Fig 1.
Quantifying food distribution within an ant colony by combining single ant tracking with fluorescent imaging.
a) Two tagged workers engaged in trophallaxis. The identity of ants (orange numbers) was determined using Bugtag barcodes. The volume of food in the ants’ crop is measured using fluorescence imaging and overlaid in red. b-d) Food distribution across the colony and at different stages of the experiment. Markers (round: non-forager, square: forager) overlaid on ants depict their crop contents. Marker size is proportional to the food load held by each ant: Pa (small markers were set to a minimal size for clarity). Color division in markers of all ants depicts the computationally derived proportions of food in their crops according to the forager that first collected it (‘food-types’): (P(f|A = a)). Scale bars are 1cm. See also supplemental movie “Food dissemination in ant colony”.
Fig 2.
Food spread and source blending across the colony.
(a) The amount of food held by each non-forager ant a at the end of the experiment, P(a), partitioned into conditional probabilities P(f|A = a) by forager origin (f = 268, green, f = 171 purple, f = 180 blue, f = 421 orange, f = 207 pink; vertically ordered by amounts received). Ants are ordered by the amount of food in their crop, and the dashed line is an exponential fit y = ae−bx,a = 0.061 ± 0.002, b = 0.062 ± 0.003, R2 = 0.96. For colonies B and C see S2 Fig. (b) The extent to which food from each forager f (color code as in panel a) was distributed among non-forager ants a: P(a|F = f). Recipient ants are ordered (per forager f) by amount received. Dashed curve is an exponential fit y = ae−bx, a = 0.095 ± 0.0013, b = 0.1 ± 0.002, R2 = 0.97. For colonies B and C see S2 Fig. (c) Mixing entropies as a function of the number of trophallactic interactions starting from the first return of a loaded forager. Entropies are normalized by to allow for data averaging over the three experiments. Lines are the mean over three experiments while shaded areas designate standard deviations. Depicted are the empirical entropy associated with the different proportions of food as brought in by each forager Htypes (blue), the empirical mixing entropy over all non-forager ants Hmix, (red) and the mixing entropy for hybrid simulations where randomized interaction volumes and transfer directions were simulated over the empirical interaction schedule (N = 30, shaded area depicts standard deviation of the outcomes). Discontinuities are a consequence of the variable number of interactions among the three experiments. (d) A histogram of normalized individual mixing entropies of all non-forager ants,
, at the end of the experiments (all three experiments, N = 203 ants).
Fig 3.
The network of pairwise interactions and the flow of food over interactions.
(a) Visualization of the undirected trophallactic network (Colony A). Ants are represented by vertices and interactions are edges using the spring embedded layout from Networkx [37]. Nodes are colored according to maximally modular communities which, nevertheless, display low modularity with 191 intra-community and 223 inter-community links (Details: Number of communities = 5, transitivity = 0.38, modularity = 0.185, quality performance = 0.76). For colonies B and C, see S3 Fig. (b) Probability density as a function of the transfer ratio. Different colors relate to the maximal potential interaction p = d(1 − r) where p ∈ [0, 1] is the volume potential as determined by d, r ∈ [0, 1] donor’s and recipient’s crop load expressed as a fraction of the capacity of each ant. The distribution of interaction volumes per each transfer potential, p, were estimated by exponential functions in which the values of the parameter δ were determined using maximal likelihood. These values of δ all produce decent fits (R2 values are indicated in figure legend) and are, largely, independent of the maximal transfer potential. This implies that the ants control the fraction of volume transferred (out of the maximal possible interaction volume) rather than absolute amounts. Data depict interactions from all three experiments (N = 2141 interactions).
Fig 4.
Mixing as a function of the number of interactions.
Plots compare empirical data and hybrid simulations. Entropies are normalized by , solid lines show the empirical mean over the three experiments, dashed lines represent means over hybrid simulations. Shaded areas depict standard deviations. (a) The mixing entropy, Hmix, in simulations with maximally mixing interactions applied over the empirically measured network (green curve) nearly saturates the empirically assessed upper bound Htypes (blue curve). Mixing entropy, Hmix, in simulations where the empirically derived interaction rule is applied over maximally mixing interaction networks shows a limited rise which compares with empirical mixing rates (red curve). (b) Hybrid simulations of two extreme interaction rules preserving the empirically measured interaction schedule. The orange curve shows Hmix using only the transfers between foragers and non-foragers (i.e., all non-forager to non-forager interactions were set to zero). The green curve depicts Hmix where every transfer is assumed to be at its maximal possible volume. These rules lead to mixing levels that are lower than those measured experimentally (red curve). Discontinuities in the plots are a consequence of the variable number of interactions among the three experiments.
Fig 5.
Trade-off between fast dissemination and efficient mixing described by the model.
(a) While the colony state (Pcolony, green) rises with the fraction of transferred volume, mixing levels among non-foragers (which we call Hmix) decrease. The mixing levels over all ants in the colony (including the foragers) is the product of these two functions,
and displays a broad maximum which spans all non-extreme values of
. Curves can be compared to the empirically measured values (red bars) of the three experiments. (b) Standard deviation of individual mixing entropies
across all ants. Standard deviations were calculated for 30 model runs. The plot depicts the mean and standard deviation of this value.