence of different cell allocation patterns across control and biopsied mouse embryos. A: Cell allocation pattern incidence in B6CBAF1 x B6CBAF1 blastocysts. B: Cell allocation pattern incidence in B6C3F1 x B6D2F1 blastocysts. *** Denotes statistical difference p < 0.001.

Figure 3 .

 3 Figure 3. Boxplots comparing the relative organ weights from 2 week old mice. a) Lungs, b) Liver, c) Pancreas, d) Spleen, e) Heart and and f) Kidneys. Relative organ weights were calculated diving the organ weight by the total body weight. A total of 45 pups were analysed: orthogonal (n=12), deviant (n=8) and random (n=25). No significant difference was found among groups for lungs, liver, pancreas and spleen. Heart and kidneys relative weights showed difference among groups (p<0.05 by Kruskal Wallis-Test). *Denotes statistical difference (p<0.05 by Mann-Whitney U-test).

Table 1 . Non-surgical embryo transfer results in mice.

 1 Total numbers and different rates (percentages) among groups are not significantly different (p>0.05 by Kruskal-Wallis test).

	Embryo group	Orthogonal	Deviant	Random
	Transferred	76	76	123
	blastocysts
	Surrogates	5	5	7
	Pregnancy rate	66.6%	83.3%	100.0%
	Implantation rate	42.3%	39.9%	50.7%
	Pregnancy loss rate	49.6%	79.1%	55.9%
	Total pups (litters)	12 (3)	8 (2)	25 (6)
	Mean litter (SD)	4.0 (2.6)	4.0 (1.4)	4.1 (2.2)
	Live offspring rate	14.7%	11.4%	22.9%

SD, standard deviation

Supplementary Table

t8 to t9 Compaction to Cavitation tB

	Mouse Strain	Group	Control	Biopsied	Control	Biopsied	Control ▫	Biopsied +
	A	Orthogonal	9.45±0.49 (16) a	10.54±0.47 (26) a,b	22.59±0.97 (20) a	22.03±0.84 (30) a,b	94.99±1.72 (20) a	96.92±0.87 (30) a
	A	Deviant	8.95±0.90 (19) a	8.66±0.47 (33) a,c	21.72±0.50 (20) a	22.01±0.48 (30) a,c	95.31±0.90 (20) a	94.27±0.86 (32) a
	A	Random	9.03±0.42 (56) a	9.70±0.25 (80) a	22.28±0.64 (57) a	22.56±0.45 (73) a	95.48±0.68 (59) a	94.53±0.42 (80) a
	B	Orthogonal	9.37±0.42 (14) a	10.18±0.65 (13) a	20.94±0.92 (10) a	20.94±0.74 (14) a	72.75±1.66 (16) a	70.05±1.00 (23) a
	B	Deviant	7.26±0.80 (14) a	8.52±0.62 (9) a	22.30±1.16 (13) a	22.11±1.44 (13) a	73.76±1.28 (18) a	70.65±1.50 (19) a
	B	Random	7.74±0.34 (26) a	8.35±0.64 (25) a	22.35±0.81 (29) a	24.51±1.12 (22) a	72.78±0.83 (35) a	73.11±1.04 (40) a

ACKNOWLEDGEMENTS

We would like to thank the Bio Support Unit at the University of Nottingham for husbandry of rodents during this study and to senior technician Ms Anne Skinner for her experienced help on dissecting the mouse pups.


Martin Quque

Olivier Bles

Annaëlle Bénard

Amélie Héraud

Bastien Meunier

François Criscuolo

Jean-Louis Deneubourg

Cédric Sueur
email: cedric.sueur@iphc.cnrs.fr

Hierarchical networks of food exchange in the black garden ant Lasius niger

Keywords: insects, network evolution, self-organisation, social evolution, social network analyses

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

There are many well-known advantages to living in societies: protection against predators, more efficient discovery of food sources and better access to information [START_REF] Krause | Living in Groups[END_REF]. Another benefit of group living is food sharing [START_REF] Isaac | The food-sharing behavior of protohuman hominids[END_REF][START_REF] Kaplan | Food sharing among ache foragers: Tests of explanatory hypotheses [and comments and reply[END_REF][START_REF] De Waal | Food sharing and reciprocal obligations among chimpanzees[END_REF][START_REF] Stevens | A conceptual framework for nonkin food sharing: Timing and currency of benefits[END_REF]. Food sharing can occur in both social and non-social species, and its evolutionary origins have been studied using the predictions of reciprocal altruism [START_REF] Trivers | The evolution of reciprocal altruism[END_REF], biological markets [START_REF] Noë | Biological markets[END_REF] and multilevel selection [START_REF] Traulsen | Evolution of cooperation by multilevel selection[END_REF].

Food exchange is central to many animal societies, including eusocial species such as ants, termites, bees and even naked mole rats [START_REF] Anderson | The evolution of eusociality[END_REF][START_REF] Jarvis | Mammalian eusociality: A family affair[END_REF][START_REF] Wilson | Eusociality: Origin and consequences[END_REF][START_REF] Nowak | The evolution of eusociality[END_REF]. In eusocial species, only a restricted number of individuals forage and retrieve food for the rest of the colony. Castes can be distinguished by . their behaviour and even by their proteome [START_REF] Quque | Division of labour in the black garden ant (Lasius niger) leads to three distinct proteomes[END_REF]. Given that trophallaxis, the mouth-to-mouth transfer of food, is the mechanism of food exchange, the exchange of food facilitates social recognition via the exchange of informative colony-specific hydrocarbons [START_REF] Boulay | Camponotus fellah colony integration : Worker individuality necessitates frequent hydrocarbon exchanges[END_REF], information on the location of food resources [START_REF] Gil | Olfactory learning by means of trophallaxis in Apis mellifera[END_REF][START_REF] Frasnelli | Asymmetry in antennal contacts during trophallaxis in ants[END_REF] and even immune-related molecules [START_REF] Hamilton | Trophallaxis and prophylaxis: Social immunity in the carpenter ant Camponotus pennsylvanicus[END_REF][START_REF] Leboeuf | Oral transfer of chemical cues, growth proteins and hormones in social insects[END_REF]. In the black garden ant (Lasius niger), the only food exchanged-aphid honeydew (Aphidoidea sp.)-is stored exclusively in the crop of individuals [START_REF] Buffin | Feeding and stocking up: Radio-labelled food reveals exchange patterns in ants[END_REF]. The foragers give food to non-forager workers (i.e., nest workers, hereafter called domestics), which may then transfer the food to other domestics, including caretakers of larvae. These chains of exchanges allow food to be disseminated throughout the nest, from the entrance to the deepest chambers [START_REF] Lee Cassill | Regulation of diet in the fire ant, Solenopsis invicta[END_REF][START_REF] Wilson | Quantitative studies of liquid food transmission in ants[END_REF].

