Fig 1.
Exploring the shapes of a) Total Benefit and b) Total Cost functions from Eq 12 in Appendix 1 with respect to various b and β values.
Note that in b), the total cost tolerated by a given young individual is illustrated for different β parameters. Hence, the curve corresponding to is equivalent to the cost borne by any old individual.
Fig 2.
Schematic diagram of different steps in the social learning paradigm of the SL model.
The social learning paradigm is followed similarly to Fig 4. After payoff calculations in each game (G1, G2), individual strategies (i.e. trait value or x) are updated. The updated population with the new trait values enters the next iteration in a loop until the steady state is reached.
Fig 3.
a) The shapes of the probability function pi of individual i adopting Task 1 with respect to xi for a set of different γ values and a fixed (see Eq 8).
The selected γ value to get the results of this manuscript is shown in solid blue line. b) The shapes of changes in Task 0 and Task 1 stimulus values with respect to for fixed values of group size,
given b = 20, and
(see Eqs 9, 10, and S1 Table in Appendix 1 for the choice of parameters) and two different initial values for S0 and S1. The selected parameter values used in our experiments below are shown in solid lines.
Fig 4.
Schematic diagram of different steps in the modified SRT-SL framework.
Each coloured circle represents a young or old individual in the colony. In the first step of the evolutionary process, the population is divided into different games (G1 and G2). The payoffs of each individual are then obtained in the corresponding games and the calculated payoffs form the basis for choosing successful individuals to copy. This step is then followed by an update in individual thresholds (i.e. trait value or x) and task stimuli (i.e. task demands or S). This step is then followed by the update of action probabilities, pi, based on the new stimulus functions in the colony. Stimulus functions for both tasks (S0 and S1 change by an amount equal to the sum of stimuli variations in all the games. The updated population with the new trait values enters the next iteration in a loop until the steady state is reached.
Fig 5.
Relative colony efficiency and simulation results for = 0.5 in different behavioural regions when varying
and b for the SRT-SL and SL model.
The simulation results of the SL model represent the evolution of engagement levels in Task 1 among the young (green) and old (purple) sub-populations. Engagement levels are defined as the fraction of the subpopulation engaging in Task 1. The simulation results of the SRT-SL model show the evolution of worker thresholds for Task 1 for the young (green) and old (purple) sub-populations. The simulation results of the SRT-SL model are also represented to show the evolution of action probabilities towards Task 1 among the young (green) and old (purple) sub-populations. The histograms illustrate the fraction of individuals at different levels of action probability towards Task 1 for young and old sub-populations in green and purple, respectively. Bar widths reflect chosen bin sizes for visualization. The simulations correspond to different environmental settings: a) b = 2, ; b) b = 20,
; c) b = 20,
; d) b = 20,
.
Fig 6.
Simulation results of the system for a) = 0 and b)
= 1 in the branching behavioural regions when varying
and b parameters.
a) Population branching behaviour: b = 20, and where both young and old sub-populations divide between the two tasks; b) Age specialization behaviour: b = 20, and
.