Social, spatial, and temporal organization in a complex insect society

High-density living is often associated with high disease risk due to density-dependent epidemic spread. Despite being paragons of high-density living, the social insects have largely decoupled the association with density-dependent epidemics. It is hypothesized that this is accomplished through prophylactic and inducible defenses termed ‘collective immunity’. Here we characterise segregation of carpenter ants that would be most likely to encounter infectious agents (i.e. foragers) using integrated social, spatial, and temporal analyses. Importantly, we do this in the absence of disease to establish baseline colony organization. Behavioural and social network analyses show that active foragers engage in more trophallaxis interactions than their nest worker and queen counterparts and occupy greater area within the nest. When the temporal ordering of social interactions is taken into account, active foragers and inactive foragers are not observed to interact with the queen in ways that could lead to the meaningful transfer of disease. Furthermore, theoretical resource spread analyses show that such temporal segregation does not appear to impact the colony-wide flow of food. This study provides an understanding of a complex society’s organization in the absence of disease that will serve as a null model for future studies in which disease is explicitly introduced.


Ant-time calculation:
To calculate ant-time, we took the number of ants in each functional group for each night of observation and multiplied by the total time they were in the nest and therefore available to engage in trophollaxis interactions with other ants. The queen, nest workers, and inactive foragers were by definition in the nest for the entire 20-minute observation period each night and accordingly the calculation of ant-time is a simple product of the number of those ants by the 1,210-second observation window. However, foragers were in the nest for variable amounts of time and so ant-time for the forager class is calculated by summing how much time each individual forager was in the nest for a precise calculation of the time they were available for within-nest interactions. The ant-time formulas are given below: Foragers: , where t i is the amount of time forager F i spent inside the nest.
All others: s , where N ant = number of ants in type ant.

Ant movement model:
In both colonies, the observed residence times in each grid cell and transitions to neighboring cells were used to fit a continuous-time discrete-space random walk model for ant movement behaviour and used to calculate a movement or transition rate between cells. We used a continuous-time discrete-space (CTDS) agent-based random walk model38, 42 to make inference about ant movement behaviour. The CTDS framework is notable in that it allows for inference on both directional (e.g., queen avoidance) and location-based (e.g., variable movement rates in different nest chambers) movement mechanisms. Drawing on standard continuous-time Markov chain models (e.g., 42), if an ant is in cell i at time t, then define the rate of transition from cell i to a neighboring cell j as λ(ij). The total rate λ(i) at which ants move (transition) out of cell i is the sum of the rates to all neighboring cells: = , and when the ant moves, the probability of moving to cell k (instead of to another neighboring cell) is the ratio: λik / λ .
To model ant movement behaviour near the queen, we will model λ(ij) as a function of a spatial covariate that measures the distance from the queen's most used locations ('Distance From Queen'-DFQ) at each grid cell. To examine local behaviour, the DFQ covariate was set to be constant out of the queen's chamber. The DFQ covariate is location-based and will allow us to model differences in movement rates when near or far from the queen. We also considered a directional covariate, a gradient of the DFQ covariate (GDFQ). The GDFQ gradient is a directional vector that points towards the queen, or along the direction of steepest ascent of the DFQ covariate, and the GDFQ covariate will be different for the transition rates to neighboring cells in different directions, thus allowing for directional preference in ant movement. We also consider potential differences in movement behaviour between foraging (F) and non-foraging (NF) ants, with F=1 for foraging ants and F=0 otherwise, and NF=0 for foraging ants and NF=0 otherwise. We model the movement rate λk(ij) of the k-th ant from cell i to cell j as a function of interactions of these covariates and corresponding regression parameters {β}: λ k (ij) = exp{ F k β 1 + NF k β 2 + (F k * DFQi)β 3 + (NF k *DFQ i )β 4 + (F k *GDFQ ij )β 5 + (Fk*GDFQ ij )β 5 } Differences in overall movement rates between foragers and non-foragers will be represented by differences in β 1 and β 2 , with positive values corresponding to higher movement rates. Positive values of β 3 correspond to higher movement rates of foraging ants when far from the queen, and decreased movement rates near the queen. Positive values of β 5 correspond to preferential directional movement by foragers away from the queen (in the direction of the increase in € Tant = Nant * 1210 € TF = ti Fi Fn ∑ the gradient of DFQ). The parameters β 4 and β 6 correspond to the response of non-foraging ants to DFQ and GDFQ, respectively. Hanks et al. (2013) have shown that inference on the parameters in this movement model can be accomplished using a Poisson GLM, which we fit using the 'glm' command in R.

Data availability:
Raw network data for colony 1 and colony 2 over all 8 nights of observation is available online at Dryad.

Supplemental Tables and Figures
Video S1: Ant nest set-up.
Video S2: Trophallaxis montage. Table S1: Major parasites of ants A non-exhaustive list of the major parasite taxa infecting and/or transmitting within ant colonies. The mechanism of entry into the colony (if known) is given as well as the major route of transmission once the parasite is inside the colony (if known). The ant life-history stage predominantly infected is also given.  Table S3: Trophallaxis count and duration statistics (a) Two-sided Kruskal-Wallis tests and (b) Dunn's tests differences in trophallaxis count and duration as a function of ant functional classification. Asterisks represent statistically significant differences between groups following a Benjamini-Hochberg correction for multiplicity of hypothesis testing.

Figure S1: Static trophallaxis networks.
Unweighted, bi-directional trophallaxis networks for all 8 nights for a) colony 1 and b) colony 2. Individual ants are represented as circles; their x-y coordinates were randomly generated and maintained in all graphs. Lines between circles represent a trophallaxis interaction between those ants; the length and width of the line conveys no additional information.

Figure S2: Time-ordered trophallaxis networks.
Unweighted, bidirectional, time-ordered networks for all 8 nights for a) colony 1 and b) colony 2. Individual ants are represented as vertical lines moving through time (time starts at y=0 and moves forward in the +y direction). Horizontal lines represent the start time of trophallaxis interaction between the two individuals connected. Active foragers are shaded in green, inactive foragers are shaded in yellow, nest workers are not shaded, and the queen is shaded in red.  Mean and standard deviation of percentage time budget engaged in trophallaxis for each functional group comparison. The functional group on the left-most side in each label is the focal group, and it is their ant-time used in the denominator.       Fig. 4)