At the entrance of the nest, the interactions between forager ants are fundamental as they regulate the dynamics of food harvesting [START_REF] Gordon | The organisation of work in social insect colonies[END_REF][START_REF] Pinter-Wollman | Persistent variation in spatial behavior affects the structure and function of interaction networks[END_REF][START_REF] Pinter-Wollman | The effect of individual variation on the structure and function of interaction networks in harvester ants[END_REF][START_REF] Schafer | Forager activation and food availability in harvester ants[END_REF]. However, domestics possess essential information on the colony's needs. Exchange between foragers and domestics is spatially confined within an area close to the entrance of the nest in both the wild [START_REF] Tschinkel | Vertical organisation of the division of labour within nests of the Florida harvester ant, Pogonomyrmex badius[END_REF] and the laboratory [START_REF] Mersch | Tracking individuals shows spatial fidelity is a key regulator of ant social organisation[END_REF]. For instance, in Pogonomyrmex badius, foragers represent less than 5% of ants inside the nest 20 cm from the entrance and are completely absent in regions 70 cm from the entrance [START_REF] Tschinkel | Vertical organisation of the division of labour within nests of the Florida harvester ant, Pogonomyrmex badius[END_REF]. This observation illustrates the spatial fidelity of castes and how this fidelity may affect network topology [START_REF] Pinter-Wollman | Persistent variation in spatial behavior affects the structure and function of interaction networks[END_REF][START_REF] Pinter-Wollman | The effect of individual variation on the structure and function of interaction networks in harvester ants[END_REF] through differences in the connectivity between colony members [START_REF] Jeanson | Long-term dynamics in proximity networks in ants[END_REF][START_REF] Mersch | Tracking individuals shows spatial fidelity is a key regulator of ant social organisation[END_REF].

To maximise fitness, the number of trophallaxes necessary to transfer food from foragers to the queen and larvae needs to be minimised to make the process of food exchange as fast as possible. Thus, efficient food exchange networks should be favoured by selection given . the restricted roles of each caste and their spatial distribution within the colony [START_REF] Sueur | Mechanisms of network evolution: a focus on socioecological factors, intermediary mechanisms, and selection pressures[END_REF]. However, ants do not have a single, optimal social network topology [START_REF] Camazine | Self-Organization in Biological Systems[END_REF]. Each colony member does not have to evaluate the needs of workers and the role of their activities in a task, as the trophallactic interactions spread relevant information through the entire colony [START_REF] Grüter | Propagation of olfactory information within the honeybee hive[END_REF]. Nevertheless, ants are known to have collective cognition [START_REF] Couzin | Collective cognition in animal groups[END_REF] or swarm intelligence [START_REF] Bonabeau | Swarm Intelligence: From Natural to Artificial Systems[END_REF]. As a result, simple interaction rules can explain the construction of complex structures, such as the Towers of Hanoi [START_REF] Reid | Optimisation in a natural system: Argentine ants solve the Towers of Hanoi[END_REF] and how ants make bridges [START_REF] Reid | Army ants dynamically adjust living bridges in response to a cost-benefit trade-off[END_REF]. [START_REF] Stroeymeyt | Social network plasticity decreases disease transmission in a eusocial insect[END_REF] showed that the interactions of ants can be modified to mitigate the spread of disease, as the network centralities of ants are critically important for the transmission of infections [START_REF] Romano | Modeling infection transmission in primate networks to predict centrality-based risk[END_REF]. This behavioural plasticity permits the topology of the interaction network to be modified so that the network can become less efficient (for definitions of network efficiency, see [START_REF] Ek | Global efficiency of graphs[END_REF][START_REF] Pasquaretta | Social networks in primates: Smart and tolerant species have more efficient networks[END_REF][START_REF] Romano | Social transmission in networks : Global efficiency peaks with intermediate levels of modularity[END_REF] and more modular to prevent epidemics. This social immunity is well known in eusocial insects [START_REF] Cremer | Social immunity[END_REF][START_REF] Cremer | Social immunity in insects[END_REF][START_REF] Liu | The mechanisms of social immunity against fungal infections in eusocial insects[END_REF][START_REF] Małagocka | Social immunity behaviour among ants infected by specialist and generalist fungi[END_REF] but has also been documented in other taxa, such as primates, where this phenomenon has been called the social bottleneck hypothesis [START_REF] Nunn | Infectious disease and group size: More than just a numbers game[END_REF][START_REF] Romano | The trade-off between information and pathogen transmission in animal societies[END_REF][START_REF] Romano | Social transmission in networks : Global efficiency peaks with intermediate levels of modularity[END_REF].

