Verification of mathematical models of response threshold through statistical characterisation of the foraging activity in ant societies

Abstract

The concept of response threshold (RT) has been developed to explain task allocation in social insect colonies, wherein individual workers engage in tasks depending on their responsiveness to the task-related stimulus. Moreover, a mathematical model of RT has been proposed to explain data obtained from task allocation experiments; however, its applicability range warrants clarification through adequate quantitative analysis. Hence, we used an automatic measuring system to count passage events between a nest chamber and a foraging arena in five colonies of ants, Camponotus japonicus. The events were measured using radio-frequency identification tags attached to all workers of each colony. Here, we examined the detailed forms of i) labour distribution during foraging among workers in each colony and ii) the persistence of rank-order of foraging among workers. We found that labour distribution was characterized by a generalized gamma-distribution, indicating that only few workers carried out a large part of the workload. The rank-order of foraging activity among workers in each colony was maintained for a month and collapsed within a few months. We compared the obtained data with testable predictions of the RT model. The comparison indicated that proper evaluation of the mathematical model is required based on the obtained data.

Figure 1

Automatic system for measuring the foraging activity of Camponotus japonicus colonies, using tiny radio-frequency identification (RFID) tags (SK-Electronics CO., Ltd.) (a) Top view of the experimental setup. (b) Side view of the sensor gate and snapshots of a passage event of an ant moving from the nest chamber (left) to the foraging arena (right) in a time sequence. (c) The time series of the number of passage events in each day of three of the most active ants in the same colony A. (d) The rank-order of foraging activity plots of 1st day and the rank foraging activity plots of typical days (10th, 20th, 30th, and 40th days) in ascending rank-order of foraging activity from day 1. (e) Spearman’s correlation coefficient (SCC) matrix of colony A determined from ROoFAs of every 2 d among workers who passes the sensor gate at least once in both days. The colour labels show Spearman correlation coefficient.

Figure 2

(a) Complementary cumulative fractions of daily foraging activities of colonies. (b) Complementary cumulative fractions of daily foraging activities of Colony A and the candidate curves for the cumulative form of the distribution function of Colony A.

Figure 3

Spearman’s correlation coefficient averaged over all pairs of daily ROoFAs for respective day-differences corresponding colonies.