Dynamics of task allocation in social insect colonies: scaling effects of colony size versus work activities

Unraveling the forces shaping foraging dynamics in harvester ant colonies: Recruitment efficiency and environmental variability

The collective foraging behavior of ant colonies is a central focus in behavioral ecology. This paper enhances the classical model of foraging dynamics in harvester ant colonies by introducing a nonlinear recruitment rate and considering environmental variability. Initially, we analyze the existence and stability of steady states in the deterministic model. The results suggest that an increase in mean recruitment time can reduce the foraging threshold, leading to both forward and backward bifurcations. Furthermore, both average recruitment time and the interference intensity of recruiters impact the number of workers in each subgroup. Subsequently, we conduct an analysis of the long-term and transient dynamics of collective foraging in random environments, providing sufficient conditions for the colony to sustain foraging activity. The findings emphasize the scene-dependent impact of environmental stochasticity on foraging dynamics. When ant colonies deterministically cease foraging, environmental stochasticity may unexpectedly prolong the foraging state. Conversely, when colonies deterministically persist in foraging, environmental stochasticity may disrupt this continuity. Additionally, the effect of environmental stochasticity on foraging status varies with the initial worker size. Sizes near the boundary of the basin of attraction between non-foraging and foraging states exhibit greater sensitivity to environmental stochasticity, and sufficiently large stochasticity can impact foraging dynamics across a broader range of initial worker sizes. These findings underscore the intricate interplay between intrinsic factors (e.g., recruitment efficiency and interference intensity) and extrinsic factors (e.g., environmental stochasticity) in shaping the collective foraging dynamics of ant colonies.

Social Learning versus Individual Learning in the Division of Labour

Division of labour, or the differentiation of the individuals in a collective across tasks, is a fundamental aspect of social organisations, such as social insect colonies. It allows for efficient resource use and improves the chances of survival for the entire collective. The emergence of large inactive groups of individuals in insect colonies sometimes referred to as laziness, has been a puzzling and hotly debated division-of-labour phenomenon in recent years that is counter to the intuitive notion of effectiveness. It has previously been shown that inactivity can be explained as a by-product of social learning without the need to invoke an adaptive function. While highlighting an interesting and important possibility, this explanation is limited because it is not yet clear whether the relevant aspects of colony life are governed by social learning. In this paper, we explore the two fundamental types of behavioural adaptation that can lead to a division of labour, individual learning and social learning. We find that inactivity can just as well emerge from individual learning alone. We compare the behavioural dynamics in various environmental settings under the social and individual learning assumptions, respectively. We present individual-based simulations backed up by analytic theory, focusing on adaptive dynamics for the social paradigm and cross-learning for the individual paradigm. We find that individual learning can induce the same behavioural patterns previously observed for social learning. This is important for the study of the collective behaviour of social insects because individual learning is a firmly established paradigm of behaviour learning in their colonies. Beyond the study of inactivity, in particular, the insight that both modes of learning can lead to the same patterns of behaviour opens new pathways to approach the study of emergent patterns of collective behaviour from a more generalised perspective.

Explaining workers' inactivity in social colonies from first principles

Social insects are among the ecologically most successful collectively living organisms, with efficient division of labour a key feature of this success. Surprisingly, these efficient colonies often have a large proportion of inactive workers in their workforce, sometimes referred to as lazy workers. The dominant hypotheses explaining this are based on specific life-history traits, specific behavioural features or uncertain environments where inactive workers can provide a 'reserve' workforce that can spring into action quickly. While there is a number of experimental studies that show and investigate the presence of inactive workers, mathematical and computational models exploring specific hypotheses are not common. Here, using a simple mathematical model, we show that a parsimonious hypothesis can explain this puzzling social phenomenon. Our model incorporates social interactions and environmental influences into a game-theoretical framework and captures how individuals react to environment by allocating their activity according to environmental conditions. This model shows that inactivity can emerge under specific environmental conditions as a by-product of the task allocation process. Our model confirms the empirical observation that in the case of worker loss, prior homeostatic balance is re-established by replacing some of the lost force with previously inactive workers. Most importantly, our model shows that inactivity in social colonies can be explained without the need to assume an adaptive function for this phenomenon.

Controlling Biological Invasions: A Stochastic Host-Generalist Parasitoid Model

On a global scale, biological invasions are seriously destroying the stability of ecosystem, sharply decreasing biodiversity and even endangering human health and causing huge economic losses. However, there exist few effective measures controlling biological invasions. To more accurately examine the prevention and control effects of biological control on biological invasions in real environments of random fluctuations, we construct a stochastic host-generalist parasitoid model. We first establish, respectively, the sufficient conditions for the persistence and extinction of invasive hosts and generalist parasitoids, including (1) only the intrusive hosts go extinct; (2) only the generalist parasitoids are extinct, and (3) the intrusive hosts and generalist parasitoids are both extinct or persistent. Then, we perform a series of numerical simulations to verify the validity of the theoretical results obtained, based on which we further discuss the impacts of stochastic environmental fluctuations on the control of intrusive hosts, especially the possible changes of qualitative behavior caused by environmental noises in the bistable scenario. Our theoretical and numerical results indicate that compared with the invasive hosts, the generalist parasitoids are more vulnerable to environmental noises, and the prevention and control effects of biological control on invasive hosts are closely dependent to the initial population sizes. Thus, improving the ability of early detection of ecosystems, including the initial densities of biological populations and their dynamic characteristics, will provide effective predictive guidance for the prevention and control of alien host invasions.

Impacts of demographic and environmental stochasticity on population dynamics with cooperative effects

Different types of stochasticity play essential roles in shaping complex population dynamics. This paper presents a novel approach to model demographic and environmental stochasticity in a single-species model with cooperative components that are measured by component Allee effects. Our work provides rigorous mathematical proof on stochastic persistence and extinction, ergodicity (i.e., the existence of a unique stationary distribution) and the existence of a nontrivial periodic solution to study the impacts of demographic and environmental stochasticity on population dynamics. The theoretical and numerical results suggest that stochasticity may affect the population system in a variety of ways, specifically: (i) In the weak Allee effects case (e.g., strong cooperative efforts), the demographic stochasticity from the attack rate contributes to the expansion of the population size, while the demographic stochasticity from the handling rate and the environmental stochasticity have the opposite role, and may even lead to population extinction; (ii) In the strong Allee effects case (cooperative efforts not strong enough), both demographic and environmental stochasticity play a similar role in the survival of population, and are related to the initial population level: if the initial population level is large enough, demographic stochasticity and environmental stochasticity may be detrimental to the survival of population, otherwise if the initial population level is small enough, demographic stochasticity and environmental stochasticity may bring survival opportunities for the population that deterministically would extinct indefinitely; (iii) In the extinction case, demographic and environmental stochasticity can not change the trend of population extinction, but they can delay or promote population extinction.