Despite the central role that trophallactic interactions play in the regulation of food flow in eusocial species, the way that chains of demands are established and how they ultimately impact network topology have been largely unexplored. Furthermore, most previous studies on these subjects have not considered the individuality and identity of the trophallactic partners [START_REF] Buffin | Collective regulatory stock management and spatiotemporal dynamics of the food flow in ants[END_REF]. One of the first studies to analyse the entire trophallactic network demonstrated a spatial reorganisation of worker positions facing starvation that accelerated the recovery of food stocks [START_REF] Sendova-Franks | Emergency networking: Famine relief in ant colonies[END_REF]. [START_REF] Waters | Information processing in social insect networks[END_REF] identified individuals and antenna interactions in Pogonomyrmex californicus and . concluded that the regulatory motif of interactions they observed supports the hypothesis that eusocial insects are shaped by selection for network patterns that integrate functionality at the group (i.e. colony) level rather than at the individual level. Lastly, [START_REF] Greenwald | Ant trophallactic networks: Simultaneous measurement of interaction patterns and food dissemination[END_REF][START_REF] Greenwald | Individual crop loads provide local control for collective food intake in ant colonies[END_REF] assessed the role of foragers and non-foragers in the dissemination of food; however, these studies did not take into account the global state of the colony or conduct a thorough analysis of the network topology of trophallactic interactions.

Given that self-organisation results in the emergence of adapted complex systems [START_REF] Camazine | Self-Organization in Biological Systems[END_REF][START_REF] Fisher | Insights from the study of complex systems for the ecology and evolution of animal populations[END_REF], we tested for the efficiency of trophallaxis networks in garden black ants. Specifically, we evaluated whether food was exchanged nonrandomly (e.g., unpredictability in the direction and time of trophallaxes), expecting that the pattern of food dissemination maximises the speed with which food circulates through the colony. In addition, we conducted laboratory experiments in which we monitored the behaviour of foragers in colonies of varying sizes and with and without broods. Overall, we tested for the effects of three main factors: brood presence, the forager/domestic ratio and behaviour (which were also response variables) and colony size. Each ant was followed during the entire test using QR codes [START_REF] Garrido-Jurado | Automatic generation and detection of highly reliable fiducial markers under occlusion[END_REF][START_REF] Stroeymeyt | Social network plasticity decreases disease transmission in a eusocial insect[END_REF], and all trophallaxes were scored. We used social network analyses to study the efficiency of food dissemination. Combining experimentation with network analyses, especially in social insects, is a powerful tool for studying the evolution of complex systems [START_REF] Charbonneau | Social insects: A model system for Nnetwork dynamics[END_REF][START_REF] Mersch | The social mirror for division of labour: What network topology and dynamics can teach us about organisation of work in insect societies[END_REF][START_REF] Sueur | Editorial: Social interaction in animals: Linking experimental approach and social network analysis[END_REF]. We made three major alternative hypotheses concerning the network properties of trophallactic exchanges (Fig. 1):

(A) Interactions are random, and foragers have the same social centralities as domestics.

Confirmation of this null hypothesis would suggest that trophallaxes do not play an important role in food exchange. We did not expect to find random networks.

. (B) Food exchange occurs exclusively between foragers and domestics. This hypothesis predicts that foragers should show higher centralities than domestics.

(C) Foragers transfer food to domestics, but some intermediary domestics are involved in the chain of food dissemination. This hypothesis predicts that these intermediary domestics should show forager-like centralities. Thus, these intermediary individuals would provide the link between the source (foragers) and the final destination of food.

We used different social network indices to assess these predictions (see Table S1). We expected colony size to affect the network topology, as previous studies have shown that centralisation and modularity increases with colony size [START_REF] Pasquaretta | Social networks in primates: Smart and tolerant species have more efficient networks[END_REF][START_REF] Nunn | Infectious disease and group size: More than just a numbers game[END_REF]. Efficiency should be stable because, theoretically speaking, efficiency should decrease with network size [START_REF] Romano | Social transmission in networks : Global efficiency peaks with intermediate levels of modularity[END_REF]; however, ants are capable of modifying their division of labour depending on the size of the colony [START_REF] Jeanson | Emergence of increased division of labour as a function of group size[END_REF][START_REF] Holbrook | Division of labour increases with colony size in the harvester ant Pogonomyrmex californicus[END_REF][START_REF] Modlmeier | Ant colonies maintain social homeostasis in the face of decreased density[END_REF]. Furthermore, the presence of broods is expected to modify the structure of the network, as broods affect both the nutritional needs of the colony and thus the demand for foragers [START_REF] Portha | Self-organized asymmetries in ant foraging: A functional response to food type and colony needs[END_REF]. Because the presence of broods adds a level of food dissemination, brood presence should have an impact on both individual and global network indices with either the same ratio of foragers contributing more work (e.g., via higher efficiency and higher centralisation) or more foragers decentralising the network.

Materials and methods

Ant colony setup

We created 52 queenless subcolonies of 11 to 120 workers, with and without broods (see details below) from 12 wild and large mother colonies (> 1000 ants) of Lasius niger collected in Brussels, Belgium during the autumn of 2016. We formed the subcolonies after the colonies had been in the lab for 18 months years to decrease the potential effect of temporal . polyethism. We tested queenless colonies for simplicity; several studies have shown that the absence of the queen does not affect the interactions between workers and the shape of the food dissemination network [START_REF] Holbrook | Division of labour increases with colony size in the harvester ant Pogonomyrmex californicus[END_REF][START_REF] Jeanson | Long-term dynamics in proximity networks in ants[END_REF][START_REF] Bazazi | Responses to nutritional challenges in ant colonies[END_REF][START_REF] Bles | Food dissemination in ants : Robustness of the trophallactic network against resource quality[END_REF]. These colonies were tested in an experimental enclosure (Fig. 2A). The dimensions of the experimental enclosure were 17.5 × 12.5 × 5 cm. The walls of the foraging area were covered with Fluon®, in addition to a glass covering the tray, to prevent ants from escaping. Ants were placed in these trays for 10 days so that they could acclimate until the repartitioning of tasks among individuals stabilised. Although the division of labour is flexible according to the needs of the colony, several other studies have suggested that 10 days is enough for the caste of each ant to stabilise [START_REF] Sendova-Franks | Task allocation in ant colonies within variable environments (A study of temporal polyethism: Experimental)[END_REF][START_REF] Huang | Regulation of honey bee division of labour by colony age demography[END_REF][START_REF] Amdam | Social reversal of immunosenescence in honey bee workers[END_REF][START_REF] Baker | Age-related learning deficits can be reversible in honeybees Apis mellifera[END_REF]. The colonies were kept at 22 ± 3 °C and 60% ± 5% relative humidity, with a constant 12 : 12 h photoperiod.

