Irrational risk aversion in an ant

Animals must often decide between exploiting safe options or risky options with a chance for large gains. Both proximate theories based on perceptual mechanisms, and evolutionary ones based on fitness benefits, have been proposed to explain decisions under risk. Eusocial insects represent a special case of risk sensitivity, as they must often make collective decisions based on resource evaluations from many individuals. Previously, colonies of the ant Lasius niger were found to be risk-neutral, but the risk preference of individual foragers was unknown. Here, we tested individual L. niger in a risk sensitivity paradigm. Ants were trained to associate one scent with 0.55 M sucrose solution and another with an equal chance of either 0.1 or 1.0 M sucrose. Preference was tested in a Y-maze. Ants were extremely risk-averse, with 91% choosing the safe option. Based on the psychophysical Weber–Fechner law, we predicted that ants evaluate resources depending on their logarithmic difference. To test this hypothesis, we designed 4 more experiments by varying the relative differences between the alternatives, making the risky option less, equally or more valuable than the safe one. Our results support the logarithmic origin of risk aversion in ants, and demonstrate that the behaviour of individual foragers can be a very poor predictor of colony-level behaviour. Supplementary Information The online version contains supplementary material available at 10.1007/s10071-021-01516-1.


.3 and 0.9 sucrose molarities
In experiment 3, the ants were presented with feeders offering 0.1, 0.3 and 0.9 molar sucrose. Relative to experiments 1 and 2, the medium-and the low-quality drop had very similar molarities in absolute terms, so that we decided to run a pilot experiment to test whether the ant could discriminate, and subsequently choose reliably between, the three molarities.
We ran two testing blocks. In the first, the ants were presented with two drops of different molarities, 0.1 and 0.3, and were trained to associate each to a smell. We followed the methodology described for the main experiment (see methods section in the main paper), alternating the presentation of the low-quality alternative and the high-quality alternative in the 8 training visits. Afterwards we tested the ants in the Y-maze, repeating the test 5 times. The second experiment was identical to the first, but the ants were presented with 0.3 and 0.9 molarities. We did this last block just as a control, since as 0.3 and 0.9 are further apart than 0.55 and 1.0 we were confident that they could discriminate between the two. We tested 20 ants for each block (40 in total), stemming from 6 different colonies. First, we tested the robustness of the ants' choices, checking whether with subsequent visits the number of ants choosing the high value drop decreased. We modelled as follows:

High value choice (all tests) = Testing visit (1-5)+ Contrast (0.1vs0.3 or 0.3vs0.9) random effect ( individual ant nested in colony )
We found that the ants did not change their preference over subsequent visits for either of the two contrasts, differently from what we observed in the main experiment (table S1). This could be because comparing two malarities is easier than the risk-vs-safe evaluation. For the subsequent analysis, we kept all 5 testing visits. We modelled the data as follows: High value choice (all tests) = Decision line+ Contrast (0.1vs0.3 or 0.3vs0.9) random effect ( individual ant nested in colony ) Then, we ran a post-hoc test to check which of the groups differed from chance level. We found that the ants significantly preferred 0.3 over 0.1 when considering both the first decision line and the second decision line. However, we found that the ants did not significantly prefer 0.9 over 0.3, remaining at chance level (Table S2). This was surprising to us, as the contrast between 0.9 and 0.3 should be easier to sense, or at least equally difficult if the ants follow the Weber-Fechner law, and in both cases easier than the contrast between 0.55 and 1.0. We suspect that, due to the lower sample size in these experiments, we have experienced a type II error (false negative). However, we decided to present our data as it is, without a post-hoc increase in sample size, following good scientific practice.

