When being flexible matters: Ecological underpinnings for the evolution of collective flexibility and task allocation

We start by investigating systems where the yields of only one of the two tasks depend on environmental conditions (${\theta }_1>1$, ${\theta }_2=1$). For example, this scenario could represent multicellular cyanobacteria where we can assume that the yields of photosynthesis, but not nitrogen fixation, depend on the time of day, or some ant colonies where we can assume that the yields of foraging, but not of nest-associated tasks such as nursing or nest maintenance, depend on food availability around the colony. For such systems, environmental variability in task yields creates an incentive to adjust task allocation to the environment: Performing the environment-sensitive task specifically under the conditions that favor it can increase task yields and thereby system fitness. At the same time, however, temporarily biasing allocation toward a task comes with the risk that the corresponding neglect of the other task reduces fitness. Therefore, it is not clear a priori whether and when environmental variability renders it optimal to adjust task allocation to the environment.

To address this question, we use our model to determine the optimal dynamic task allocation as a function of the three ecological time scales considered: adjustment of task allocation (Fig. 2A), task stock depletion (Fig. 2B), and environmental variability (Fig. 2C). We characterize this optimal task allocation by its equilibrium allocations $z_{1,A}$ and $z_{1,B}$ (toward task 1 in environments A and B, respectively), as well as the corresponding average allocations $\overline{a_{1,A}}=\frac{\delta }{\delta +\lambda }\cdot z_{1,A}+\frac{\lambda }{\delta +\lambda }\cdot \frac{z_{1,A}+z_{1,B}}{2}$ and $\overline{a_{1,B}}=\frac{\delta }{\delta +\lambda }\cdot z_{1,B}+\frac{\lambda }{\delta +\lambda }\cdot \frac{z_{1,A}+z_{1,B}}{2}$ (SI Appendix), which take into account that the system is not necessarily able to reach its equilibrium allocation. Indeed, the average allocation closely matches the equilibrium allocation when the system is able to adjust its task allocation quickly relative to the time scale of environmental fluctuations ($\delta /\lambda$ sufficiently large; e.g., scenario iii in Fig. 2), but deviates from the equilibrium allocation when the system adjusts too slowly to be able to reach its equilibrium allocation before the environment changes again ($\delta /\lambda$ not large enough; e.g., scenario ii in Fig. 2). We quantify collective flexibility as the difference between the average allocations toward task 1 in environments A and B, i.e., $\overline{a_{1,A}}-\overline{a_{1,B}}=\left(z_{1,A}-z_{1,B}\right)\cdot \frac{\delta }{\delta +\lambda }$. This measure of collective flexibility equals 0 when $\overline{a_{1,A}}=\overline{a_{1,B}}$, meaning that there is no difference in average task allocation between the two environments, and 1 when $\overline{a_{1,A}}=1$ and $\overline{a_{1,B}}=0$, meaning that, in environment A, only task 1 is performed, and in environment B, only task 2 is performed.

We find that the evolution of task allocation depends strongly on all three ecological time scales considered and that diverse task allocation dynamics can be evolutionarily optimal. We first focus on each time scale separately and vary the rate parameters $\delta$, $\gamma$, and $\lambda$ independently (while keeping the other two fixed; see SI Appendix for formal analysis); subsequently, we consider all time scales simultaneously to derive general conditions for the evolution of collective flexibility that depend on the relative magnitudes of $\delta$, $\gamma$, and $\lambda$.

In Fig. 2 D–I, we show the optimal task allocation dynamics for three choices of parameters that differ in the rate $\delta$ at which the system can adjust its task allocation to the environment (corresponding to cases i through iii in Fig. 2A). For low $\delta$, we find that it is optimal to be unresponsive to the environment and equally allocate individuals to both tasks, thereby ensuring that the system properly balances its attention toward them ($\overline{a_{1,A}}\approx \overline{a_{1,B}}\approx 1/2$; Fig. 2 A, D, and E). As $\delta$ increases, the system evolves to adjust its task allocation to its environment (Fig. 2 A and F–I), preferentially performing the environment-sensitive task under conditions that favor it (i.e., $\overline{a_{1,A}}>1/2$ and $\overline{a_{1,B}}<1/2$). Adjusting task allocation to the environment allows the system to obtain higher task yields, maintain higher task stocks (compare Fig. 2 G and I with E), and therefore achieve higher fitness (SI Appendix, Fig. S2). The level of collective flexibility $\overline{a_{1,A}}-\overline{a_{1,B}}$ that evolves increases with $\delta$, because for higher $\delta$ the system evolves more biased equilibrium allocations $z_{1,A}$ and $z_{1,B}$ (Fig. 2A), and it reaches these equilibrium allocations faster (e.g., compare scenario ii, where the equilibrium allocation is typically not reached before the environment changes [Fig. 2F], to scenario iii, where the system spends most of its time at the equilibrium allocation for the current environment [Fig. 2H]).