The experimental enclosure was divided into two parts: the nest area and the feeding area.

Two food sources were placed in the feeding area at equal distances relative to the nest entrance: 0.3 mol/L of milk powder and 0.3 mol/L of sucrose. The position of the food sources relative to the nest entrances (i.e. left or right) was randomised. Ants were starved for 5 days in the nest area before experiments to increase foraging activity and the rate of trophallaxis. The experiments ran for one hour. Video data were recorded using a Panasonic® Lumix DMC-GH4-R mounted with a 30-mm Olympus® ED lens capturing 25 frames/s at a resolution of 4180×2160 p.

Ant identification through QR codes

Labelling of ants with Aruco tags (QR codes, Garrido-Jurado et al., 2014), along with the software USETracker (https://sites.google.com/site/usetrackerac/), allowed individual ants to . be identified continuously (Fig. 2B). Ants were placed in the freezer until they were inert (about one minute). Each unique tag was then stuck to the abdomen and had a side length of 0.8 mm, weighed 0.1 mg (corresponding to approximately 5% of the average mass of an adult worker or less than 10% of the amount of food that a worker carries) and was printed on waterproof paper at a resolution of 1200 dpi. The tags were hand-cut using a scalpel and a steel ruler as a guide. Following a 5-min acclimatisation period, the labelling did not appear to impede the ant behaviours, movements or interactions. We discriminated foragers from domestics. An individual was considered a forager if it spent at least 5 consecutive seconds feeding at the food source (not in the feeding area but at either one of the two food sources or both) during the experiment. This discrimination was possible by analysing the position of each individual per frame during the experiment (see Fig. S1).

Data scoring

Each trophallaxis that occurred in the entire observation area, its duration as well as the identities (unique tag) and caste (forager vs. domestic) of both the donor and the receiver ant were scored. A trophallactic event was recorded when ants engaged in mandible-to-mandible contact for greater than 2 seconds (the minimum time needed to exchange a piece of food).

The directionality of the food flow and the role of the donor and the receiver were determined by body posture and mandible positions: The donor opens her mandibles and displays a droplet of sucrose solution between them while the receiver turns and moves her head forward to receive it [START_REF] Greenwald | Ant trophallactic networks: Simultaneous measurement of interaction patterns and food dissemination[END_REF][START_REF] Lee Cassill | Regulation of diet in the fire ant, Solenopsis invicta[END_REF].

We only analysed videos where 100% of the trophallaxis interactions could be identified.

Of the 52 experimental runs, a total of 34 videos were analysed. Each of the 12 colonies was tested 2.8 ± 1.1 times (min = 1, max = 5). On the 34 videos, broods were present in 21 colonies and absent from 13 (proportion per colony: 0.66 ± 0.24). The colony size ranged . from 11 to 120 ants (mean = 42 ± 26). Colony replications were incorporated into the statistical analyses. Different observers scored the videos; however, we found that there was weak inter-observer bias, as an inter-observer reliability test on eight videos revealed that the minimum score that we observed was 88.5% (generally, reliability scores greater than 80% are considered sufficient ;[START_REF] Hartmann | Considerations in the choice of interobserver reliability estimates[END_REF][START_REF] Watkins | Interobserver agreement in behavioral research : importance and calculation[END_REF][START_REF] Borgeaud | Intergroup variation of social relationships in wild vervet monkeys: A dynamic network approach[END_REF].

Social network measures

General statements For each test, an edgelist was created with the trophallaxis time from individual i to individual j as the edge strength. The network was directed and weighted. We then calculated different individual and global measures using the ANTs [START_REF] Sosa | A multilevel statistical toolkit to study animal social networks: Animal Network Toolkit (ANT) R package[END_REF] and igraph [START_REF] Csardi | The igraph software package for complex network research[END_REF]) R packages. We avoided measures that were not interpretable with the directionality of the edges (see [START_REF] Mersch | The social mirror for division of labour: What network topology and dynamics can teach us about organisation of work in insect societies[END_REF][START_REF] Sueur | How can social network analysis improve the study of primate behavior?[END_REF][START_REF] Sosa | Network measures in animal social network analysis : Their strengths, limits, interpretations and uses[END_REF]; instead, we selected those that allowed us to make expectations based on our three aforementioned hypotheses. Table S1 shows the different indices and their associated expectations.

Global network measures

The global measures included maximum modularity, the centralisation index, global efficiency and resilience. Maximum modularity is the strength of subgrouping or division of a network into modules or clusters [START_REF] Newman | Analysis of weighted networks[END_REF]. It ranges from 0 to 1 with 0 corresponding to a network where all individuals are equally connected and indices close to 1 corresponding to networks where the number and strengths of connections between individuals of different subgroups are low. The centralisation index captures the strength of centralisation of a network towards one or several individuals and how these central individuals gather relationships [START_REF] Sueur | Fast and accurate decisions as a result of scale-free network properties in two primate species[END_REF][START_REF] Pasquaretta | Social networks in primates: Smart and tolerant species have more efficient networks[END_REF]. It ranges from 0 to 1 with 0 for corresponding to an equal network (i.e. all individuals are equally connected) and 1 for a star network (i.e. individuals are all connected to a single . central individual). Global efficiency is the strength or speed of the exchange of entitiesinformation or food-throughout the network [START_REF] Latora | Efficient behavior of small-world networks[END_REF][START_REF] Ek | Global efficiency of graphs[END_REF].

Specifically, global efficiency equals N/(I×D) where N is the number of nodes, I is the number of edges and D is the network diameter. In other words, global efficiency indicates how quickly an entity is transmitted from the spreader (i.e. source) to the most peripheral individual in the group via the fewest number of connections. Global efficiency can range from 0 to 1, with more efficient networks having values closer to 1 [START_REF] Romano | Social transmission in networks : Global efficiency peaks with intermediate levels of modularity[END_REF].