Ant preference among 3 molarities
In the main experiment the ants were presented with three different food qualities, and were required to remember all three in order to make a choice between the two feeders. We decided to run a pilot experiment on order to test whether the ants could remember three molarities, rather than just the best one among others.
The ants performed 9 sequential visits to a runway, identical to the one of the main experiment. At the end of the runway the ant may find either a 1.5M drop, always unscented, a 1.0M drop, either rosemary or lemon scented, and a 0.25M drop, scented with the other odour (see table S3).
Visit 1 Visit 2 Visit 3 Visit 4 Visit 5 Visit 6 Visit 7 Visit 8 Visit 9 Table S3 -Training visit sequence for the three molarity experiment. The two rows represent the two possible patterns for the reward presentation. Each ant would experience only one.
Afterwards we tested the ant preference between the 1.0M scent and the 0.25M scent in the Ymaze, repeating the test 5 times. If the ants could only learn the best alternative among the presented ones, they should choose randomly between the second best and the worst. However, if the ants can remember and compare all three values, they should prefer the 1.0M.
We planned to test 32 ants coming from 8 different colonies. However, after having tested 15 ants coming from 5 different colonies we decided to stop the pilot, given the clear preference of the animals: On the first trial, both initial and final decision, 100% of the ants choose the scent associated with 1.0M. We observed a decrease on the ants performance in subsequent files, but the the overall percentage remained at 92%. While we are aware that stopping an experiment prematurely when results are as expected can lead to type I errors (false positives), we felt that the unambiguous nature of these results warranted doing so here.
2 Risk preference in the context of losses (maintained on 1.5M sucrose) Prospect Theory predicts that individuals should be risk averse in the context of gains and risk prone in the context of losses. The reference point from which we decide if something is a gain or a loss is not necessarily 0: we may take an expected value as a reference. For ants, this value it could be the feeding solution they are maintained on, normally 0.5M. We decided to replicate experiment 1 (see main paper) with 4 colonies that had been fed ad libitum 1.5M sucrose instead of the usual 0.5M for one month prior testing. 63 ants were tested in total. Training and testing procedure were identical to those described in the main paper. We found that 82% (52/63) of the ants preferred the safe alternative. All data and analysis are provided in supplement S2

Pheromone deposition data
Pheromone deposition count was modelled using a poisson distribution and logit link function. Good model fit was confirmed using the DHARMa package (Hartig 2018), and the pscl package (Zeileis et al. 2008; Jackman 2017) was used to produce the zero-inflated poisson models when needed. Pheromone deposition was not the focus of the current study, but we include it as descriptive data since it may shed light the relationship between individual risk perception and collective decision. We modelled pheromone deposited towards the nest and pheromone deposited on the way back separately, since these are conceptually very different: depositions towards the food reflect the ants' expectation, and depositions on the return to the nest reflect the ants' perception. The models used were the following: Pheromone deposition data from each of the five experiments were analysed separately, as they were taken by three separate experimenters, and so could not reliably be compared between experiments. Path choice decisions allow much less observer error, so Y-maze data can be pooled between experiments.

Experiment 1 -Risk preference between options of equal absolute value
Considering pheromone deposition towards the feeder, we found an effect of molarity (GLMM Analysis of Deviance, Chi square=12.992, DF=2, p=0.001) and an effect of the interaction between molarity and visit number (GLMM Analysis of Deviance, Chi square=14.469, DF=2, p=0.0007). Specifically, we found that the ants deposited overall more pheromone when going towards the 0.55M drop in comparison to the 1.0M drop (figure S4A, GLMM post-hoc with estimated means, estimate=0.657, SE=0.227, z=2.891, p=0.015). Note that the ant may be expecting to find the 0.1M drop when going towards the 1.0M, because it last experienced the low value associated with that scent. Note that this will be the case also for the other experiments. We found no differences in pheromone deposition between the other molarities. Overall, the ants deposited more pheromone on the way to the safe feeder relative to the risky one (GLMM post-hoc with estimated means, estimate=0.498, SE=0.19, z=2.616, p=0.036).
Considering pheromone deposited when returning to the nest, we found an effect of molarity (GLMM Analysis of Deviance, Chi square=85.97, DF=2, p<0.0001), an effect of visit (GLMM Analysis of Deviance, Chi square=5.11, DF=1, p=0.024), but no effect of their interaction. Specifically, we found that the ants deposited overall less pheromone when going back from the 0. Overall the ants deposited more pheromone on the way back from the safe feeder relative to the risky one (GLMM post-hoc with estimated means, estimate=1.28, SE=0.14, z=9.149, p<0.0001).

Experiment 2 -Risk preference between options of different absolute value
Considering pheromone deposited towards the drop, we found an effect of the molarity (figure S4B, GLMM Analysis of Deviance, Chi square=7.489, DF=2, p=0.024). However, post-hoc analysis revealed no difference between any of the molarities: the differences were probably so small that the Bonferroni correction in the post-hoc analysis brought them above significance.
Considering the pheromone deposited back to the nest, we found an effect of molarity ( Overall the ants deposited more pheromone on the way back from the safe feeder relative to the risky one (GLMM post-hoc with estimated means, estimate=0.947, SE=0.14, z=6.341, p<0.0001).