When we instead vary the rate of task stock depletion $\gamma$, we find that adjustments of task allocation fail to evolve when task stocks are depleted too quickly (high $\gamma$; Fig. 2B), because then temporarily neglecting tasks is strongly selected against. In contrast, when task stocks are depleted more slowly and the fitness consequences of temporarily neglecting tasks are less dire ($\gamma \to 0$), it becomes optimal to bias task allocation as much as possible ($z_{1,A}\to 1$, $z_{1,B}\to 0$). In this case, the level of collective flexibility approaches ${\displaystyle \delta /(\delta +\lambda )}$ and is thus determined by how quickly the system adjusts its task allocation relative to the time scale of environmental fluctuations (SI Appendix and Fig. 2B).

Finally, when we vary the rate of environmental fluctuations $\lambda$, we find that adjustments of task allocation evolve only if the environment changes sufficiently quickly ($\lambda$ sufficiently large; Fig. 2C). If the environment changes too slowly, biasing task allocation toward a specific task would again lower fitness, because it causes the other task to go neglected for too long. As $\lambda$ increases, the equilibrium task allocations $z_{1,A}$ and $z_{1,B}$ become progressively more biased, although, eventually, adjustments to the environment fail to be realized because the environment changes too quickly for the system to be able to adjust to it (i.e., $\overline{a_{1,A}}$ and $\overline{a_{1,B}}$ approach 1/2; Fig. 2C).

The task allocation dynamics that evolve have some surprising features. For example, as Fig. 2D shows, it may be optimal to continue to perform tasks when their yields are low (or even zero; SI Appendix, Fig. S3): In environment B, task 1 is still being performed by half of the individuals, even though its yield is 4 times lower than in environment A. Thus, the apparent inefficiency of performing tasks under suboptimal conditions can be evolutionarily optimal. Another unexpected finding is that, even though both tasks contribute equally to fitness, the optimal task allocation can be asymmetric. For example, in scenario iii (Fig. 2 H and I), individuals spend on average 30% more time performing task 2 than task 1 and only the performance of task 1 is restricted to specific environmental conditions. We can show analytically that if the environment-sensitive task 1 is sufficiently sensitive to the environment (i.e., provided ${\theta }_1>({\displaystyle 4\gamma +\lambda )/\lambda }$; SI Appendix), then for large enough $\delta$ it becomes optimal to only perform it in environment A ($z_{1,B}$ becomes 0 and $\overline{a_{1,B}}$ approaches 0 as $\delta \to \infty$; Fig. 2A). In contrast, for the environment-insensitive task 2, it is always optimal to perform it in both environments (i.e., $z_{1,A}$ and $\overline{a_{1,A}}$ never become 1; Fig. 2A), with allocation toward it never dropping below ${\displaystyle \gamma /(2\gamma +\lambda )}$ (SI Appendix). Thus, only for sufficiently environment-sensitive tasks can it be optimal to temporarily ignore them, and, as a result, total allocation—over the lifespan of the system—may be biased toward environment-insensitive tasks.

Having explored the effect of each of the three ecological time scales separately, we now look at the effect of all three varying simultaneously. The level of collective flexibility that evolves in the model varies continuously as a function of $\lambda$, $\delta$, and $\gamma$, ranging from a regime in which negligible collective flexibility evolves ($\overline{a_{1,A}}-\overline{a_{1,B}}\approx 0$) to a regime in which near-maximal levels of collective flexibility evolve ($\overline{a_{1,A}}-\overline{a_{1,B}}\approx 1$), with intermediate levels of collective flexibility in between (Fig. 3A, and see SI Appendix, Fig. S4 for the corresponding values of $z_{1,A}$, $z_{1,B}$, $\overline{a_{1,A}}$, and $\overline{a_{1,B}}$). We see that the evolution of nonnegligible collective flexibility requires two conditions to be met simultaneously (Fig. 3B). First, the rate of task stock depletion must be sufficiently low relative to the rate at which the environment fluctuates ($\gamma /\lambda$ sufficiently small), so that tasks can be temporarily left unattended without the corresponding task stock being depleted to such low levels that fitness is compromised. Second, the rate of adjustment of task allocation should be sufficiently high relative to the rate at which the environment fluctuates ($\delta /\lambda$ sufficiently large), so that a biased task allocation can be achieved before the environment changes.

