Passage counts for each colony (A-E).

Social insects often share tasks among individuals. In this study, we analyzed the foraging activity of ants (Camponotus japonicus) and recorded the daily passage event counts of individual workers between a nest chamber and a foraging arena in five monodomous colonies. We proposed two hypotheses on the time series of foraging frequency by individual worker ants as follows: (i) for the time series of foraging frequency by individual worker ants, the foraging frequency on a certain day could be expressed by the product of the foraging frequency on the previous day and the exponential of a random number. (ii) The random numbers are correlated between some pairs of worker ants. The results for the five tested ant colonies showed that the probability of total daily passage counts (the sum of an individual’s passage count) followed a log-normal distribution. The worker ants behaved differently in terms of active days and foraging frequency. However, for > 54% of the worker ants, the probability of the daily passage count was characterized by a log-normal distribution, and these worker ants performed > 72% of the tasks in each colony. Furthermore, for > 73% of the worker ants, the time development of the passage count was mathematically modeled; the logarithmic first difference between the passage counts on a certain day and those on the previous day was a random normal variable. These results support hypothesis (i). Additionally, the random numbers that were equivalent to the logarithmic first difference were correlated for some pairs of worker ants. These results support hypothesis (ii).

社会性昆虫通常会在个体间分担任务。本研究以日本弓背蚁（Camponotus japonicus）为受试对象，分析其觅食行为，记录了5个单巢群（monodomous）蚁群中，单只工蚁在巢室与觅食场地之间的每日通行事件次数。我们针对单只工蚁觅食频率的时间序列提出了如下两个假说：（i）就单只工蚁的觅食频率时间序列而言，单日觅食频率可表示为前一日觅食频率与某随机数的指数项的乘积；（ii）部分工蚁对之间的随机数存在相关性。对5个受试蚁群的分析结果显示，单日总通行次数（即单只工蚁通行次数的总和）的概率分布服从对数正态分布。不同工蚁的活跃天数与觅食频率存在显著差异。然而，在超过54%的工蚁中，其单日通行次数的概率分布均服从对数正态分布，且这类工蚁承担了每个蚁群中超过72%的觅食任务。此外，在超过73%的工蚁中，通行次数的时间动态可通过数学建模刻画：单日通行次数与前一日通行次数的对数一阶差分服从随机正态分布。上述结果支持假说（i）。此外，与对数一阶差分等价的随机数在部分工蚁对之间存在相关性，该结果支持假说（ii）。