Experiment 3 -Risk preference between psychophysically-balanced options
Considering pheromone depositions towards the feeder, we found an effect of molarity (GLMM,Chi square=16.133,DF=2,p=0.0003 Considering pheromone deposition back to the nest, we found an effect of molarity (GLMM, Chi square=12.713, DF=2, p=0.0017) and an effect of the interaction between visit number and molarity (GLMM, Chi square=9.447, DF=2, p=0.0088). Ants deposited less pheromone for the 0.3M in comparison to the 0.9M (GLMM post-hoc with estimated means, estimate=−0.515, SE=0.144, z=−3.569, p=0.0014). Overall the ants deposited the same amount of pheromone on the way back from the safe feeder relative to the risky one (GLMM post-hoc with estimated means, estimate=−0.252, SE=0.211, z=−1.199, p=0.922).
Considering pheromone deposition back to the nest, we found an effect of molarity (

Experiment 5 -Risk preference with an absolutely higher-valued risky alternative.
Considering pheromone depositions towards the feeder, we found no effect of molarity (GLMM, Chi square=0.2882, DF=2, p=0.8658) but an effect of visit number (GLMM, Chi square=7.2851, DF=1, p=0.0069). There was also a slight effect, although not significant, of the interaction between the two (GLMM, Chi square=5.7211, DF=2, p=0.0572). Indeed, the amount of pheromone deposited towards the 0.25M and the 0.5M drops remains the same over the course of the trial, while it increases for the 1.5M drop (GLMM post-hoc trend, slope=0.1364, SE=0.0306, z=4.455, p<0.0001) Considering pheromone deposition back to the nest, we found an effect of molarity (GLMM, Chi square=38.663, DF=2, p<0.0001) and an effect of the interaction between molarity and visit number (GLMM,Chi square=8.191,DF=2,p=0.0166

Discussion
Does our understanding of individual behaviour in a risk-choice situation help explain the risk indifference of ants at a colony level (Hübner and Czaczkes 2017)? Pheromone deposition rates of individual foragers vary hugely between individuals, even when presented with identical food sources. This is to be expected, given the fact that individual variability may aid collective decisions (Dussutour et al. 2009;O'Shea-Wheller et al. 2017). However, the appropriate measure of pheromone for colony-level decisions is total pheromone deposited. Examining the mean deposition rates for both feeders in experiment 1, we see that ants, on average, deposited more pheromone to the safe feeder (5.5 dots per ant) than the risky feeder (3.9 dots per ants; for the full data see ESM1). In Hübner & Czaczkes (2017) each ant made only one or two visits to the feeder, but even when considering only the first two visits, ants made more pheromone depositions to the safe (1.5 dots per ant) than to the risky (0.89 dots per ant) feeder. The finding of risk neutrality at the colony level is thus still a puzzle. However, the two experiments are not directly comparable. Firstly, in the current experiment pheromone was removed from the trail every visit. Pheromone presence is known to reduce further pheromone deposition (Czaczkes et al. 2013), perhaps damping out the differences between the two feeders. Secondly, the presence of odours on a path affects pheromone deposition: while pheromone deposition on odourless paths is usually higher on the nestward journey (Beckers et al. 1993;Czaczkes et al. 2013Czaczkes et al. , 2016Czaczkes and Heinze 2015), pheromone deposition is higher on outward journeys on scented paths (This study; Czaczkes et al. 2018b, a). Finally, it should be noted that perception of pheromone, much like perception of quality, is also not linear (von Thienen et al. 2014), thus emphasising initial differences in pheromone concentration but damping out differences between strong trails. Nevertheless, it seems that colony-level decisionmaking effectively filters out the ants' individual perceptual constraints (This study; Sasaki and Pratt 2011;Sasaki et al. 2019), but the mechanism used to achieve this is still unknown. Figure S4 -Frequency of pheromone deposition for the 5 experiments (columns), both for the path to the drop (top row) and the path back to the nest (bottom). In orange, visits in which the risky option is presented. In blue, the safe option. In the box-plots, the line a the centre of the box represents the median value; the coloured area contains al values of the second and third quartile, the lines on top and below the boxes represent the first and fourth quartiles.