These general theoretical conditions for the evolution of collective flexibility comport with empirical observations in desert harvester ants (P. barbatus), where collective flexibility—in the form of regulating foraging activity levels in response to day-to-day variation in humidity—has been shown to be adaptive (7, 8). Relative to the daily time scale of environmental fluctuations, in harvester ant colonies the adjustment of task allocation indeed takes place on a much faster time scale [within minutes, via interactions with returning foragers or patrollers (8, 36)], while their task stocks deplete on a much slower time scale [collected seeds are stored for up to months (7)].

Based on our results, we predict that across systems that face similar constraints on task allocation (i.e., have similar values of $\gamma$, $\delta$), such as closely related species of ants, collective flexibility is least likely to evolve in systems living in environments that change very quickly or very slowly and is most likely to evolve in systems living at intermediate degrees of temporal environmental variability (Fig. 3C). Indeed, the evolution of collective flexibility requires the environment to change quickly enough for the system to be able to exploit environmental variability, but not so quickly that the system loses the ability to adjust its task allocation in time.

Our results generalize to scenarios in which not one but both tasks are sensitive to environmental conditions. In this case, either one environment maximizes yields for both tasks (correlated task yields across environments; ${\theta }_1$, ${\theta }_2>1$ or ${\theta }_1$, ${\theta }_2<1$), or the yields for the two tasks are maximized in opposite environments (anticorrelated task yields; ${\theta }_1<1<{\theta }_2$ or ${\theta }_2<1<{\theta }_1$). As an example of correlated task yields, consider pollen and nectar foraging in a honey bee colony (37), both of which may result in higher yields during good weather conditions. In contrast, a hypothetical primitive multicellular organism that allocates cells to feeding and motility and navigates a spatially heterogeneous resource environment could be an example of anticorrelated task yields, if feeding (but not motility) is favored when resources are plentiful while motility (but not feeding) is favored when resources are scarce.

In this more general setup where both tasks are sensitive to the environment, we find that collective flexibility can evolve as long as the two tasks differ in how they depend on environmental conditions (${\theta }_1\ne {\theta }_2$; Fig. 3C), but that no collective flexibility can evolve when ${\theta }_1={\theta }_2$ (see Fig. 3C for ${\theta }_1={\theta }_2=4$ and SI Appendix for a general mathematical derivation). In particular, collective flexibility can evolve even when task yields are correlated (Fig. 3C; ${\theta }_1=4$, ${\theta }_2=2$). In this case, the more environment-sensitive task will be prioritized under conditions favorable to both tasks, increasing the yield for this task to such an extent that it outweighs a concomitant decrease in yield for the less environment-sensitive task (which is now preferentially performed under conditions unfavorable to both tasks). While collective flexibility can evolve even when task yields are correlated, it is most pronounced (Fig. 3C) and provides the largest fitness benefits (SI Appendix, Fig. S2) when task yields are, instead, anticorrelated across environments, so that adjusting task allocation to the environment can simultaneously increase the yields obtained for both tasks.

One way in which systems adjust their task allocation to changing conditions is by reallocating existing individuals to different tasks (i.e., task switching).* Task switching may be associated with fitness costs, because adjusting to a new task can require time and/or energy (42–44). So far, we have not considered such costs to flexibility: While in our original model systems are constrained by how quickly they can adjust their task allocation, these adjustments are not costly. We therefore extend our model to incorporate task-switching costs and explore what task-switching strategies evolve when task switching is costly but at the same time required for collective flexibility.

Incorporating task-switching costs requires specifying how the net change in the overall task allocation (as given by Eq. 1) comes about from individuals switching between tasks (Fig. 4A). For simplicity, we make the minimal assumption that task-switching rates depend only on the task being performed and on the current environment. Consequently, we parametrize our task-switching model by four parameters, $r_{1\to 2,A}$, $r_{1\to 2,B}$, $r_{2\to 1,A}$, and $r_{2\to 1,B}$, that describe the per capita rates of task switching in either direction (from task 1 to task 2 or vice versa) and in either environment (A or B). In SI Appendix, we show that there is a unique way to choose these parameters that is consistent with Eq. 1: We must have $r_{1\to 2,A}=\delta z_{2,A}$, $r_{1\to 2,B}=\delta z_{2,B}$, $r_{2\to 1,A}=\delta z_{1,A}$, and $r_{2\to 1,B}=\delta z_{1,B}$. These equations can be interpreted as individuals reevaluating their current task at rate $\delta$ (prompted, for example, by observations of the environment) and then adopting task 1 with probability $z_1$ and task 2 with probability $z_2$. While this setup is an oversimplification of the decision-making processes underlying task switching in many real systems, it suffices to explore theoretically the trade-off between the benefits of collective flexibility and the costs of task switching.