Finally, we calculated resilience by dividing global efficiency by the centralisation index [START_REF] Naug | Structure and resilience of the social network in an insect colony as a function of colony size[END_REF][START_REF] Puga-Gonzalez | Social style and resilience of macaques' networks, a theoretical investigation[END_REF]. Resilience assesses whether the strength or speed of the exchange of food can be maintained in the absence of central individuals, generally called bridges or hubs [START_REF] Kitsak | Identification of influential spreaders in complex networks[END_REF].

Individual network measures

The individual network measures included the degree (the number of edges of a node; i.e. the number of individuals giving or receiving trophallaxes from an ant), strength (the total time of trophallaxes of an ant; here we considered in-strength, the total time of trophallaxes received, and out-strength, the total time of trophallaxes given), betweenness (the number of shortest paths passing by a node; i.e. how many individuals an ant connects) and the clustering coefficient (whether individuals with which an ant exchanges food also exchange food). Detailed explanations of these different measures have been provided by previous reviews and books on animal networks [START_REF] Whitehead | Analysing animal social structure[END_REF][START_REF] Croft | Exploring Animal Social Networks[END_REF][START_REF] Sueur | How can social network analysis improve the study of primate behavior?[END_REF][START_REF] Sosa | Network measures in animal social network analysis : Their strengths, limits, interpretations and uses[END_REF]

Statistical analysis

Food exchanges We first analysed the direction of trophallaxes between foragers and domestics. We used the ratio between the in-strength and out-strength to assess whether one . caste gave more than it received (ratio > 1) or received more than it gave (ratio < 1). We used a student t-test to test for differences between the two castes.

We used linear mixed models (package lme4 in R, [START_REF] Bates | lme4: Linear mixed-effects models using Eigen and S4[END_REF] to test for the effect of brood presence and colony size on global variables, such as the number of trophallaxes, the duration of trophallaxes and the forager/domestic ratio. Colony origin was included as a random effect. Data for all response variables were normally distributed (Shapiro-Wilk normality test, W>0.93, P > 0.074). Therefore, all models were type-III ANOVAs using Satterthwaite's method and had normally distributed residuals.

Global and individual network measures

We then analysed the effect of brood presence, the number of individuals and the forager/domestic ratio for the global network measures (e.g., centralisation, global efficiency, modularity and resilience) as well as the caste (forager or domestic) for the individual network measures (e.g., degree, strength, betweenness and the clustering coefficient). Because data on the interactions and the network measures were not independent, we used Monte Carlo Markov Chain GLMM (package MCMCglmm in R, [START_REF] Hadfield | MCMC methods for multi-response generalized linear mixed models: The MCMCglmm R package[END_REF]. This approach is a powerful and standard technique for comparing statistical models based on the original data observed to distributions of null models based on randomised data [START_REF] Pasquaretta | Social networks in primates: Smart and tolerant species have more efficient networks[END_REF][START_REF] Balasubramaniam | The influence of phylogeny, social style, and sociodemographic factors on macaque social network structure[END_REF][START_REF] Sosa | Impact of group management and transfer on individual sociality in highland cattle (Bos taurus)[END_REF]. We ran MCMCglmm models for a minimum of 43 000 iterations after a burn-in of 3000 to minimise autocorrelation and a thinning interval of 10 (i.e. one out of every 10 iterations in the Markov chain was used to estimate the posterior distribution of the parameters). We also assessed the robustness of the parameter estimates by checking the stability of the models. For all models, we assessed for approximate convergence of the MCMC chain (chain stability). We evaluated a final model's validity by assessing the distribution of residuals through residual normality distribution plots. The 95% credible intervals were calculated using Bayesian methods in the MCMCglmm package. We used a .

Poisson law for the degree and strength and a zero-inflated Poisson law for the betweenness and clustering coefficient. Modularity followed a normal law while centralisation, global efficiency and resilience followed a log-normal law.

We then used individual network measures and the function PCA and HCPC of the FactormineR package in R to perform a hierarchical clustering analysis using principal components analysis to assess the presence of intermediary domestics. The HCPC function permitted us to determine whether some domestics acted as intermediaries (i.e. whether certain domestics had higher strength, in-strength, out-strength, degree and betweenness relative to other domestics). We also performed Pearson correlations between the different individual network measures.

All tests were conducted on R 3.6 (R Development Core Team, 2009). The significance level was set at 0.05. Results are shown as mean ± stdv [median].

Results

Food exchange

At the individual level, foragers spent more time giving than receiving food (t = 75.7, df = 33, P < 0.0001, Table 1). The opposite pattern was observed for domestics (t = -138.1, df = 33, P < 0.0001) (Fig. 3). However, Figure 3 shows a high level of variability among both foragers and domestics: some foragers spent more time receiving than giving and some domestics spent more time giving than receiving. This result was also recovered at the global (Fig. 3) and test levels (Fig. S2).

At the colony level, the mean duration of trophallaxes (31.7 ± 12.8 s, corrected by colony size) was not influenced by the presence of broods (df = 29.9, t value=1.34, P = 0.189) nor by colony size (df = 29.9, t value = 2.03, P = 0.051, Fig. S3). The total number of trophallaxes (77.6 ± 49.1) significantly increased with colony size (df = 30, t value=7.62, P < 0.0001, Fig.

. S4A) but did not change significantly with brood presence (df = 30, t value = 1.32, P = 0.197). However, the number of trophallaxes corrected by colony size (mean number: 2.04 ± 1.13) did not change with colony size (df = 30, t value = 0.51, P = 0.613) showing that the effect was more or less linear. This corrected number of trophallaxes did not change with brood presence (df = 30, t value = 1.31, P = 0.197). Lastly, the forager/domestic ratio (0.47 ± 0.21) was not influenced by colony size (df = 27.7, t value=1.02, P = 0.315) but was increased when broods were present (df = 28.6, t value = 3.07, P = 0.005, Fig. S4B).

