Braess's paradox in tandem-running ants: When shortest path is not the quickest

Abstract

Braess's paradox -- where adding network capacity increases travel time -- is typically attributed to selfish agents. Although eusocial colonies maximize collective fitness, we find experimentally that \emph{Diacamma indicum} ants exhibit this paradox: Leaders favour the shortest path even when it slows the colony. We present a quantitative model of the exploration-exploitation trade-off, demonstrating that evolutionary forces selecting for shortest-path identification can force suboptimal global states. This proves the paradox can emerge in highly cooperative systems without individual selfishness.

Figures (7)

• Figure 1: Schematic setup of Braess's paradox: This figure shows a path network involving only two symmetric paths---$N_1W_2$ and $W_1N_2$---connecting origin, $A$, and destination, $B$, and the link L, effecting almost zero travel time between $C$ and $D$.
• Figure 2: Braess's paradox in tandem-running ants: Subfigure (a) is the experimental design of the path network used in the experiment, whereas subfigure (b) presents photos of the two path networks: $P_0$ (without the bridge) and $P_L$ (with the bridge). Subfigure (c) shows that the relocation time per individual is statistically higher in $P_L$ than in $P_0$ (different Latin letters above the box-whisker plots indicate statistically significant differences). A Mann--Whitney $U$ test was performed for hypothesis testing with a significance level of $0.05$.
• Figure 3: Exploration--exploitation paradigm explains Braess's paradox: In subfigures (a) and (b), the path-choice-frequencies of leaders are shown using box-whisker plots, respectively, in experiments and in simulations. The subfigures tagged with (i) and (ii), respectively, denote that the corresponding plot correspond to path network $P_0$ and $P_L$. Different Latin letters above the box-whisker plots indicate statistically significant differences---same letters mean statistically similar. Here, we plot the choice-frequencies of 46 and 61 leaders---who individually performed at least four tandem runs and collectively accounted for more than 80% of total tandem runs---across eight colonies for $P_0$ and $P_L$, respectively. Statistical comparisons were performed using the Wilcoxon test to compare choice frequencies across paths and the Mann--Whitney U test to compare experimental results with simulation outputs. In both cases, a significance level of $0.05$ was used.
• Figure 4: Experimental setup for Braess's paradox grounded on the unidirectional Braess's paradox. (i) Path network $P_0$ used as the control setup without a bridging link for the relocation experiments. (ii) Path network $P_N$, where two narrow segments are connected by the linking bridge $L$. (iii) Path network $P_W$, where two wide segments are connected by the bridge $L$. (iv) Distribution of $\overline{T}$ (total relocation time per ant) for colonies relocating through the three path networks. The mean relocation time on path $P_0$ is significantly lower than that on $P_N$ and $P_W$, while the relocation time on $P_N$ is lower than that on $P_W$. Thus, the ordering of relocation times satisfies the requirement for observing the unidirectional Braess's paradox, motivating the use of this setup in our experiments. Statistical comparisons were performed using the Wilcoxon signed-rank test (significance level $0.05$), as repeated relocations were conducted using the same colony.
• Figure 5: Unbiased exploration by secondary leaders on $P_0$ path network: Subfigure (i) compares (using Wilcoxon signed-rank test, with significance level $0.05$) the following two frequencies of choosing $N_1$ path segment by the secondary leaders during the entire transport phase: frequency corresponding to the secondary leaders who, as followers, were relocated to new nest via $N_1$ and frequency corresponding to the secondary leaders who, as followers, were relocated to new nest via $W_1$. The similar subfigure (ii) corresponds to secondary leaders taking $N_2$ and $W_2$ path segments as followers. Subfigures unequivocally indicate that the path chosen by secondary leaders is independent of the path through which they were previously guided as followers by TLs. The box-whisker plots summarize the distribution of choice frequencies of 45 secondary leaders.