The above assumptions on the rates of task switching allow the net change in task allocation to be decomposed into flows of individuals switching from task 2 to task 1 (at a per capita rate $\delta z_1$) and from task 1 to task 2 (at a per capita rate $\delta z_2$) (Fig. 4A). The average rate of task switching now equals

(SI Appendix). Total (i.e., system-level) task-switching costs can therefore be implemented by subtracting from fitness a cost $c\overline{\delta }$, where $c$ is a parameter that controls how costly one task switching event is, regardless of the direction of the switch. To characterize the evolution of task switching, we will calculate what combination of $\delta \in (0,\infty )$ and $z_{1,A}$, $z_{1,B}\in [0,1]$ maximizes fitness. Thus, $\delta$ is now evolvable rather than being a fixed constraint on task allocation. Higher values of $\delta$ allow the system to adjust its task allocation more quickly, but may also lead to higher total task-switching costs (Eq. 2).

We find that, in the extreme case of no task-switching costs ($c=0$), arbitrarily large reevaluation rates $\delta$ evolve, as increasing $\delta$ allows for quicker collective adjustments of task allocation at no additional cost (Fig. 4B). At the other extreme of very high task-switching costs, arbitrarily small reevaluation rates evolve ($\delta \to 0$) because the costs of task switching outweigh any potential benefits of collective flexibility. As a result, individuals rarely switch tasks, and end up being essentially irreversibly committed to their current task (Fig. 4C). This confirms that task-switching costs can suffice to drive the evolution of specialization, a result that has been previously obtained with simulation models (43, 45). Our analysis additionally reveals an ecological dimension to this phenomenon: How high task-switching costs need to be to drive the evolution of irreversible specialization depends on the potential benefits of collective flexibility. The higher the benefits of collective flexibility (which are maximized at intermediate environmental fluctuation rates $\lambda$; SI Appendix, Fig. S2), the higher the task-switching costs needed to offset those benefits and drive the evolution of irreversible specialization (Fig. 4B).

When task-switching costs are not high enough to completely impede the evolution of flexibility, we find that two types of flexible task-switching strategies can evolve (Fig. 4B). In environments that change sufficiently quickly (relative to the time scale of task stock depletion), individuals evolve to instantaneously and deterministically switch tasks ($\delta =\infty$; $z_{1,A}=1$, $z_{1,B}=0$) in response to shifts in environmental conditions (Fig. 4D), akin to undifferentiated cyanobacteria in which all cells switch between photosynthesis during the day and nitrogen fixation at night. While this strategy limits task-switching costs by having individuals switch between tasks only in response to environmental change (indeed, we have $\overline{\delta }=\lambda /2$, so the total costs of task switching remain bounded), it is not feasible in environments that change too slowly, where it would cause tasks to go neglected for too long. In those environments, a task-switching strategy evolves instead in which individuals switch tasks stochastically, even in the absence of environmental change, thereby making sure that both tasks receive attention at all times (Fig. 4E).

These results provide theoretical corroboration for the empirical observation that in some real systems individuals frequently switch tasks, even in the apparent absence of environmental changes that would necessitate a shift in overall task allocation. In paper wasps (Polybia), for example, workers constructing the nest flexibly switch between water collection, pulp collection, and building (46, 47). Similarly, while most animal cells are irreversibly assigned a task during development and therefore never switch tasks, some multicellular animals exhibit a more labile (and evolutionarily more ancient) form of cell differentiation in which cells readily transition between different cell types (48–51). For example, in sponges (e.g., Amphimedon queenslandica), archeocytes can spontaneously transdifferentiate to become choanocytes, and vice versa (52–54). Our results suggest that such individual-level flexibility can be adaptive—even when it leads to unnecessary and potentially costly task switching in the absence of environmental change—because it enables collective adjustments of task allocation when environmental conditions do change.