Global network measures

Four illustrations of trophallaxis networks are shown in figure 4. The number of ants negatively influenced network centralisation (l-95% CI = -0.017, u-95% CI = -0.008, P <0.001, Fig. 5A) and global efficiency (l-95% CI = -0.02, u-95% CI = -0.0001, P = 0.04, Fig. 5C), positively influenced modularity (l-95% CI = -0.001, u-95% CI = 0.005, P = 0.002, Fig. 5B) and did not impact resilience (l-95% CI = -0.009, u-95% CI = 0.013, P = 0.626).

However, resilience increased in the presence of broods (l-95% CI = -1.51, u-95% CI = -0.14, P = 0.026, Fig. 5D); in contrast, brood presence had no effect on the other global network measures (centralisation: l-95% CI = -2.40, u-95% CI = -1.47, P = 0.116; modularity: l-95% CI = -0.125, u-95% CI = 0.11, P = 0.882; global efficiency: l-95% CI = -1.20, u-95% CI = 0.013, P = 0.059). The forager/domestic ratio did not influence the global measures (P > 0.225; Fig. S5). Results of all statistical tests are shown in the supplementary material.

Individual network measures: Distributions of individual network measures (table 1) are

shown in Figure S6. Local peaks were observed for foragers and domestics in the distributions for degree, out-strength and clustering coefficient. The degree decreased in the presence of broods (l-95% CI = -0.057, u-95% CI = 0.293, P = 0.001) and decreased with . colony size (l-95% CI = -0.004, u-95% CI = -0.0004, P = 0.015). Domestics had a lower degree than foragers (l-95% CI = -0.370, u-95% CI = -0.197, P < 0.0001). Strength was negatively influenced by the forager/domestic ratio (l-95% CI = -3.061, u-95% CI= -1.576, P <0.0001). Surprisingly, caste did not influence strength. Foragers had a higher betweenness than domestics (l-95% CI = -0.590, u-95% CI = -0.067, P = 0.013). Betweenness also increased with the forager/domestic ratio (l-95% CI = -0.590, u-95% CI = -0.066, P = 0.013) and with colony size (l-95% CI = 0.016, u-95% CI = 0.028, P < 0.0001) but decreased in the presence of broods (l-95% CI = -0.284, u-95% CI = -0.066, P = 0.012). Similar to betweenness, the clustering coefficient was lower in the presence of broods (l-95% CI = -0.014, u-95% CI = 0.083, P = 0.002) and decreased with colony size (l-95% CI = -0.002, u-95% CI = -0.001, P < 0.0001). All other variables had no effect on the clustering coefficient.

Results of all statistical tests are provided in the supplementary material.

A hierarchical clustering analysis following a principal components analysis confirmed the presence of three clusters in the domestics. Details of this analysis are provided in the supplementary material (Fig. S7). All individual network measures, as well as brood presence, colony size and the ratio foragers/domestics, significantly affected the clustering.

Cluster 3 was composed of domestics with higher strength, in-strength, out-strength, degree and betweenness compared with the other two clusters identified.

Correlations between individual network properties showed that only in-strength and outstrength (r = 0.03; P = 0.246, n = 1096), as well as betweenness and the clustering coefficient (r = 0.02; P = 0.513, n = 1096), were not correlated. All other indices were correlated (0.10 < r < 0.73; P < 0.0005, n = 1096, Fig. 6, Table S2)

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Discussion

The goal of this study was to understand the organisation of trophallaxes in black garden ants, assess the topology of the trophallaxis network and characterise variation in the centralities among foragers and domestics. Consistent with expectation, our results showed that the trophallaxis network in black garden ants was not random and that the directionality of this network was oriented from foragers to domestics. The high betweenness and out-strength values indicated that intermediary domestics existed. In addition, local peaks and clusters were observed in the distribution of some domestic centralities. These intermediary individuals provided the link between the source (foragers) and the final destination of food. This division of labour resulted in a food dissemination chain in the form of a hierarchical network. We also observed high variability among individuals, consistent with previous studies that have examined the distribution of activities (specifically, the percentage of time foraging, distributing food or working inside colonies on a per-individual basis) among workers [START_REF] Kolmes | A quantitative analysis of behavioral specialization among worker stingless bees (Melipona favosa F.) performing hive duties (Hymenoptera, Apidae)[END_REF][START_REF] Dornhaus | Larger colonies do not have more specialized workers in the ant Temnothorax albipennis[END_REF][START_REF] Tenczar | Automated monitoring reveals extreme interindividual variation and plasticity in honeybee foraging activity levels[END_REF][START_REF] Quevillon | Social, spatial, and temporal organisation in a complex insect society[END_REF][START_REF] Bles | Food dissemination in ants : Robustness of the trophallactic network against resource quality[END_REF].

Variation in global network values: The rise of intermediate workers

The mean duration of a trophallaxis (tendency) and the total number of trophallaxes increase with colony size and were not influenced by the presence of a brood. Moreover, the forager/domestic ratio was not influenced by colony size (as was found in [START_REF] Dornhaus | Larger colonies do not have more specialized workers in the ant Temnothorax albipennis[END_REF] but in the presence of a queen) but increased in the presence of a brood. This finding demonstrates the behavioural plasticity of ants and their capacity to respond to changes in the demand for food by the colony, regardless of its size and composition [START_REF] Portha | Self-organized asymmetries in ant foraging: A functional response to food type and colony needs[END_REF][START_REF] Mailleux | Recruitment in starved nests: The role of direct and indirect interactions between scouts and nestmates in the ant Lasius niger[END_REF][START_REF] Tenczar | Automated monitoring reveals extreme interindividual variation and plasticity in honeybee foraging activity levels[END_REF]. When broods are present during experiments, domestics can become foragers to address the increased protein needs of the brood (Lee .

