Models for honeybee nest-site selection: a survey with cross-model comparisons

Abstract

Throughout their lives honeybees engage in a variety of complex, cooperative, tasks that require re markable group-level coordination between thousands of worker bees. These tasks include foraging, provisioning stores and offspring, and guarding the entrance to their home. Another such task is the nest-site selection process that reproductive swarms must undertake to find and establish a new home in a limited period of time. One general way to view nest-site selection by honeybees is as a best-of-N decision-making process, where the swarm members must first find and then choose the best between many alternative sites, some of which can be at distances many kilometres from the location of the swarm, to establish a new home. The process has a finite time-limit, as reproductive swarms cannot store food, and are exposed until they establish a new home.

Nest-site selection is best understood for the western hive bee, Apis mellifera, particularly due to a sequence of studies performed since 1999, but it seems that all species of honeybee apply processes with at least some similarities in choosing a new location to establish a colony. Part of the process of better understanding how the nest-site selection process of A. mellifera works has been the development and analysis of a variety of mathematical models based on current knowledge of the system at the time that the models were developed, starting with systems of nonlinear ordinary differential equations proposed by Britton et al. (2002). Since the seminal work of Britton et al. (2002), the types of models used to study nest-site selection have grown to include matrix models, individual based models, stochastic simulation models, and systems of nonlinear stochastic differential equations, across more than a dozen studies. One of the most important advances in understanding the details of nest-site selection in the last decade has been the study of the role that inhibitory stop-signals play in the overall decision-making process (Seeley et al., 2012), which required a combination of empirical observations and the analysis of an appropriate model to understand properly.

As models of nest-site selection are based on the same biological process, they often include mathematical terms or algorithmic mechanisms that represent the same components of the decision making process, and that are broadly similar whilst at the same time differing in fine detail. This study is devoted to examining if differences in the details of models for nest-site selection result

in quantitatively different predictions by these models. Chapter 1 provides an overview of current

understanding of the real-world, biological, nest-site selection process for A. mellifera. Chapter 2 briefly details each of the current models of nest-site selection, the aspects of nest-site selection that these models have been used to examine, and the broad similarities between the models. In Chapter 3, I then chose a smaller sample of the available models for nest-site selection to examine in greater detail (one matrix model, one differential equation model and two individual based simulation models, one with relatively simple components and another that is more complex). I examine a process for choosing within-model parameters for each model so that equivalent components of the nest-site selection process will produce quantitatively similar outcomes for a standard, simplified, problem of choosing between two nest-sites - one that is of excellent quality, and another that is of poorer quality, but still acceptable. I then examine and compare the overall predictions of the models with parameters chosen so that equivalent elements of the nest-site selection process behave as similarly as possible. When parameter sets are chosen to try to maintain quantitative similarities between model components, the broad qualitative predictions of the models remain the same (with the best nest-site identified by model swarms as being the best site). However, the quantitative predictions of the models, particularly the absolute number of workers "devoted" to a particular site and some details of the system's dynamics, differ markedly across the models, in some cases by a factor of more than ten.