Variation in behaviour among group members often impacts collective outcomes. Individuals may vary both in the task that they perform and in the persistence with which they perform each task. Although both the distribution of individuals among tasks and differences among individuals in behavioural persistence can each impact collective behaviour, we do not know if and how they jointly affect collective outcomes. Here, we use a detailed computational model to examine the joint impact of colony-level distribution among tasks and behavioural persistence of individuals, specifically their fidelity to particular resource sites, on the collective trade-off between exploring for new resources and exploiting familiar ones. We developed an agent-based model of foraging honeybees, parametrized by data from five colonies, in which we simulated scouts, who search the environment for new resources, and individuals who are recruited by the scouts to the newly found resources, i.e. recruits. We varied the persistence of returning to a particular food source of both scouts and recruits and found that, for each value of persistence, there is a different optimal ratio of scouts to recruits that maximizes resource collection by the colony. Furthermore, changes to the persistence of scouts induced opposite effects from changes to the persistence of recruits on the collective foraging of the colony. The proportion of scouts that resulted in the most resources collected by the colony decreased as the persistence of recruits increased. However, this optimal proportion of scouts increased as the persistence of scouts increased. Thus, behavioural persistence and task participation can interact to impact a colony's collective behaviour in orthogonal directions. Our work provides new insights and generates new hypotheses into how variations in behaviour at both the individual and colony levels jointly impact the trade-off between exploring for new resources and exploiting familiar ones.

Gain control is essential for the proper function of any sensory system. However, the precise mechanisms for achieving effective gain control in the brain are unknown. Based on our understanding of the existence and strength of connections in the insect olfactory system, we analyze the conditions that lead to controlled gain in a randomly connected network of excitatory and inhibitory neurons. We consider two scenarios for the variation of input into the system. In the first case, the intensity of the sensory input controls the input currents to a fixed proportion of neurons of the excitatory and inhibitory populations. In the second case, increasing intensity of the sensory stimulus will both, recruit an increasing number of neurons that receive input and change the input current that they receive. Using a mean field approximation for the network activity we derive relationships between the parameters of the network that ensure that the overall level of activity of the excitatory population remains unchanged for increasing intensity of the external stimulation. We find that, first, the main parameters that regulate network gain are the probabilities of connections from the inhibitory population to the excitatory population and of the connections within the inhibitory population. Second, we show that strict gain control is not achievable in a random network in the second case, when the input recruits an increasing number of neurons. Finally, we confirm that the gain control conditions derived from the mean field approximation are valid in simulations of firing rate models and Hodgkin-Huxley conductance based models.

Asteroids provide fundamental clues to the formation and evolution of planetesimals. Collisional models based on the depletion of the primordial main belt of asteroids predict 10–15 craters >400 km should have formed on Ceres, the largest object between Mars and Jupiter, over the last 4.55 Gyr. Likewise, an extrapolation from the asteroid Vesta would require at least 6–7 such basins. However, Ceres’ surface appears devoid of impact craters >∼280 km. Here, we show a significant depletion of cerean craters down to 100–150 km in diameter. The overall scarcity of recognizable large craters is incompatible with collisional models, even in the case of a late implantation of Ceres in the main belt, a possibility raised by the presence of ammoniated phyllosilicates. Our results indicate that a significant population of large craters has been obliterated, implying that long-wavelength topography viscously relaxed or that Ceres experienced protracted widespread resurfacing.