Cassill [START_REF] Lee Cassill | Regulation of diet in the fire ant, Solenopsis invicta[END_REF][START_REF] Dussutour | Carbohydrate regulation in relation to colony growth in ants[END_REF], 2009). In contrast, when broods are absent, foragers can become domestics [START_REF] Sendova-Franks | Task allocation in ant colonies within variable environments (A study of temporal polyethism: Experimental)[END_REF][START_REF] Huang | Regulation of honey bee division of labour by colony age demography[END_REF][START_REF] Amdam | Social reversal of immunosenescence in honey bee workers[END_REF][START_REF] Baker | Age-related learning deficits can be reversible in honeybees Apis mellifera[END_REF]. This adaptability is also supported by our global network measures. Network efficiency is an important network parameter contributing to the success of colonies [START_REF] Sendova-Franks | Emergency networking: Famine relief in ant colonies[END_REF][START_REF] Waters | Information processing in social insect networks[END_REF][START_REF] Stroeymeyt | Social network plasticity decreases disease transmission in a eusocial insect[END_REF]. Colony members are known to modulate their interactions, and thereby the network, based on food availability and the needs of the colony [START_REF] Sendova-Franks | Emergency networking: Famine relief in ant colonies[END_REF][START_REF] Pinter-Wollman | The effect of individual variation on the structure and function of interaction networks in harvester ants[END_REF], the spread of disease [START_REF] Stroeymeyt | Social network plasticity decreases disease transmission in a eusocial insect[END_REF] and group/colony size [START_REF] Pasquaretta | Social networks in primates: Smart and tolerant species have more efficient networks[END_REF][START_REF] Romano | Social transmission in networks : Global efficiency peaks with intermediate levels of modularity[END_REF]. The relationship between network efficiency and network size is non-linear, as there are different peaks of efficiency at different values of modularity based on group size [START_REF] Romano | Social transmission in networks : Global efficiency peaks with intermediate levels of modularity[END_REF]. This non-linearity is interpreted as an adaptive mechanism for optimising the social transmission of information and impeding the transmission of pathogens [START_REF] Waters | Information processing in social insect networks[END_REF][START_REF] Nunn | Infectious disease and group size: More than just a numbers game[END_REF][START_REF] Sueur | Mechanisms of network evolution: a focus on socioecological factors, intermediary mechanisms, and selection pressures[END_REF][START_REF] Romano | The trade-off between information and pathogen transmission in animal societies[END_REF].

We found that global efficiency decreases with colony size. However, resilience-the ratio between efficiency and centralisation-was stable with colony size but increased in the presence of a brood, presumably in response to the needs of the larvae. Improving or maintaining network resilience while ensuring reproduction, can increase the ability of the colony to recover from cascading failures (i.e. breaks in the transmission chain, [START_REF] Wang | An ant colony based resilience approach to cascading failures in cluster supply network[END_REF]. Moreover, modularity increases with colony size. Interestingly, caste-specific adaptations to colony size might also occur, and the role of intermediary domestics may be crucial. For example, intermediary domestics may stabilise the link between foragers and domestics, promoting network resilience with increasing group size. Indeed, the hierarchical clustering analysis revealed the presence of a cluster of intermediary domestics with higher strength, in-strength, out-strength, degree and betweenness compared with other domestics.

. In sum, our global measures indicate-similar to the findings of [START_REF] Stroeymeyt | Social network plasticity decreases disease transmission in a eusocial insect[END_REF] for disease-that the food dissemination process and interactions at the colony level are highly flexible and depend on colony size and needs. All subcolonies used had been in the lab for 18 months to decrease the potential effect of temporal polyethism. The possibility of a potential age effect was also minimised by the fact that we conducted multiple tests with different colony sizes as well as the 10-day buffer that we provided to colonies before scoring interactions. Moreover, ants can continually adapt to the needs of colonies as individuals change castes-even to changes from foragers to domestics [START_REF] Sendova-Franks | Task allocation in ant colonies within variable environments (A study of temporal polyethism: Experimental)[END_REF][START_REF] Huang | Regulation of honey bee division of labour by colony age demography[END_REF][START_REF] Amdam | Social reversal of immunosenescence in honey bee workers[END_REF][START_REF] Baker | Age-related learning deficits can be reversible in honeybees Apis mellifera[END_REF]. Thus, we believe that the effect of temporal polyethism on our findings was negligible.

Variation in individual network values: Towards a decentralised and hierarchical organisation

We found that foragers had higher degree and betweenness but the same strength and clustering coefficient as domestics (see supplementary material for detailed statistics). This pattern is consistent with foragers giving more than they received and domestics receiving more than they gave [START_REF] Quevillon | Social, spatial, and temporal organisation in a complex insect society[END_REF]. Because foragers gave more food to more ants than domestics did, they also had a higher betweenness (degree and betweenness are correlated). Thus, the degree, betweenness and out-strength values clearly indicate that foragers were the ones distributing food in the network, supporting the centralised network hypothesis. This finding was further confirmed by the fact that betweenness increased with the forager/domestic ratio. Specifically, foragers became more important for food exchange as the number of intermediaries decreased, and when intermediaries were few, the number of foragers increased. However, the fact that foragers had a similar strength and clustering coefficient compared with domestics suggested that there were connections between . domestics and that the network was not highly centralised, allowing the trophallaxis network to retain its adaptability and resilience. Decentralisation was supported by the decrease in strength (but not degree) as the forager/domestic ratio increased. Specifically, foragers gave less per trophallaxis when their number was higher or domestics served as intermediaries by giving more when the number of foragers was low. While the trophallaxis network was not randomly organised, the presence of intermediary ants, confirmed by the local peaks and the hierarchical clustering analysis, indicated that the form of the trophallaxis network was most consistent with the hierarchical network hypothesis. Trophallaxes were clearly directed in different steps and levels, which made the networks hierarchical.

