Study organism and colony rearing

The study organism is Myrmica kotokui, a typical monomorphic ant48. This species forms colonies in fallen rotten wood/trunks and moves deep into the ground only during winter. The average colony size is approximately a few hundred individuals with a single queen. Details of field collection and rearing of colonies are described in a previous paper24. We collected five and three queenright colonies in May of 2006 and 2007, respectively, from the Tomakomai Experimental Forest of Hokkaido University in southwestern Hokkaido, Japan. All of the collected colonies contained a single queen, and workers ranged from 225 to 421 individuals. These collected colonies were reared in the laboratory for one month before experiments were conducted.

From each of these collected colonies, we established eight experimental colonies consisting of 150 workers, a queen, eggs and larvae housed in an artificial nest (plastic container with a plaster floor; 30 × 22 × 6 cm). In each plastic container, a single square chamber (10 × 8 × 1 cm) for a nest site was set at the center of the container. The chamber was covered with a clear glass plate with a thin red transparent cover so that individual markings on ants (see below) could be identified, and the ants behaved naturally. The nest space was connected to an adjacent foraging area by a 1-cm tunnel. We fed the colonies with commercially available insect food (Konchu-no-mitsu DXTM, Marukan, Osaka, Japan) ad libitum.

All workers in the experimental colonies were marked individually with Paint MarkersTM (Mitsubishi Inc., Tokyo, Japan). Ten colors and three marking points (between the eyes, pronotum and gaster) allowed us to discriminate among max. 1000 individuals. New workers emerging from pupae were marked within one day of emergence. All of the experimental colonies were reared in the laboratory for at least two weeks before beginning behavioral observations.

Simulation

We randomly placed 75 workers on a lattice space with 2500 (50 × 50) cells on which tasks appeared randomly following a given probability (0.006 to 0.3) in each time step. A task has a stimulus (initial value = 5.001) at emergence. This stimulus increases by one value in the next step when the task is not processed. Each worker is assigned a threshold value. In the variable threshold system, the value is taken randomly from an integer between 0 and 10 following a normal distribution (mean = 5, binomial approximation). In addition, all of the workers are given the threshold value of 5 in the invariable system. In the next time step, a worker moves to any of adjacent four cells with a probability of 0.5. When another worker is already on the cell to which a worker moves, this movement is canceled. When the worker moves to a cell with a task, the worker will process the task if it has a higher stimulus than the worker’s threshold value.

An inactive worker becomes active due to the presence of a high stimulus. However, an inactive worker will return to inactivity immediately after this high-stimulus task has been processed because the threshold value of inactive workers is kept constant within a simulation.

We selected a cell randomly. We then processed all of the operations (move, task processing, task emergence) on this cell. Then, we placed a flag on the selected cell. Next, we selected a cell with no flag randomly. We repeated this procedure 2500 times. At this stage, all of the cells had been processed once. We then deleted all of the flags and performed the next time step. To set fatigue in the model, we set a variable “power” for each worker. The initial power was 10. When a worker processes a task, the worker’s power becomes zero. The worker cannot do anything until its power is back to 10. The worker’s power increases by a given recovery rate in each time step. We varied the degree of fatigue by altering this rate. We repeated this procedure for 1000 time steps per trial, and five trials were repeated for a set of the two parameters: (1) degree of fatigue and (2) task appearance rate. We recorded the following data in each time step and compared them between the cases with and without threshold variance: 1) the number of processed tasks and 2) the first step with no task processing. The colony was assumed to go extinct at this first blank step.

Behavioral observations

We conducted observations on 8 colonies of the ant Myrmica kotokui using a scan-sampling method49. Once these behaviors had been defined through preliminary observations, scan data were collected over a 32-day period from late July to late August in 2006 and 2007. An observation cycle consisted of three continuous days of observations and one day without. A total of eight observation cycles were conducted during the observation period. To minimize the effect of diurnal changes in activity, each colony was scanned in the morning (9:00–10:00), early afternoon (13:00–14:00), and late afternoon (16:00–17:00). As a result, each individual ant was observed a total of nine times per observation cycle for a total of 72 scans (9 observations x 8 cycles) for each individual. However, because we were unable to view the identification marks of ants at the backside of the transparent cover of the nest chamber during any given scan, the total number of behavioral records was less than 72 for some individuals. We followed a previous study24 for the definitions and categorization of social behavior conducted by nest colony members. The categories of activities are allo-grooming, brood care, regurgitation and foraging. Categories of non-activities are rest, walking and self-grooming.

Examination of task replacement by inactive workers

The average proportion of the resting behavior in a scanning was calculated for each colony. We calculated the activity (rate of social behaviors out of all behaviors) of each individual after defining each behavioral type (see above)24. Workers were divided into three classes following their activities in all the scans: inactive (the lowest 10%), active (the highest 10%) and intermediate (the middle 80%). If the inactive workers replace the tasks of the active workers, a negative correlation in the activity is expected between the highest and lowest classes. However, in a real colony, there is a cyclical change in colony activities14. When a colony is active, both active and inactive workers exhibit high activities. In contrast, when it is less active, they show low activities. By pooling these data, we get an apparent positive correlation between active and inactive workers even if there is no real positive correlation between them. In order to eliminate this apparent correlation, we used partial correlation to normalize the activity levels. Perform partial correlation requires an index that estimates the activity of the entire colony. This index cannot include data from the most active and least active workers to avoid tautological and double-counting problems. Therefore, the colony activity index was calculated from the activities of intermediate workers in a colony. There is no problem with using partial members of a colony for the determination of this index because we only use them to remove cyclical effects. Here, the activities of intermediate workers represent the real activities contributed to their colony (not including wandering/walking). Thus, we evaluated the partial correlation between the most active workers and the least active workers using the mid-active workers as an index of the overall activity of the entire colony. We used partial correlations for the empirical data and rank correlations for the simulation data. The partial correlation between active and inactive workers over the 72 scans (=[(3 observations/day) × 3 days + one resting day] × 8 times =3 × 3 × 8 samples) was calculated while controlling for the activity of the entire colony. Three samples taken in the same day were treated as independent samples. We used the activity of intermediate workers in a scanning as an index of the activity of the entire colony at that time. In this paper, “activities” are defined as behaviors that directly contribute to the health of other colony members. Therefore, all kinds of walking (including wandering) are excluded from activities (as the first approximation) since we find no direct colony benefits. Note that this definition is different from that used by Charbonneau and others20,21,22. For example, patrolling (a type of walking) for nursing needs is recognized as activity for mid-level workers specialized in nursing. Note that what definitions of activities are valid/better may depend on experiments, ant species, working clusters and various other conditions.