So far, we have been agnostic toward which individuals are performing what tasks. In a second extension of our original model, we consider how the system may distribute the performance of different tasks across different individuals (i.e., spatially) in addition to distributing them across different environmental conditions (i.e., temporally). In many extant collective systems, individuals indeed exhibit persistent differences in task performance, although to varying degrees (46, 55–63). We reason that such specialization may be favored because it has the potential—albeit not universal (64)—intrinsic benefit of improved efficiency (i.e., specialists may be more efficient at a task due to experience or task-specific physiological adaptations) (33, 34, 65–67). At the same time, however, specialization limits an individual’s ability to be reallocated to other tasks when needed, thereby constraining the system’s collective flexibility. We therefore use our model to explore how environmental variability impacts the evolution of specialization.

We consider the evolution of specialists “one task at a time,” which allows us to capture how the evolution of specialists may potentially differ between tasks. Specifically, we assume that a fraction $s$ of individuals are identical “specialists” that perform only task 1, and the remaining fraction, $1-s$, are identical “generalists” that can perform both tasks and adjust their task allocation at a rate $\delta$ without an associated cost, as in the original model. We introduce a parameter $\alpha$ that controls the efficiency gains of specialization: specifically, the yields specialists obtain for task 1 are multiplied by $1+\alpha$. Treating the efficiency parameter $\alpha$ as a fixed constraint, we allow the proportion of specialists $s$ and the task allocation of generalists to evolve, and ask what combination of $s\in [0,1]$ and $z_{1,A}, z_{1,B}\in [0,1]$ maximizes fitness (SI Appendix).

We first determine how the minimum efficiency benefits ${\alpha }^{*}$ required for the evolution of at least some specialists (i.e., $s>0$) depend on ecological conditions. We find that specialization is easiest to evolve (i.e., requires the lowest ${\alpha }^{*}$) when the potential benefits of collective flexibility are limited. In particular, when it is optimal to perform a task under all conditions, minimal efficiency benefits suffice: Specialists for such a task can evolve as soon as $\alpha >0$ (Fig. 5A and SI Appendix). In contrast, when the benefits of collective flexibility render it optimal to restrict the performance of a task to specific environmental conditions, evolving specialists is more difficult. In this case, the efficiency gains of specialization must outweigh the fitness costs incurred by sacrificing some collective flexibility, and substantial gains in efficiency may be required for specialization to evolve (Fig. 5A).

How easy it is to evolve specialists for a task depends on the task’s sensitivity to environmental conditions. Individuals specialize most easily on tasks whose yields are relatively insensitive to environmental fluctuations because, for those tasks, it tends to be evolutionarily optimal to perform them most or all of the time (thereby allowing specialists to evolve even when efficiency benefits are small; SI Appendix, Fig. S6). For example, we predict that an undifferentiated cyanobacterium that can photosynthesize only during the day but can fix nitrogen at any time would require smaller efficiency benefits to evolve cells specialized for nitrogen fixation (a less environment-sensitive task) than to evolve cells specialized for photosynthesis (a more environment-sensitive task). Consistent with this, some species of cyanobacteria (e.g., Anabaena variabilis) have evolved specialized nitrogen-fixing cells, while the remaining cells continue to perform both tasks: They photosynthesize during the day but also engage in environmentally regulated nitrogen fixation, for example at night (68). Similarly, in the context of reproductive division of labor, we predict that reproductive specialists (e.g., an ant queen whose only task is to lay eggs, or a stem cell in a multicellular tissue whose only task is to produce new cells) evolve most easily in environments where the demand for new individuals is relatively insensitive to environmental fluctuations. In contrast, a more balanced distribution of reproductive tasks [e.g., in ant colonies with worker reproduction (69–71)] would be more favored in environments that require flexibility in the production of new individuals, for example, due to recurring but unpredictable disturbances in which substantial numbers of individuals are lost from the system.

The optimal fraction of specialists varies across ecological conditions (Fig. 5B). First, when the benefits of collective flexibility outweigh the efficiency gains of specialization, no specialists evolve ($s=0$), and all individuals are generalists, dividing their attention over both tasks in response to the environment as in the original model (Fig. 5C). Second, in the absence of substantial benefits to collective flexibility, complete division of labor evolves in which half the individuals become task 1 specialists ($s=0.5$), and the remaining generalists perform only task 2—essentially becoming specialists as well, even though they do not derive an efficiency benefit (Fig. 5E). Finally, in between these two extremes, a compromise between improved efficiency and collective flexibility emerges in which a minority of individuals are specialists ($0<s<0.5$), and the task they specialize on is also performed by generalists under some environmental conditions (Fig. 5D). Thus, it can be evolutionarily optimal to employ a mix of generalists and specialists, thereby reaping some efficiency benefits of specialization while still being able to adjust to the environment.

