Fig 1.
Diagram of the closed-loop model with two components inside the nest and one component outside the nest.
The “Interactions” component maps the sequence of incoming foragers λin to a stimulus s to represent the result of interactions of available foragers inside the nest entrance chamber with incoming food-bearing foragers. The mapping uses a leaky integrator that increases by a fixed magnitude with every incoming forager and has a natural decay rate. The “Response of available foragers” component maps s to the sequence of outgoing foragers λout using the nonlinear FitzHugh-Nagumo oscillator dynamics. Each oscillation represents an ant leaving the nest to forage. The “Foraging” component maps λout to λin using a random time delay with an associated probability distribution to represent the time an ant spends outside the nest foraging.
Fig 2.
A) Sequence of incoming foragers λin. B) Stimulus signal s associated with λin. C) FN output v for input s. D) Sequence of outgoing foragers λout obtained by thresholding FN output from below at 0.75.
Fig 3.
Block diagram of proposed mechanism for response of colony to environmental conditions.
The available foragers inside the nest comprise two sets: fu corresponds to those that have not yet left the nest and so are uninformed about the conditions outside the nest, and fi corresponds to those informed during a previous foraging trip. The response of each set to s is represented by a different FN model, distinguished by the volatility parameter cu for the uninformed and ci for the informed. The outputs of these two oscillator dynamics are weighted probabilistically using thinning to get an outgoing stream of foragers λout(t).
Fig 4.
Plots of incoming foraging rate rin (blue) and outgoing foraging rate rout (red) versus time of day on August 20, 2016 for A) Colony 1357 and B) Colony 1317.
The quasi steady-state (QSS) where incoming and outgoing rates equilibrated to a near-equal value can be observed for both colonies. The QSS rate for Colony 1317 was more than twice as great as it was for Colony 1357.
Fig 5.
Time series plots show incoming foraging rate rin (blue), outgoing foraging rate rout (red), and cumulative difference between the number of incoming and outgoing foragers (green) versus time of day. Input-output plots show rout(t) versus rin(t) with the color scale representing time of day t. A) and B) Colony 664 on August 27, 2015. C) and D) Colony 664 on August 31, 2015. E) and F) Colony 863 on September 1, 2015.
Fig 6.
A) Analytical approximations for the nest I/O curves. B) Simulated nest I/O curves for different values of c. Each pair of error bars correspond to 10 simulation trials, each 5 minutes long, with a constant expected incoming rate and constant volatility c. The dashed black line represents points at which the mean incoming rate is equal to the mean outgoing rate
.
Fig 7.
Model dynamics illustrating response of foraging rates to environmental conditions.
Red, purple, and blue curves show closed-loop trajectories of rout(t) versus rin(t) for fixed volatility c equal to 5.0, 2.0, and 0.1, respectively. Initially, all available foragers are uninformed about the environment and have volatility cu = 5.0. The darker gray dashed curve shows the dynamics in the case when foragers exposed to the environment reduce their volatility to ci = 2.0, as might happen on a moderately hot and dry day. The lighter gray dashed curve shows the dynamics in the case when foragers exposed to the environment reduce their volatility to ci = 0.1, as might happen on a very hot and dry day.
Fig 8.
A. Analytical magnitude of the quasi steady-state (QSS) foraging rate obtained from numerically solving Eq (8). B. Closed-loop model simulations for 7 different values of volatility c. The initial sequence of incoming foragers for all simulations was set equal to the sequence of incoming foragers recorded during the first 11 minutes for Colony 859 on August 20, 2017, which has a mean incoming rate of 0.01 ants/sec. The total time for all simulations was 3 hours. The mean foraging time was set to 10 minutes (D = 10).
Fig 9.
Simulations of the closed-loop model with the adaptation mechanism.
Plots are of the same form as in Fig 5, and qualitative comparisons can be made between A and B here and Fig 5A and 5B, between C and D here and Fig 5C and 5D, and between E and F here and Fig 5E and 5F. A) and B) cu = 3, ci = 0.9, N = 500, D = 5. C) and D) cu = 3, ci = 0.75, N = 200, D = 5. E) and F) cu = 5, ci = 0.02, N = 600, D = 15.