PATTERNS OF ROOSTING IN A COLONY OF BATS BASED ON STATE-DEPENDENT DECISIONS, BENEFITS, AND COSTS

Why do social behaviors such as settlement and/or synchronized movement happen? This study is motivated by this question. We design a dynamic network of individuals who execute roost selection based on simple social rules. In this model, each individual communicates with other group members to find the best roost to stay during discrete time intervals. An essential characteristic of this dynamical system is the health condition of individuals which is a probabilistic function of living condition. Results of this model show different patterns of social behavior. For some conditions, we observe settlement behavior, while for other combinations of free parameters, we observe fission-fusion behavior. The communication features of the colony are explored through order parameters of the communication network using graph theory. With constraints set on the number of peers that an individual can communicate with for both in-roost and out-roost connections, the pattern of roosting behavior describes the richness of the communication network, and therefore, the network features. Results of this study help us to understand when and how the strategy of maximizing individual benefits would yield desired advantages. INTRODUCTION This study is inspired by the specific social behaviors settlement and fission-fusion; observed in some groups of animals such as bats, birds and fishes. Settlement behavior is the long term stay of almost all the colony population in one roost and fission-fusion behavior refers to the cycles of dividing/splitting and joining together of individuals among multiple roosts. This pattern of social life may occur in different situations. For some species of bats, this sequence is observed in their choices of the residing roosts. Birds and fishes that fly or swim in groups are other examples. In these cases, small schools merge together and, after a while and for some reason, the group divides into smaller sub-groups. There are different evolutionary benefits and costs for developing such behaviors. Some of these outcomes are: confronting/avoiding predators, finding food, heading toward the best direction during migration time, temperature regulation, stabilizing the number of infected individuals and optimizing the flow of information [1–4]. We use a mathematical model to simulate and reproduce settlement and fission-fusion behavior in a colony of bats. Results of this study show conditions for observing settlement and/or fission-fusion behavior. Also outcomes of this work reveal some benefits and costs of those social actions. To do this study, we consider a dynamic network of bats where each member (or equivalently node/agent/individual) interacs with some of others. The configuration of this network is highly time and state dependent. In this model, the state of the system is defined as the roost that each bat stays in during the daily rest time and the health condition of each bat which is considered zero if the bat is sick and one if the bat is healthy. So for R roosts and N bats in a colony the state of the system is (2N) dimensional. To design the mathematical model for this system, we implement some essential modifications to the model that is introduced by Kashima et al. [5]. In [5], the model defines an all-to-all communication network where roost qualities are considered independent of state of the system (constant quality). The most important modification that we consider in this paper is the state dependency of the quality of roosts, limited number of communications [6], and more realistic process of changing the health status of each agent [7, 8]. In our model, the quality of a roost is defined as a function of three factors: inherent quality of a roost (e.g., ventilation quality), population factor, and the number infected individuals in a roost. Selection between roosts is based on the overall quality of each roost. Each agent decides to go to the best roost with a degree of probability. This selection is based on individuals perception about the roosts’ qualities. So, one important factor is the level of randomness of decisions. We observe qualitatively different behaviors when we consider different levels of stochasticity in decision making process. A very important aspect of this model is the communications between agents. Each agent has a direct experience and estimate about its own roost. Agents obtain information about the other roosts by communicating with each other. In our model, the maximum number of probabilistic communication channels is considered to be confined to a saturation limit which is observed in animal behavior [6]. We consider the health condition (infected/healthy) of a bat as another dimension of this system. To update the health status of each agent, we consider a short term history of the selected roosts by each individual and also a probabilistic duration for remedial time. Changes of the health status of each agent (1 to 0 and 0 to 1) are considered to be probabilistic functions of these two variables. In addition to this point, we consider a random rate of infection at each time step. This modification is similar to external excitation and it has sizeable impact on the behavior of the system. Our model helps us have a better understanding about the benefits and costs of living in a colony, as well as the dynamics of roosting. Our results show that, if a large enough number of roosts exists, then the time average of health status of individuals improves significantly when active communication and the ability to search for the best quality roost are available. In addition, we observe that, to have advantages of living with the other members, each agent should sacrifice some of its own individual benefits. In addition, we explore the communication features of bats in this model by constructing a bat-to-bat communication network. A bat is considered to be connected to another bat if it shares roost quality information with the other bat. With a constraint set on the number of peers that each bat can consult with in both in-roost and out-roost communications, we study the influence of bat roosting behavior on the network properties. Our simulation results show that, as the bats exhibit fission behavior rather than settlement behavior, they have better individual centrality as they can communicate with more peers within the communication network. Thus, the communication network is richer and the bats are more clustered. However, a bat becomes less important in connecting others as the bats have more choices to reach others. PROBLEM STATEMENT Model description We consider a system of R roosts each with a specific characteristic and Nbats in a colony which uses the roosts. At discrete time intervals, these bats stay in their selected roosts. Each bat communicates with its roost-mates and other out-roost individuals. We consider an equal probability for one bat to use communication channels with roost-mates and out-roost individuals. For a bat to determine the quality of a roost, we consider a state dependent method. In this method, three factors are selected to show different conditions of a roost. First, we consider a constant factor (ηinherent) to show some inherent characteristic of a roost such as its ventilation quality. In addition, we consider the population inside a roost as another factor. This factor (η1) shows the optimal population for each roost. This factor could be the representative of optimal temperature regulation inside a roost due to the mutual thermal effects of roost-mate bats. Figure 1 shows how this factor is defined with respect to the time-varying population of each roost. We choose the interval [a,b] based on the works of Willis et al. [9] and Kalcounis et al. [10]. The other effective factor for the overall quality of a roost