While, for simplicity, we have considered specialists that perform only task 1, we can relax this assumption by allowing specialists to also occasionally perform task 2, albeit less frequently than generalists (SI Appendix, Fig. S7). As before, we find that evolving specialists requires the smallest efficiency gains for tasks whose yields are relatively insensitive to environmental conditions. However, in this more general setup, the evolution of specialists depends not only on gained efficiency for task 1 but also on whether and to what extent specialists incur a reduction in efficiency for task 2 as a result of specializing on task 1. Thus, in general, whether specialists for a task can evolve depends on the interplay between how strongly specialists bias their task performance toward it, how sensitive the task is to environmental conditions, and how gains in efficiency for the task trade-off with a loss in efficiency for other tasks (SI Appendix, Fig. S7).

As a final application of our original model, we consider the possibility of inactivity. While we have so far assumed that individuals are continually active, individuals could also be temporarily inactive (i.e., not performing any task). Low levels of inactivity are not necessarily surprising (they could be explained by constraints on activity, e.g., the need to rest), but some systems show perplexingly high levels of inactivity (72, 73). For example, Leptothorax allardycei ants appear to spend most (55%) of their time doing nothing (74). This raises the question of whether temporary inactivity could, in fact, be adaptive, despite inactive individuals not contributing to productivity. Multiple hypotheses have been suggested for why high levels of temporary inactivity could be beneficial (72, 75–78). We use our model to explore one such hypothesis, which proposes that inactivity may be adaptive because it increases the system’s flexibility (72, 77). Specifically, temporarily inactive individuals could enhance collective flexibility if they can be more quickly recruited (e.g., due to being more attentive to increased demand for any task) to tasks that require additional attention than individuals that are actively performing other tasks.

We implement inactivity by letting active individuals quit their task at a rate $\tau$, upon which they join an inactive pool. As in our task-switching model, we assume that individuals actively performing the other task are recruited to task $i$ at rate $\delta z_i$ (Fig. 4A), but that inactive individuals are recruited to task $i$ at rate $\kappa \delta z_i$ (SI Appendix, Fig. S8A). Setting $\kappa >1$ incorporates the assumption that inactive individuals can be more quickly recruited to a task than active individuals performing a different task. Because individuals switch from being active to being inactive at rate $\tau$ and switch from being inactive to active at total rate $\kappa \delta$, each individual spends, on average, a fraction ${\displaystyle \tau /(\tau +\kappa \delta )}$ of its time inactive. Thus, while the composition of the inactive pool will change over time, its total size (as a fraction of the total number of individuals) stabilizes at ${\displaystyle \tau /(\tau +\kappa \delta )}$. In response to the environment, the system can adjust what tasks active individuals perform, but not what fraction of individuals are (in)active.

To determine whether inactivity can evolve even though temporarily inactive individuals do not contribute to productivity, we calculate what combination of task quitting rate $\tau \in [0,\infty )$ and $z_{1,A}$, $z_{1,B}\in [0,1]$ maximizes fitness. Although task quitting is not required to achieve collective flexibility, we find that having a positive $\tau$ (and thereby a pool of temporarily inactive individuals) may indeed be evolutionarily advantageous (SI Appendix, Fig. S8B). Moreover, high levels of inactivity (up to 25% of each individual’s time, in some cases) can evolve, resulting in a correspondingly sizable pool of inactive individuals at any one time (up to 25% of individuals; see SI Appendix, Fig. S8D). Thus, inactivity can indeed evolve to enhance collective flexibility, allowing the system to more rapidly adjust its task allocation to changing circumstances (SI Appendix, Fig. S8 C and E). We expect inactivity to evolve for this reason when collective flexibility is adaptive but not fully realizable due to constraints on the rate at which the system can adjust its task allocation (SI Appendix, Fig. S8 B and D).

These results provide theoretical support for the previously proposed hypothesis that observed worker inactivity in social insects could be a component of an adaptive colony-level task allocation strategy (72, 77). Specifically, they confirm that high levels of inactivity could have evolved to allow colonies to adjust more rapidly what task is being performed by active workers in response to environmental fluctuations, even when the number of active workers stays constant over time. This hypothesis is consistent with empirical evidence from some species of social insects, where temporarily inactive workers have been confirmed to act as a “reserve” labor force [i.e., Temnothorax rugatulus ants (76)], although other explanations might be required for inactivity in other species (61, 76–79).