Modeling And Analysis On The Colony Behavior Dynamics Of Social Insects

Social insects,including ants,termites,bees,and wasps,are the most socialized nonhuman organisms known in the world.Social insects have a highly developed and intricate social organization system,can operate flexibly like organisms,and exhibit complex collective problem-solving capabilities.The study of the collective behavior of social insects will not only help biologists have a more comprehensive and deeper understanding of the theoretical mechanism of the collective behavior of social insect colonies,but some of these techniques can also be applied to understand human society.By using mathematical modeling methods,this dissertation studies the effects of colony size,metabolic scaling,and stochasticity on the task allocation of social insect colonies,the influence of variable selection on the recruitment dynamics of social insect colonies based on direct interaction,the effects of stochasticity and resource constraints on the collective foraging dynamics of social insects,and the combined effects of stochasticity and component Allee effects on the dynamics of social insect colonies.This dissertation is a preliminary study on the dynamic modeling of social insect collective behavior.The main idea of this dissertation includes the following aspects:(1)By incorporating variation both in task performance and task-related metabolic rates,an adaptive modeling framework on task allocation is proposed to study the scaling effects of colony size on the resting probability as well as task allocation.The research result shows that changes in colony size can regulate the probability of colony resting and the allocation of tasks,and the direction of regulation depends on the nonlinear metabolic scaling effects of tasks.(2)The task allocation framework is applied to study the dynamic of working effort versus resting in four different scenarios,and the effect of stochasticity on task demand and work activity is discussed.The theoretical and numerical results show that:(i)The activity level of the colony is closely related to the colony size and metabolic scaling.(ii)Increased response thresholds may cause colonies to rest in varied patterns.In this case,we observed an interesting bubble phenomenon in the task allocation of social insect colonies for the first time.(iii)The stochasticity can cause work activities and task demand to fluctuate within a range,where the amplitude of the fluctuation is positively correlated with the intensity of noise.(3)A four-compartment model and its simplified version are proposed to explore how we should model the recruitment dynamics of workers in social insect colonies properly.The fourcompartment model has the components of the unalarmed patrollers,the alarmed patrollers,the alarmed recruiters,and the available workers,while its simplified version has three components: the patrollers,the alarmed recruiters,and the available workers where we combine the unalarmed patrollers and the alarmed patrollers into the patrollers.The theoretical and numerical results show that: the simplified three-compartment system has only simple equilibrium dynamics,while the full four-compartment system can have up to three subcritical Hopf bifurcations,two supercritical Hopf bifurcations,two limit point bifurcations,and a Fold bifurcation of the limit cycle.Those important results provide theoretical guidance for modeling and studying recruitment dynamics of social insect colonies: It is critical to have proper compartments for social insect systems as the number of compartments could lead to totally different dynamics,hence affect our policy-making.(4)Although experiments have shown that the foraging activities of social insect colonies may be affected by stochasticity,there are still few theoretical mechanism for how stochasticity affects the foraging behavior of social insect colonies.By establishing a suitable mathematical framework,the foraging dynamics of social insect colonies in random environments is explored.Stochasticity and resource constraints are incorporated in the proposed framework.The stochastic dynamics,including the global existence and uniqueness of the positive solution and the ergodicity are theoretically studied.The result suggests that higher resource growth rate,as well as lower noise intensity and colony size contribute to the sustainability of the foraging-resource system.(5)The combined effects of stochasticity and component Allee effect on the dynamics of social insect colonies were studied.The theoretical and numerical results show that the effects of demographic and environmental stochasticity on population dynamics are diverse,specifically:(i)In the weak Allee effects case,the demographic stochasticity from the attack rate plays a positive role in the survival of the population,while the demographic stochasticity from the handling rate as well as the environmental stochasticity play the opposite role.(ii)In the strong Allee effects case,demographic and environmental stochasticity play a similar role in the survival of the population,which is related to the initial population level: if the initial population level is large enough,demographic and environmental stochasticity may be detrimental to the survival of the population,otherwise,if the initial population level is small enough,demographic and environmental stochasticity may bring the possibility of survival for the population that deterministically would extinct indefinitely.(iii)In the extinction case,demographic and environmental stochasticity can not change the population being extinct,but they can delay or advance the population being extinct.