Social network and brood

The presence of a brood did not influence individual strength. Strength was quite stable given that no parameter, except the forager/domestic ratio, affected it. Strength reflects the duration of trophallaxis of an individual, and this should depend more strongly on intrinsic characteristics [START_REF] Greenwald | Individual crop loads provide local control for collective food intake in ant colonies[END_REF], such as the quantity of food present in the social stomach. The crop capacity is generally stable between individuals measured at distinct foraging events [START_REF] Greenwald | Individual crop loads provide local control for collective food intake in ant colonies[END_REF]. Thus, foragers should always transfer stable quantities of food but some might occasionally give large quantities of food to domestics and at other times several small quantities of food. Our results highlight that the pattern of food distribution is independent of colony size and the presence of a brood. In contrast to expectation, the degree and betweenness of foragers and intermediary domestics did not increase in the presence of a brood. This finding may stem from increases in the number of foragers. As a consequence of such a decentralised organisation, the degree and betweenness per individual decreases. Thus, a more decentralised and resilient network with intermediary domestics may arise, preventing food exchange from being concentrated to a small number of . foragers. The change in the forager/domestic ratio in the presence of a brood indicated that the system balances foraging and caregiving effort [START_REF] Schafer | Forager activation and food availability in harvester ants[END_REF][START_REF] Mailleux | Recruitment in starved nests: The role of direct and indirect interactions between scouts and nestmates in the ant Lasius niger[END_REF]. The mechanisms underlying the responses of the system, namely behavioural plasticity of the workers, reinforce the hypothesis that the network was more hierarchical than centralised [START_REF] Middleton | Resilience in social insect infrastructure systems[END_REF].

Social network and colony size

An increase in colony size negatively influenced the degree and the clustering coefficient of ants, positively affected their betweenness and had no effect on their strength. These results corroborate the findings of several previous studies [START_REF] Naug | Structure and resilience of the social network in an insect colony as a function of colony size[END_REF][START_REF] Pasquaretta | Social networks in primates: Smart and tolerant species have more efficient networks[END_REF][START_REF] Puga-Gonzalez | Emergence of complex social networks from spatial structure and rules of thumb: A modelling approach[END_REF]. As colony size increases, the probability of interactions between each pair of ants inherently decreases, resulting in a decrease in network density and as consequence, in the clustering coefficient. However, in larger colonies, as the network becomes more centralised, the mean individual betweenness should decrease. This expectation should hold if interactions are more or less random but not directed towards specific individuals as trophallaxes often are. Thus, one explanation that might explain our finding of betweenness decreasing with colony size is that in larger colonies, some individuals-either foragers or intermediary domestics-become more important in the transfer of food, allowing us to reject the random network hypothesis. Because some domestics had an out-strength/in-strength ratio greater than one (Fig. 3), our data most strongly support the hierarchical network hypothesis.

Conclusion

Behavioural flexibility and decentralised control (the presence of several individuals per caste) are parameters characterising the organisational resilience of ants [START_REF] Middleton | Resilience in social insect infrastructure systems[END_REF]. Several studies have already demonstrated the presence of decentralised but hierarchical networks in mammals [START_REF] Hill | Network scaling reveals consistent fractal pattern in hierarchical mammalian societies[END_REF]. Various hierarchical networks have been described in nature ranging from protein complexes [START_REF] Ravasz | Hierarchical organisation of modularity in metabolic networks[END_REF], to neural networks [START_REF] Chatterjee | Understanding the mind of a worm: Hierarchical network structure underlying nervous system function in C. elegans[END_REF][START_REF] Clune | The evolutionary origins of modularity[END_REF], to animal groups [START_REF] Hill | Network scaling reveals consistent fractal pattern in hierarchical mammalian societies[END_REF] and to organisation in social insects [START_REF] Linksvayer | Developmental evolution in social insects: Regulatory networks from genes to societies[END_REF]. Hierarchical networks are more resilient than centralised networks but less costly in terms of connections (time to find partners and exchanges) than complete networks [START_REF] Banavar | Size and form in efficient transportation networks[END_REF][START_REF] Bode | Social networks and models for collective motion in animals[END_REF][START_REF] Guimera | Communication and optimal hierarchical networks[END_REF][START_REF] Barabasi | Scale-free and hierarchical structures in complex networks[END_REF][START_REF] Ravasz | Hierarchical organisation in complex networks[END_REF]. Changes in our global network measures, such as efficiency, centralisation or resilience, may ultimately result in increases in group performance as mentioned by [START_REF] Sueur | Fast and accurate decisions as a result of scale-free network properties in two primate species[END_REF] and described by [START_REF] Fontanari | Influence of network topology on cooperative problemsolving systems[END_REF]. The two latter authors hypothesised that the collective cognition behind the complex systems built by social insects suggests that the topology of social networks is selected to optimise problem-solving competence at the group level. However, although individuals are selected and not the group or networks, feedbacks exist between these two levels [START_REF] Farine | From individuals to groups and back: The evolutionary implications of group phenotypic composition[END_REF][START_REF] Fisher | Social traits, social networks and evolutionary biology[END_REF]. This process of multilevel selection previously described as -collective social niche construction‖ by [START_REF] Sueur | Mechanisms of network evolution: a focus on socioecological factors, intermediary mechanisms, and selection pressures[END_REF] deserves increased attention. Indeed, study of this process promises to enhance our understanding of the evolutionary mechanisms contributing to the emergence of complex systems.

Acknowledgments

MQ was funded by the Ministère Français de l'Enseignement Supérieur et de la Recherche. OB was funded by the Fonds pour la Recherche dans l'Industrie et dans l'Agriculture and the Van Buuren Fund (Belgium). CS is a junior member of IUF (Academic Institute of France) and a fellow of USIAS (University of Strasbourg Institute for Advanced Studies).

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Tables:

Table 1 Mean ± standard deviation of individual network measures according to brood (presence/absence) and then caste (foragers/domestics). The relative difference between foragers and domestics is also indicated. . . . (the bigger, the higher) whilst colour fits with the degree (the redder, the higher). Graphs were drawn with Gephi 0.9.2 [START_REF] Bastian | Gephi: An Open Source Software for Exploring and Manipulating Networks[END_REF] using the force Atlas 2 package for the spatial visualisation.

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